{
 "license": "CC BY 4.0 — https://creativecommons.org/licenses/by/4.0/",
 "attribution": "Wheel Cue (wheelcue.com)",
 "source": "https://wheelcue.com/research/how-uneven-does-a-chore-wheel-get/",
 "slug": "how-uneven-does-a-chore-wheel-get",
 "generatedAt": "2026-10-10T14:36:29.118Z",
 "node": "v24.21.0",
 "randomJsSha256": "946e82a3c426d698779d3246c37c732f771db3873c93239ef3952aea39be1e2d",
 "totalSpins": 107700000,
 "wheelSpins": 102300000,
 "teamPresses": 2100000,
 "shuffleDraws": 5400000,
 "leftOverTurns": 12100000,
 "rawDraws": 107700000,
 "runtimeSeconds": 171.3,
 "checksTotal": 120,
 "checksPassed": 120,
 "checksSimulatedVsExact": 107,
 "checksDeterministic": 13,
 "params": {
  "daily": {
   "rule": "names on the wheel, remove-the-winner off (the default on the chore wheel and the random name picker), one spin a day",
   "people": [
    2,
    3,
    4,
    5
   ],
   "days": [
    7,
    14,
    30
   ],
   "months": 200000,
   "gapThreshold": {
    "7": 3,
    "14": 4,
    "30": 7
   },
   "note": "Each simulated month is 30 daily spins; the 7- and 14-day values are read from the first 7 and 14 days of the same months."
  },
  "rounds": {
   "rule": "remove-the-winner on: each spin takes the winner off; the last person of a round is left over (the wheel does not spin with one line) and takes the next turn; then Reset puts everyone back",
   "people": [
    2,
    3,
    4,
    5
   ],
   "days": [
    7,
    14,
    30
   ],
   "months": 150000
  },
  "longRun": {
   "people": [
    2,
    3,
    4,
    5
   ],
   "days": [
    7,
    14,
    30,
    60,
    90,
    180,
    365
   ],
   "simulated": {
    "people": 4,
    "days": 365,
    "years": 20000
   }
  },
  "threeChores": {
   "kids": 3,
   "chores": [
    "Dishes",
    "Trash",
    "Laundry"
   ],
   "days": 30,
   "spinMonths": 150000,
   "roundMonths": 100000,
   "teamMonths": 50000,
   "note": "spin: each chore spun on a wheel of the 3 kids with removal off; rounds: removal on, Reset every day (two spins, the third kid left over); team generator: the kids as names, 3 teams, team names 'Dishes, Trash, Laundry' (one press a day)"
  },
  "fiveChores": {
   "kids": 3,
   "chores": [
    "Dishes",
    "Trash",
    "Laundry",
    "Vacuum",
    "Feed the dog"
   ],
   "days": 30,
   "spinMonths": 40000,
   "teamMonths": 20000,
   "roundMonths": 40000,
   "carryMonths": 40000,
   "note": "spin: each chore spun with removal off; teamFixed: the chores as names, 3 teams named after the kids in the same order every day; teamRotated: the same press with the team names rotated one place each day; roundsDaily: removal on, Reset every morning (5 chores = one round of 3 + two picks of the next); roundsCarried: removal on, the round carries over to the next day, Reset only when the wheel is used up"
  },
  "weighted": {
   "days": 30,
   "months": 200000,
   "olderWeight": 2,
   "families": [
    {
     "kids": 2,
     "weights": [
      2,
      1
     ]
    },
    {
     "kids": 3,
     "weights": [
      2,
      1,
      1
     ]
    }
   ],
   "roundOrder": {
    "weights": [
     2,
     1,
     1
    ],
    "rounds": 200000,
    "note": "removal on with weighted lines: a weighted line leaves whole"
   },
   "lastTimeLighter": {
    "people": [
     3,
     4
    ],
    "days": 30,
    "months": 200000,
    "rule": "re-weighting before every spin: whoever had it last time *1, everyone else *2 (the first spin is unweighted). The chore wheel page's tip is for a weekly job such as the bathroom, with the weights edited by hand; applying it before every one of 30 daily spins is this study's test, not the page's recommendation"
   }
  },
  "widgetGrid": {
   "people": [
    2,
    3,
    4,
    5,
    6,
    7,
    8
   ],
   "days": [
    7,
    14,
    21,
    30,
    45,
    60
   ],
   "gapCdfTail": 0.000001
  }
 },
 "notes": {
  "simulatedVsExact": "results holds simulated spins and team-generator presses (never site usage); theory holds exact values only and is the same on every run. Quote theory values; call results values 'simulated'. Nothing here is simulation-only: every reported quantity has an exact counterpart.",
  "spins": "totalSpins = wheelSpins + shuffleDraws: every CueRandom draw that picks a result (one per wheel spin; L - 1 per team-generator press of L names, as in the teams study). wheelSpins counts CueRandom.pickWeighted() calls; teamPresses counts presses of Generate; leftOverTurns counts turns given to the last name of a remove-the-winner round, which the wheel hands over without a spin (not counted as spins). rawDraws counts 32-bit numbers from crypto.getRandomValues(), including draws the rejection step discards. Most of totalSpins are wheel spins; if the article quotes totalSpins under the title it should say 'simulated spins and draws' or set drawsLabel accordingly.",
  "siteBehavior": "Chore wheel template (/templates/chore-wheel/): options as on every template page: 'Remove the winner after each spin' OFF by default, Weighted choices OFF by default; its preset is 16 chores, and the page describes two ways to use it: chores on the wheel (pick a job for yourself; with remove-the-winner on it becomes a shrinking cleaning list) or names on the wheel (read out a chore, spin for who does it). The page's weighting tip for the names version: whoever did the bathroom last week gets *1, everyone else *2. Random name picker: removal OFF by default. Random student picker: removal ON by default, labelled 'Take each student off the wheel once picked', description 'Everyone gets a turn before anyone repeats. Press Reset to start the round again.' Classroom jobs wheel page recommends remove-after-spin on so nothing is assigned twice. Weighted lines: 'Name *2' (or 'Name x2') counts only when Weighted choices is on; with removal on, a weighted line is removed whole. The wheel never spins with fewer than two lines ('Add at least two choices first'), so the last name of a round is the one left over. Reset after removals puts back the list as it was when the first removal happened (roundStart, kept in the open page only); typing in the list, loading a saved wheel, a preset chip or Clear forgets it. After loading a saved wheel, Reset brings back the page's example list if pressed before any new removal, and the list as loaded (which may be a remainder, not everyone) if pressed after a removal. Nothing keeps the list or the round between visits: only the theme and saved wheels go to localStorage, and reloading the page brings back the example list, so a remove-the-winner round spread over several days needs the tab left open or a careful Save/Load; the simple way is to draw the whole round in one sitting (removal on, spin until one name is left, or press Shuffle) and post the order, which is statistically the same as the rounds model here. The result window also has a 'Remove & spin' button. Shuffle reorders the lines (CueRandom.shuffle); Save keeps a wheel in this browser only (the list as it is at that moment). Random team generator: Number of teams mode deals a shuffled list round-robin, so with more names than teams the FIRST teams get the extra names; custom team names are applied in the order typed; teams cannot outnumber names (5 chores cannot be dealt as teams to 3 kids the other way round). The team generator has no Save.",
  "checks": "Each check: z = (simulated - exact)/se, pass when |z| <= 4 (tolerance = 4 se). A share's se uses its exact p; an average's se uses the exact SD of the quantity. Pooled per-day shares (3 chores a day, team generator) pool days that are independent by construction. Deterministic checks (kind 'deterministic', se 0) pass only if the simulated value equals the exact one in every simulated month (gap of rounds, no triple runs in rounds, fixed and rotated team-name totals).",
  "rounding": "Probabilities rounded to 6 decimals, averages to 4. pmf / pAtLeast arrays are indexed from 0; trailing values below 5e-7 are cut."
 },
 "display": {
  "headline": {
   "fourPeopleMonth": {
    "fairShare": 7.5,
    "expectedGap": 5.6114,
    "pGapAtLeast7": "33.5%",
    "pDouble": "62.5%",
    "pThreeInARow": "77.9%",
    "pWaitBeyondRounds": "99.88%",
    "pGapBetweenTurnsBeyondRounds": "97.94%",
    "pGapBetweenTurnsAtLeast10": "67.7%",
    "pWaitAtLeast10InclEdges": "83.9%",
    "onePersonRange": "4 to 12",
    "onePersonRangeCovers": "94.10%"
   },
   "twoPeopleMonth": {
    "expectedGap": 4.3339,
    "pGapAtLeast7": "20.0%",
    "gapAtLeast7Means": "one of the two people on 19 or more of the 30 days (the other on 11 or fewer): a gap of 8 or more",
    "pThreeInARow": "99.75%",
    "onePersonRange": "11 to 19",
    "onePersonRangeCovers": "90.13%"
   },
   "threePeopleMonth": {
    "expectedGap": 5.3414,
    "pGapAtLeast7": "31.1%",
    "pThreeInARow": "92.85%"
   },
   "roundsFourPeopleMonth": {
    "gap": 1,
    "pAnyBackToBack": "86.7%",
    "boundaries": 7,
    "longestWaitMax": 6
   },
   "someoneNeverInAWeek": {
    "2": "1.56%",
    "3": "17.4%",
    "4": "48.7%",
    "5": "78.5%"
   }
  },
  "drawsLabel": "simulated spins and draws",
  "note": "drawsLabel: totalSpins counts wheel spins (wheelSpins) plus the team generator's shuffle draws (shuffleDraws), so the page's meta line must not call the total 'simulated spins'; set drawsLabel in the article to this value. Display strings: two decimals below 10% or above 90%, one decimal between; never 100% or 0% unless exact. Quote exact values from theory; simulated values from results must be called 'simulated'."
 },
 "theory": {
  "daily": {
   "note": "Exact. gap = busiest person's count minus the luckiest person's, from exact multinomial counting (BigInt, every one of the n^D day sequences equally likely). onePerson = Binomial(D, 1/n). pSomeoneNever = P(the luckiest count is 0). pSomeoneDoubleSomeone = P(busiest >= 2 × luckiest, a count of 0 included, so it is exactly 1 whenever someone must have none: 4 or 5 people over 7 days); pSomeoneDoubleSomeoneAllHadOne = the same with everyone on at least one (luckiest >= 1), so pSomeoneDoubleSomeone = pSomeoneDoubleSomeoneAllHadOne + pSomeoneNever. pSomeoneNever is rounded to 6 decimals, or to 4 significant digits below 1e-4 (2 people over 30 days: 1/536,870,912; quote fractionSomeoneNever or displaySomeoneNever, never 0%). Percentiles (p5, median, p95) are the smallest value whose cumulative probability reaches the level, so the inclusive range p5..p95 covers MORE than 90% of months (onePerson.pP5ToP95 gives the exact coverage): say '5th to 95th percentile' or 'in more than 9 months out of 10', not 'exactly 90%'. longestRun = the longest run of one name on consecutive days (exact chain, BigInt). longestWaitAnyone = the longest stretch of consecutive days that anyone goes without the chore in the D days, counting a stretch at the start or end of the period (no turn until day 11 counts as a 10-day wait; exact Markov chain over the multiset of days-since-last-turn, double precision); roundsMax = 2n-2, the longest wait remove-the-winner rounds ever allow. longestGapBetweenTurns = the longest run of days off BETWEEN two turns of the same person (stretches before a first turn or after a last turn do not count; exact Markov chain over the multiset of per-person states, double precision): this is what 'waited N days between turns' means; it is smaller than longestWaitAnyone (4 people, 30 days: P(10+) about 68% between turns versus 84% counting the edges). longestWaitOnePerson = the same for one particular person (BigInt chain). pmf and pAtLeast arrays are indexed by value (pAtLeast[g] = P(gap >= g)); trailing values below 5e-7 are cut. gap.threshold: 3 for 7 days, 4 for 14, 7 for 30 (the busiest person did a week's worth more turns than the luckiest in a month; it compares the two extremes, not anyone with the fair share). With 2 people the gap always has the parity of D (it is |2X - D|), so for 2 people over 30 days gap >= 7 means gap >= 8 (one child on 19 or more of 30): gap.effectiveThreshold and gap.thresholdMeaning give the wording for each row.",
   "byPeople": [
    {
     "people": 2,
     "byDays": [
      {
       "days": 7,
       "fairShare": 3.5,
       "onePerson": {
        "mean": 3.5,
        "sd": 1.3229,
        "p5": 1,
        "median": 3,
        "p95": 6,
        "pP5ToP95": 0.984375,
        "displayP5ToP95": "98.44%",
        "pmf": [
         0.007813,
         0.054688,
         0.164063,
         0.273438,
         0.273438,
         0.164063,
         0.054688,
         0.007813
        ],
        "pAtLeastFairPlus3": 0.007813,
        "pAtMostFairMinus3": 0.007813
       },
       "gap": {
        "pmf": [
         0,
         0.546875,
         0,
         0.328125,
         0,
         0.109375,
         0,
         0.015625
        ],
        "mean": 2.1875,
        "sd": 1.4882,
        "median": 1,
        "p5": 1,
        "p95": 5,
        "pAtLeast": [
         1,
         1,
         0.453125,
         0.453125,
         0.125,
         0.125,
         0.015625,
         0.015625
        ],
        "threshold": 3,
        "effectiveThreshold": 3,
        "thresholdMeaning": "one of the two people on 5 or more of the 7 days (the other on 2 or fewer): a gap of 3 or more",
        "pAtLeastThreshold": 0.453125,
        "displayAtLeastThreshold": "45.3%",
        "pZero": 0,
        "displayZero": "0%"
       },
       "busiest": {
        "pmf": [
         0,
         0,
         0,
         0,
         0.546875,
         0.328125,
         0.109375,
         0.015625
        ],
        "mean": 4.5938,
        "median": 4
       },
       "luckiest": {
        "pmf": [
         0.015625,
         0.109375,
         0.328125,
         0.546875
        ],
        "mean": 2.4063,
        "median": 3
       },
       "pSomeoneNever": 0.015625,
       "displaySomeoneNever": "1.56%",
       "fractionSomeoneNever": "1/64",
       "pSomeoneDoubleSomeone": 0.453125,
       "displayDouble": "45.3%",
       "pSomeoneDoubleSomeoneAllHadOne": 0.4375,
       "displayDoubleAllHadOne": "43.8%",
       "longestRun": {
        "pAtLeast": [
         1,
         1,
         0.984375,
         0.671875,
         0.3125,
         0.125,
         0.046875,
         0.015625
        ],
        "mean": 3.1563,
        "median": 3,
        "p95": 5,
        "pThreeInARow": 0.671875,
        "displayThreeInARow": "67.2%",
        "pFourInARow": 0.3125,
        "displayFourInARow": "31.3%"
       },
       "longestWaitAnyone": {
        "definition": "days in a row without the chore, counting a stretch at the start or end of the period",
        "pAtLeast": [
         1,
         1,
         0.984375,
         0.671875,
         0.3125,
         0.125,
         0.046875,
         0.015625
        ],
        "mean": 3.1563,
        "median": 3,
        "p5": 2,
        "p95": 5,
        "roundsMax": 2,
        "pBeyondRoundsMax": 0.671875,
        "displayBeyondRoundsMax": "67.2%",
        "pAtLeast10": 0,
        "displayAtLeast10": "0%"
       },
       "longestGapBetweenTurns": {
        "definition": "days off between two turns of the same person; stretches before someone's first turn or after their last do not count",
        "pAtLeast": [
         1,
         0.890625,
         0.65625,
         0.265625,
         0.078125,
         0.015625
        ],
        "mean": 1.9063,
        "median": 2,
        "p5": 0,
        "p95": 4,
        "pBeyondRoundsMax": 0.265625,
        "displayBeyondRoundsMax": "26.6%",
        "pAtLeast7": 0,
        "displayAtLeast7": "0%",
        "pAtLeast10": 0,
        "displayAtLeast10": "0%"
       },
       "longestWaitOnePerson": {
        "definition": "one particular person's longest run of days without the chore, counting a stretch at the start or end of the period",
        "pAtLeast": [
         1,
         0.992188,
         0.734375,
         0.367188,
         0.15625,
         0.0625,
         0.023438,
         0.007812
        ],
        "mean": 2.3438,
        "median": 2,
        "p95": 5,
        "pAtLeast10": 0,
        "displayAtLeast10": "0%"
       }
      },
      {
       "days": 14,
       "fairShare": 7,
       "onePerson": {
        "mean": 7,
        "sd": 1.8708,
        "p5": 4,
        "median": 7,
        "p95": 10,
        "pP5ToP95": 0.942627,
        "displayP5ToP95": "94.26%",
        "pmf": [
         0.000061,
         0.000854,
         0.005554,
         0.022217,
         0.061096,
         0.122192,
         0.183289,
         0.209473,
         0.183289,
         0.122192,
         0.061096,
         0.022217,
         0.005554,
         0.000854,
         0.000061
        ],
        "pAtLeastFairPlus3": 0.089783,
        "pAtMostFairMinus3": 0.089783
       },
       "gap": {
        "pmf": [
         0.209473,
         0,
         0.366577,
         0,
         0.244385,
         0,
         0.122192,
         0,
         0.044434,
         0,
         0.011108,
         0,
         0.001709,
         0,
         0.000122
        ],
        "mean": 2.9326,
        "sd": 2.3237,
        "median": 2,
        "p5": 0,
        "p95": 8,
        "pAtLeast": [
         1,
         0.790527,
         0.790527,
         0.42395,
         0.42395,
         0.179565,
         0.179565,
         0.057373,
         0.057373,
         0.012939,
         0.012939,
         0.001831,
         0.001831,
         0.000122,
         0.000122
        ],
        "threshold": 4,
        "effectiveThreshold": 4,
        "thresholdMeaning": "one of the two people on 9 or more of the 14 days (the other on 5 or fewer): a gap of 4 or more",
        "pAtLeastThreshold": 0.42395,
        "displayAtLeastThreshold": "42.4%",
        "pZero": 0.209473,
        "displayZero": "20.9%"
       },
       "busiest": {
        "pmf": [
         0,
         0,
         0,
         0,
         0,
         0,
         0,
         0.209473,
         0.366577,
         0.244385,
         0.122192,
         0.044434,
         0.011108,
         0.001709,
         0.000122
        ],
        "mean": 8.4663,
        "median": 8
       },
       "luckiest": {
        "pmf": [
         0.000122,
         0.001709,
         0.011108,
         0.044434,
         0.122192,
         0.244385,
         0.366577,
         0.209473
        ],
        "mean": 5.5337,
        "median": 6
       },
       "pSomeoneNever": 0.000122,
       "displaySomeoneNever": "0.01%",
       "fractionSomeoneNever": "1/8192",
       "pSomeoneDoubleSomeone": 0.179565,
       "displayDouble": "18.0%",
       "pSomeoneDoubleSomeoneAllHadOne": 0.179443,
       "displayDoubleAllHadOne": "17.9%",
       "longestRun": {
        "pAtLeast": [
         1,
         1,
         0.999878,
         0.925537,
         0.617188,
         0.324219,
         0.154053,
         0.07019,
         0.03125,
         0.013672,
         0.005859,
         0.002441,
         0.000977,
         0.000366,
         0.000122
        ],
        "mean": 4.1458,
        "median": 4,
        "p95": 7,
        "pThreeInARow": 0.925537,
        "displayThreeInARow": "92.55%",
        "pFourInARow": 0.617188,
        "displayFourInARow": "61.7%"
       },
       "longestWaitAnyone": {
        "definition": "days in a row without the chore, counting a stretch at the start or end of the period",
        "pAtLeast": [
         1,
         1,
         0.999878,
         0.925537,
         0.617188,
         0.324219,
         0.154053,
         0.07019,
         0.03125,
         0.013672,
         0.005859,
         0.002441,
         0.000977,
         0.000366,
         0.000122
        ],
        "mean": 4.1458,
        "median": 4,
        "p5": 2,
        "p95": 7,
        "roundsMax": 2,
        "pBeyondRoundsMax": 0.925537,
        "displayBeyondRoundsMax": "92.55%",
        "pAtLeast10": 0.005859,
        "displayAtLeast10": "0.59%"
       },
       "longestGapBetweenTurns": {
        "definition": "days off between two turns of the same person; stretches before someone's first turn or after their last do not count",
        "pAtLeast": [
         1,
         0.998291,
         0.98877,
         0.806885,
         0.457397,
         0.215088,
         0.09375,
         0.039185,
         0.015747,
         0.005981,
         0.002075,
         0.00061,
         0.000122
        ],
        "mean": 3.6239,
        "median": 3,
        "p5": 2,
        "p95": 6,
        "pBeyondRoundsMax": 0.806885,
        "displayBeyondRoundsMax": "80.7%",
        "pAtLeast7": 0.039185,
        "displayAtLeast7": "3.92%",
        "pAtLeast10": 0.002075,
        "displayAtLeast10": "0.21%"
       },
       "longestWaitOnePerson": {
        "definition": "one particular person's longest run of days without the chore, counting a stretch at the start or end of the period",
        "pAtLeast": [
         1,
         0.999939,
         0.939758,
         0.647949,
         0.348694,
         0.168457,
         0.07782,
         0.035156,
         0.015625,
         0.006836,
         0.00293,
         0.001221,
         0.000488,
         0.000183,
         0.000061
        ],
        "mean": 3.2451,
        "median": 3,
        "p95": 6,
        "pAtLeast10": 0.00293,
        "displayAtLeast10": "0.29%"
       }
      },
      {
       "days": 30,
       "fairShare": 15,
       "onePerson": {
        "mean": 15,
        "sd": 2.7386,
        "p5": 11,
        "median": 15,
        "p95": 19,
        "pP5ToP95": 0.901263,
        "displayP5ToP95": "90.13%",
        "pmf": [
         0,
         0,
         0,
         0.000004,
         0.000026,
         0.000133,
         0.000553,
         0.001896,
         0.005451,
         0.013325,
         0.027982,
         0.050876,
         0.080553,
         0.111535,
         0.135435,
         0.144464,
         0.135435,
         0.111535,
         0.080553,
         0.050876,
         0.027982,
         0.013325,
         0.005451,
         0.001896,
         0.000553,
         0.000133,
         0.000026,
         0.000004
        ],
        "pAtLeastFairPlus3": 0.180797,
        "pAtMostFairMinus3": 0.180797
       },
       "gap": {
        "pmf": [
         0.144464,
         0,
         0.270871,
         0,
         0.22307,
         0,
         0.161106,
         0,
         0.101751,
         0,
         0.055963,
         0,
         0.026649,
         0,
         0.010902,
         0,
         0.003792,
         0,
         0.001106,
         0,
         0.000265,
         0,
         0.000051,
         0,
         0.000008,
         0,
         0.000001
        ],
        "mean": 4.3339,
        "sd": 3.3492,
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         0.065536
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        "mean": 2.4343,
        "median": 2,
        "p5": 0,
        "p95": 5,
        "pBeyondRoundsMax": 0,
        "displayBeyondRoundsMax": "0%",
        "pAtLeast7": 0,
        "displayAtLeast7": "0%",
        "pAtLeast10": 0,
        "displayAtLeast10": "0%"
       },
       "longestWaitOnePerson": {
        "definition": "one particular person's longest run of days without the chore, counting a stretch at the start or end of the period",
        "pAtLeast": [
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         0.999987,
         0.985088,
         0.869171,
         0.65536,
         0.458752,
         0.314573,
         0.209715
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        "mean": 4.4926,
        "median": 4,
        "p95": 7,
        "pAtLeast10": 0,
        "displayAtLeast10": "0%"
       }
      },
      {
       "days": 14,
       "fairShare": 2.8,
       "onePerson": {
        "mean": 2.8,
        "sd": 1.4967,
        "p5": 1,
        "median": 3,
        "p95": 5,
        "pP5ToP95": 0.912165,
        "displayP5ToP95": "91.22%",
        "pmf": [
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         0.153932,
         0.250139,
         0.250139,
         0.17197,
         0.085985,
         0.032244,
         0.009213,
         0.002015,
         0.000336,
         0.000042,
         0.000004
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        "pAtLeastFairPlus3": 0.043854,
        "pAtMostFairMinus3": 0
       },
       "gap": {
        "pmf": [
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         0.027553,
         0.154984,
         0.239019,
         0.275251,
         0.185843,
         0.082924,
         0.026279,
         0.006632,
         0.001305,
         0.00019,
         0.000019,
         0.000001
        ],
        "mean": 3.8332,
        "sd": 1.407,
        "median": 4,
        "p5": 2,
        "p95": 6,
        "pAtLeast": [
         1,
         1,
         0.972447,
         0.817464,
         0.578445,
         0.303194,
         0.117351,
         0.034427,
         0.008148,
         0.001516,
         0.000211,
         0.00002,
         0.000001,
         0,
         0
        ],
        "threshold": 4,
        "effectiveThreshold": 4,
        "thresholdMeaning": "the busiest person had the chore 4 or more times more than the luckiest person",
        "pAtLeastThreshold": 0.578445,
        "displayAtLeastThreshold": "57.8%",
        "pZero": 0,
        "displayZero": "0%"
       },
       "busiest": {
        "pmf": [
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         0,
         0,
         0.027553,
         0.375405,
         0.379262,
         0.159736,
         0.046058,
         0.010076,
         0.001679,
         0.00021,
         0.000019,
         0.000001
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        "mean": 4.8595,
        "median": 5
       },
       "luckiest": {
        "pmf": [
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         0.549577,
         0.23833
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        "mean": 1.0262,
        "median": 1
       },
       "pSomeoneNever": 0.212093,
       "displaySomeoneNever": "21.2%",
       "fractionSomeoneNever": "51780457/244140625",
       "pSomeoneDoubleSomeone": 0.972447,
       "displayDouble": "97.24%",
       "pSomeoneDoubleSomeoneAllHadOne": 0.760355,
       "displayDoubleAllHadOne": "76.0%",
       "longestRun": {
        "pAtLeast": [
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         1,
         0.945024,
         0.345605,
         0.070784,
         0.013093,
         0.002368,
         0.000422,
         0.000074,
         0.000013,
         0.000002
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        "mean": 2.3774,
        "median": 2,
        "p95": 4,
        "pThreeInARow": 0.345605,
        "displayThreeInARow": "34.6%",
        "pFourInARow": 0.070784,
        "displayFourInARow": "7.08%"
       },
       "longestWaitAnyone": {
        "definition": "days in a row without the chore, counting a stretch at the start or end of the period",
        "pAtLeast": [
         1,
         1,
         1,
         1,
         1,
         1,
         0.99992,
         0.995891,
         0.965074,
         0.87678,
         0.737205,
         0.580378,
         0.433685,
         0.309975,
         0.212093
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        "mean": 11.111,
        "median": 11,
        "p5": 8,
        "p95": 14,
        "roundsMax": 8,
        "pBeyondRoundsMax": 0.87678,
        "displayBeyondRoundsMax": "87.7%",
        "pAtLeast10": 0.737205,
        "displayAtLeast10": "73.7%"
       },
       "longestGapBetweenTurns": {
        "definition": "days off between two turns of the same person; stretches before someone's first turn or after their last do not count",
        "pAtLeast": [
         1,
         0.99998,
         0.999351,
         0.991586,
         0.956157,
         0.865319,
         0.712993,
         0.527785,
         0.351388,
         0.210222,
         0.110639,
         0.04791,
         0.013744
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        "mean": 6.7871,
        "median": 7,
        "p5": 4,
        "p95": 10,
        "pBeyondRoundsMax": 0.210222,
        "displayBeyondRoundsMax": "21.0%",
        "pAtLeast7": 0.527785,
        "displayAtLeast7": "52.8%",
        "pAtLeast10": 0.110639,
        "displayAtLeast10": "11.1%"
       },
       "longestWaitOnePerson": {
        "definition": "one particular person's longest run of days without the chore, counting a stretch at the start or end of the period",
        "pAtLeast": [
         1,
         1,
         0.999864,
         0.989793,
         0.929559,
         0.805835,
         0.651338,
         0.503316,
         0.369099,
         0.268435,
         0.193274,
         0.137439,
         0.096207,
         0.065971,
         0.04398
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        "mean": 7.0541,
        "median": 7,
        "p95": 13,
        "pAtLeast10": 0.193274,
        "displayAtLeast10": "19.3%"
       }
      },
      {
       "days": 30,
       "fairShare": 6,
       "onePerson": {
        "mean": 6,
        "sd": 2.1909,
        "p5": 3,
        "median": 6,
        "p95": 10,
        "pP5ToP95": 0.930205,
        "displayP5ToP95": "93.02%",
        "pmf": [
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         0.009285,
         0.033656,
         0.078532,
         0.132522,
         0.172279,
         0.179457,
         0.153821,
         0.110559,
         0.067564,
         0.035471,
         0.016123,
         0.006382,
         0.002209,
         0.000671,
         0.000179,
         0.000042,
         0.000009,
         0.000002
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        "pAtLeastFairPlus3": 0.128651,
        "pAtMostFairMinus3": 0.122711
       },
       "gap": {
        "pmf": [
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         0,
         0.057677,
         0.087095,
         0.16216,
         0.188744,
         0.178732,
         0.139261,
         0.091206,
         0.051365,
         0.025128,
         0.010854,
         0.004199,
         0.001467,
         0.000465,
         0.000133,
         0.000034,
         0.000008,
         0.000002
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        "mean": 5.6575,
        "sd": 2.0947,
        "median": 6,
        "p5": 2,
        "p95": 9,
        "pAtLeast": [
         1,
         0.998528,
         0.998528,
         0.940851,
         0.853756,
         0.691596,
         0.502852,
         0.32412,
         0.184859,
         0.093653,
         0.042289,
         0.017161,
         0.006308,
         0.002109,
         0.000641,
         0.000177,
         0.000044,
         0.00001,
         0.000002,
         0,
         0,
         0,
         0,
         0,
         0,
         0
        ],
        "threshold": 7,
        "effectiveThreshold": 7,
        "thresholdMeaning": "the busiest person had the chore 7 or more times more than the luckiest person",
        "pAtLeastThreshold": 0.32412,
        "displayAtLeastThreshold": "32.4%",
        "pZero": 0.001472,
        "displayZero": "0.15%"
       },
       "busiest": {
        "pmf": [
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         0,
         0,
         0,
         0,
         0,
         0.001472,
         0.111565,
         0.30224,
         0.286068,
         0.171038,
         0.080169,
         0.031893,
         0.011046,
         0.003353,
         0.000894,
         0.00021,
         0.000043,
         0.000008,
         0.000001
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        "mean": 8.9655,
        "median": 9
       },
       "luckiest": {
        "pmf": [
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         0.046165,
         0.161602,
         0.325296,
         0.342482,
         0.116796,
         0.001472
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        "mean": 3.308,
        "median": 3
       },
       "pSomeoneNever": 0.006187,
       "displaySomeoneNever": "0.62%",
       "fractionSomeoneNever": "46100388979605653/7450580596923828125",
       "pSomeoneDoubleSomeone": 0.841139,
       "displayDouble": "84.1%",
       "pSomeoneDoubleSomeoneAllHadOne": 0.834952,
       "displayDoubleAllHadOne": "83.5%",
       "longestRun": {
        "pAtLeast": [
         1,
         1,
         0.998453,
         0.625708,
         0.163215,
         0.033215,
         0.006451,
         0.001241,
         0.000238,
         0.000046,
         0.000009,
         0.000002
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        "mean": 2.8286,
        "median": 3,
        "p95": 4,
        "pThreeInARow": 0.625708,
        "displayThreeInARow": "62.6%",
        "pFourInARow": 0.163215,
        "displayFourInARow": "16.3%"
       },
       "longestWaitAnyone": {
        "definition": "days in a row without the chore, counting a stretch at the start or end of the period",
        "pAtLeast": [
         1,
         1,
         1,
         1,
         1,
         1,
         1,
         1,
         0.99994,
         0.998529,
         0.988793,
         0.957194,
         0.89377,
         0.800635,
         0.689479,
         0.574091,
         0.465021,
         0.368378,
         0.286934,
         0.220601,
         0.167832,
         0.126543,
         0.094631,
         0.070198,
         0.051637,
         0.037631,
         0.027132,
         0.019312,
         0.013526,
         0.009279,
         0.006187
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        "mean": 15.8673,
        "median": 15,
        "p5": 11,
        "p95": 24,
        "roundsMax": 8,
        "pBeyondRoundsMax": 0.998529,
        "displayBeyondRoundsMax": "99.85%",
        "pAtLeast10": 0.988793,
        "displayAtLeast10": "98.88%"
       },
       "longestGapBetweenTurns": {
        "definition": "days off between two turns of the same person; stretches before someone's first turn or after their last do not count",
        "pAtLeast": [
         1,
         1,
         1,
         1,
         0.999999,
         0.99998,
         0.999675,
         0.997252,
         0.986117,
         0.95358,
         0.888023,
         0.789341,
         0.669601,
         0.544984,
         0.428539,
         0.327665,
         0.244862,
         0.179431,
         0.129125,
         0.091251,
         0.063233,
         0.042837,
         0.028231,
         0.017962,
         0.010902,
         0.006187,
         0.003167,
         0.001354,
         0.000387
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        "mean": 13.4037,
        "median": 13,
        "p5": 9,
        "p95": 20,
        "pBeyondRoundsMax": 0.95358,
        "displayBeyondRoundsMax": "95.36%",
        "pAtLeast7": 0.997252,
        "displayAtLeast7": "99.73%",
        "pAtLeast10": 0.888023,
        "displayAtLeast10": "88.8%"
       },
       "longestWaitOnePerson": {
        "definition": "one particular person's longest run of days without the chore, counting a stretch at the start or end of the period",
        "pAtLeast": [
         1,
         1,
         1,
         0.99997,
         0.998019,
         0.981475,
         0.930876,
         0.842041,
         0.728289,
         0.607449,
         0.49306,
         0.392247,
         0.307609,
         0.238749,
         0.183867,
         0.140737,
         0.10696,
         0.081065,
         0.061249,
         0.046117,
         0.034588,
         0.025825,
         0.019185,
         0.014167,
         0.010389,
         0.007556,
         0.00544,
         0.003869,
         0.002708,
         0.001857,
         0.001238
        ],
        "mean": 10.2666,
        "median": 9,
        "p95": 18,
        "pAtLeast10": 0.49306,
        "displayAtLeast10": "49.3%"
       }
      }
     ]
    }
   ]
  },
  "rounds": {
   "byPeople": [
    {
     "people": 2,
     "pSameNameEndsAndStarts": 0.5,
     "fraction": "1/2",
     "display": "50.0%",
     "daysOffBetweenTurns": {
      "pmf": [
       0.25,
       0.5,
       0.25
      ],
      "mean": 1,
      "min": 0,
      "max": 2,
      "pBackToBack": 0.25,
      "note": "for one particular person, across one round boundary"
     },
     "shuffleOnceAndRotate": {
      "gap": "0 or 1",
      "daysOffBetweenTurns": 1,
      "backToBack": 0,
      "longestWait": 1
     },
     "byDays": [
      {
       "days": 7,
       "rounds": 4,
       "daysInLastRound": 1,
       "boundaries": 3,
       "gap": 1,
       "turnsEach": [
        3,
        4
       ],
       "pExtraTurn": 0.5,
       "pAnyBackToBack": 0.875,
       "displayAnyBackToBack": "87.5%",
       "expectedBackToBack": 1.5,
       "maxRunPossible": 2,
       "longestWaitAnyone": {
        "pmf": [
         0,
         0.125,
         0.875,
         0
        ],
        "mean": 1.875,
        "median": 2,
        "max": 2,
        "maxAnyLength": 2
       }
      },
      {
       "days": 14,
       "rounds": 7,
       "daysInLastRound": 2,
       "boundaries": 6,
       "gap": 0,
       "turnsEach": [
        7
       ],
       "pExtraTurn": 0,
       "pAnyBackToBack": 0.984375,
       "displayAnyBackToBack": "98.44%",
       "expectedBackToBack": 3,
       "maxRunPossible": 2,
       "longestWaitAnyone": {
        "pmf": [
         0,
         0.015625,
         0.984375,
         0
        ],
        "mean": 1.9844,
        "median": 2,
        "max": 2,
        "maxAnyLength": 2
       }
      },
      {
       "days": 30,
       "rounds": 15,
       "daysInLastRound": 2,
       "boundaries": 14,
       "gap": 0,
       "turnsEach": [
        15
       ],
       "pExtraTurn": 0,
       "pAnyBackToBack": 0.999939,
       "displayAnyBackToBack": ">99.99%",
       "expectedBackToBack": 7,
       "maxRunPossible": 2,
       "longestWaitAnyone": {
        "pmf": [
         0,
         0.000061,
         0.999939,
         0
        ],
        "mean": 1.9999,
        "median": 2,
        "max": 2,
        "maxAnyLength": 2
       }
      }
     ]
    },
    {
     "people": 3,
     "pSameNameEndsAndStarts": 0.333333,
     "fraction": "1/3",
     "display": "33.3%",
     "daysOffBetweenTurns": {
      "pmf": [
       0.111111,
       0.222222,
       0.333333,
       0.222222,
       0.111111
      ],
      "mean": 2,
      "min": 0,
      "max": 4,
      "pBackToBack": 0.111111,
      "note": "for one particular person, across one round boundary"
     },
     "shuffleOnceAndRotate": {
      "gap": "0 or 1",
      "daysOffBetweenTurns": 2,
      "backToBack": 0,
      "longestWait": 2
     },
     "byDays": [
      {
       "days": 7,
       "rounds": 3,
       "daysInLastRound": 1,
       "boundaries": 2,
       "gap": 1,
       "turnsEach": [
        2,
        3
       ],
       "pExtraTurn": 0.333333,
       "pAnyBackToBack": 0.555556,
       "displayAnyBackToBack": "55.6%",
       "expectedBackToBack": 0.6667,
       "maxRunPossible": 2,
       "longestWaitAnyone": {
        "pmf": [
         0,
         0,
         0.055556,
         0.611111,
         0.333333,
         0
        ],
        "mean": 3.2778,
        "median": 3,
        "max": 4,
        "maxAnyLength": 4
       }
      },
      {
       "days": 14,
       "rounds": 5,
       "daysInLastRound": 2,
       "boundaries": 4,
       "gap": 1,
       "turnsEach": [
        4,
        5
       ],
       "pExtraTurn": 0.666667,
       "pAnyBackToBack": 0.802469,
       "displayAnyBackToBack": "80.2%",
       "expectedBackToBack": 1.3333,
       "maxRunPossible": 2,
       "longestWaitAnyone": {
        "pmf": [
         0,
         0,
         0.000772,
         0.196759,
         0.802469,
         0
        ],
        "mean": 3.8017,
        "median": 4,
        "max": 4,
        "maxAnyLength": 4
       }
      },
      {
       "days": 30,
       "rounds": 10,
       "daysInLastRound": 3,
       "boundaries": 9,
       "gap": 0,
       "turnsEach": [
        10
       ],
       "pExtraTurn": 0,
       "pAnyBackToBack": 0.973988,
       "displayAnyBackToBack": "97.40%",
       "expectedBackToBack": 3,
       "maxRunPossible": 2,
       "longestWaitAnyone": {
        "pmf": [
         0,
         0,
         0,
         0.026012,
         0.973988,
         0
        ],
        "mean": 3.974,
        "median": 4,
        "max": 4,
        "maxAnyLength": 4
       }
      }
     ]
    },
    {
     "people": 4,
     "pSameNameEndsAndStarts": 0.25,
     "fraction": "1/4",
     "display": "25.0%",
     "daysOffBetweenTurns": {
      "pmf": [
       0.0625,
       0.125,
       0.1875,
       0.25,
       0.1875,
       0.125,
       0.0625
      ],
      "mean": 3,
      "min": 0,
      "max": 6,
      "pBackToBack": 0.0625,
      "note": "for one particular person, across one round boundary"
     },
     "shuffleOnceAndRotate": {
      "gap": "0 or 1",
      "daysOffBetweenTurns": 3,
      "backToBack": 0,
      "longestWait": 3
     },
     "byDays": [
      {
       "days": 7,
       "rounds": 2,
       "daysInLastRound": 3,
       "boundaries": 1,
       "gap": 1,
       "turnsEach": [
        1,
        2
       ],
       "pExtraTurn": 0.75,
       "pAnyBackToBack": 0.25,
       "displayAnyBackToBack": "25.0%",
       "expectedBackToBack": 0.25,
       "maxRunPossible": 2,
       "longestWaitAnyone": {
        "pmf": [
         0,
         0,
         0,
         0.041667,
         0.291667,
         0.416667,
         0.25,
         0
        ],
        "mean": 4.875,
        "median": 5,
        "max": 6,
        "maxAnyLength": 6
       }
      },
      {
       "days": 14,
       "rounds": 4,
       "daysInLastRound": 2,
       "boundaries": 3,
       "gap": 1,
       "turnsEach": [
        3,
        4
       ],
       "pExtraTurn": 0.5,
       "pAnyBackToBack": 0.578125,
       "displayAnyBackToBack": "57.8%",
       "expectedBackToBack": 0.75,
       "maxRunPossible": 2,
       "longestWaitAnyone": {
        "pmf": [
         0,
         0,
         0,
         0.000145,
         0.055411,
         0.506944,
         0.4375,
         0
        ],
        "mean": 5.3818,
        "median": 5,
        "max": 6,
        "maxAnyLength": 6
       }
      },
      {
       "days": 30,
       "rounds": 8,
       "daysInLastRound": 2,
       "boundaries": 7,
       "gap": 1,
       "turnsEach": [
        7,
        8
       ],
       "pExtraTurn": 0.5,
       "pAnyBackToBack": 0.866516,
       "displayAnyBackToBack": "86.7%",
       "expectedBackToBack": 1.75,
       "maxRunPossible": 2,
       "longestWaitAnyone": {
        "pmf": [
         0,
         0,
         0,
         0,
         0.000686,
         0.177293,
         0.822021,
         0
        ],
        "mean": 5.8213,
        "median": 6,
        "max": 6,
        "maxAnyLength": 6
       }
      }
     ]
    },
    {
     "people": 5,
     "pSameNameEndsAndStarts": 0.2,
     "fraction": "1/5",
     "display": "20.0%",
     "daysOffBetweenTurns": {
      "pmf": [
       0.04,
       0.08,
       0.12,
       0.16,
       0.2,
       0.16,
       0.12,
       0.08,
       0.04
      ],
      "mean": 4,
      "min": 0,
      "max": 8,
      "pBackToBack": 0.04,
      "note": "for one particular person, across one round boundary"
     },
     "shuffleOnceAndRotate": {
      "gap": "0 or 1",
      "daysOffBetweenTurns": 4,
      "backToBack": 0,
      "longestWait": 4
     },
     "byDays": [
      {
       "days": 7,
       "rounds": 2,
       "daysInLastRound": 2,
       "boundaries": 1,
       "gap": 1,
       "turnsEach": [
        1,
        2
       ],
       "pExtraTurn": 0.4,
       "pAnyBackToBack": 0.2,
       "displayAnyBackToBack": "20.0%",
       "expectedBackToBack": 0.2,
       "maxRunPossible": 2,
       "longestWaitAnyone": {
        "pmf": [
         0,
         0,
         0,
         0,
         0.05,
         0.35,
         0.6,
         0,
         0,
         0
        ],
        "mean": 5.55,
        "median": 6,
        "max": 6,
        "maxAnyLength": 8
       }
      },
      {
       "days": 14,
       "rounds": 3,
       "daysInLastRound": 4,
       "boundaries": 2,
       "gap": 1,
       "turnsEach": [
        2,
        3
       ],
       "pExtraTurn": 0.8,
       "pAnyBackToBack": 0.36,
       "displayAnyBackToBack": "36.0%",
       "expectedBackToBack": 0.4,
       "maxRunPossible": 2,
       "longestWaitAnyone": {
        "pmf": [
         0,
         0,
         0,
         0,
         0.000069,
         0.017708,
         0.184722,
         0.4375,
         0.36,
         0
        ],
        "mean": 7.1397,
        "median": 7,
        "max": 8,
        "maxAnyLength": 8
       }
      },
      {
       "days": 30,
       "rounds": 6,
       "daysInLastRound": 5,
       "boundaries": 5,
       "gap": 0,
       "turnsEach": [
        6
       ],
       "pExtraTurn": 0,
       "pAnyBackToBack": 0.67232,
       "displayAnyBackToBack": "67.2%",
       "expectedBackToBack": 1,
       "maxRunPossible": 2,
       "longestWaitAnyone": {
        "pmf": [
         0,
         0,
         0,
         0,
         0,
         0.000042,
         0.018411,
         0.309227,
         0.67232,
         0
        ],
        "mean": 7.6538,
        "median": 8,
        "max": 8,
        "maxAnyLength": 8
       }
      }
     ]
    }
   ],
   "note": "Exact. With removal on, each round is a uniformly random order of the n people: n-1 spins on a shrinking wheel, and the last name is left over because the wheel never spins with one line. Rounds start on day 1 and Reset is pressed when the wheel is used up. Within complete rounds every count is equal, so the gap is 0 when D is a multiple of n and exactly 1 otherwise (turnsEach; pExtraTurn = the chance a particular person is among the D mod n who get the extra turn). The only repeats are across a round boundary: the person who ended one round starts the next with chance 1/n at each of the floor((D-1)/n) boundaries, independently, so pAnyBackToBack = 1 - (1-1/n)^boundaries and no one ever gets three in a row (maxRunPossible = 2 is the most that can happen, not a typical value: say 'never more than 2 in a row'). daysOffBetweenTurns: (n - i) + (j - 1) for positions i, j in consecutive rounds, 0 to 2n-2, mean n-1. longestWaitAnyone: exact over every round order (independent boundaries, BigInt), counting a stretch at the start or end of the period like the daily study; max = the largest value that can happen within D days (it is 2n-2, maxAnyLength, once the period is long enough, but 6 for 5 people over 7 days). The model needs only a uniformly random order for each round: the wheel does not keep a round between visits (the list and the round live in the open page only; a reload brings back the page's example list), so in practice the round is drawn in one sitting (removal on, spin until one name is left, or press Shuffle) and the order is posted; that is statistically the same as one spin a day. shuffleOnceAndRotate: press Shuffle once, then go down the list in that order forever: no randomness after the first day."
  },
  "longRun": {
   "note": "Exact expected gap (busiest minus luckiest) for one spin a day, computed by an exact DP in double precision (it matches the BigInt counts at 7, 14 and 30 days to 1e-9). gapPerFairShare = expected gap / (D/n): the gap keeps growing in chores (roughly with the square root of the number of days) while shrinking as a share of each person's total. With remove-the-winner rounds the gap is never more than 1. gap20pct / gap10pct = the smallest whole gap that is at least 20% / 10% of a fair share.",
   "rows": [
    {
     "people": 2,
     "series": [
      {
       "days": 7,
       "fairShare": 3.5,
       "sdPerson": 1.3229,
       "expectedGap": 2.1875,
       "gapPerFairShare": 0.625,
       "pGapAtLeast7": 0.015625,
       "pGapAtLeast20pctOfFair": 1,
       "gap20pct": 1,
       "pGapAtLeast10pctOfFair": 1,
       "gap10pct": 1
      },
      {
       "days": 14,
       "fairShare": 7,
       "sdPerson": 1.8708,
       "expectedGap": 2.9326,
       "gapPerFairShare": 0.4189,
       "pGapAtLeast7": 0.057373,
       "pGapAtLeast20pctOfFair": 0.790527,
       "gap20pct": 2,
       "pGapAtLeast10pctOfFair": 0.790527,
       "gap10pct": 1
      },
      {
       "days": 30,
       "fairShare": 15,
       "sdPerson": 2.7386,
       "expectedGap": 4.3339,
       "gapPerFairShare": 0.2889,
       "pGapAtLeast7": 0.200488,
       "pGapAtLeast20pctOfFair": 0.584665,
       "gap20pct": 3,
       "pGapAtLeast10pctOfFair": 0.855536,
       "gap10pct": 2
      },
      {
       "days": 60,
       "fairShare": 30,
       "sdPerson": 3.873,
       "expectedGap": 6.1547,
       "gapPerFairShare": 0.2052,
       "pGapAtLeast7": 0.366294,
       "pGapAtLeast20pctOfFair": 0.518958,
       "gap20pct": 6,
       "pGapAtLeast10pctOfFair": 0.698883,
       "gap10pct": 3
      },
      {
       "days": 90,
       "fairShare": 45,
       "sdPerson": 4.7434,
       "expectedGap": 7.5484,
       "gapPerFairShare": 0.1677,
       "pGapAtLeast7": 0.460792,
       "pGapAtLeast20pctOfFair": 0.342833,
       "gap20pct": 9,
       "pGapAtLeast10pctOfFair": 0.598412,
       "gap10pct": 5
      },
      {
       "days": 180,
       "fairShare": 90,
       "sdPerson": 6.7082,
       "expectedGap": 10.6899,
       "gapPerFairShare": 0.1188,
       "pGapAtLeast7": 0.601969,
       "pGapAtLeast20pctOfFair": 0.204992,
       "gap20pct": 18,
       "pGapAtLeast10pctOfFair": 0.502445,
       "gap10pct": 9
      },
      {
       "days": 365,
       "fairShare": 182.5,
       "sdPerson": 9.5525,
       "expectedGap": 15.254,
       "gapPerFairShare": 0.0836,
       "pGapAtLeast7": 0.753529,
       "pGapAtLeast20pctOfFair": 0.059372,
       "gap20pct": 37,
       "pGapAtLeast10pctOfFair": 0.346122,
       "gap10pct": 19
      }
     ]
    },
    {
     "people": 3,
     "series": [
      {
       "days": 7,
       "fairShare": 2.3333,
       "sdPerson": 1.2472,
       "expectedGap": 2.5638,
       "gapPerFairShare": 1.0988,
       "pGapAtLeast7": 0.001372,
       "pGapAtLeast20pctOfFair": 1,
       "gap20pct": 1,
       "pGapAtLeast10pctOfFair": 1,
       "gap10pct": 1
      },
      {
       "days": 14,
       "fairShare": 4.6667,
       "sdPerson": 1.7638,
       "expectedGap": 3.6405,
       "gapPerFairShare": 0.7801,
       "pGapAtLeast7": 0.080824,
       "pGapAtLeast20pctOfFair": 1,
       "gap20pct": 1,
       "pGapAtLeast10pctOfFair": 1,
       "gap10pct": 1
      },
      {
       "days": 30,
       "fairShare": 10,
       "sdPerson": 2.582,
       "expectedGap": 5.3414,
       "gapPerFairShare": 0.5341,
       "pGapAtLeast7": 0.310655,
       "pGapAtLeast20pctOfFair": 0.973039,
       "gap20pct": 2,
       "pGapAtLeast10pctOfFair": 0.973039,
       "gap10pct": 1
      },
      {
       "days": 60,
       "fairShare": 20,
       "sdPerson": 3.6515,
       "expectedGap": 7.5616,
       "gapPerFairShare": 0.3781,
       "pGapAtLeast7": 0.556334,
       "pGapAtLeast20pctOfFair": 0.837837,
       "gap20pct": 4,
       "pGapAtLeast10pctOfFair": 0.986369,
       "gap10pct": 2
      },
      {
       "days": 90,
       "fairShare": 30,
       "sdPerson": 4.4721,
       "expectedGap": 9.2642,
       "gapPerFairShare": 0.3088,
       "pGapAtLeast7": 0.675722,
       "pGapAtLeast20pctOfFair": 0.753342,
       "gap20pct": 6,
       "pGapAtLeast10pctOfFair": 0.937918,
       "gap10pct": 3
      },
      {
       "days": 180,
       "fairShare": 60,
       "sdPerson": 6.3246,
       "expectedGap": 13.106,
       "gapPerFairShare": 0.2184,
       "pGapAtLeast7": 0.821452,
       "pGapAtLeast20pctOfFair": 0.544208,
       "gap20pct": 12,
       "pGapAtLeast10pctOfFair": 0.86764,
       "gap10pct": 6
      },
      {
       "days": 365,
       "fairShare": 121.6667,
       "sdPerson": 9.0062,
       "expectedGap": 18.6663,
       "gapPerFairShare": 0.1534,
       "pGapAtLeast7": 0.909358,
       "pGapAtLeast20pctOfFair": 0.258567,
       "gap20pct": 25,
       "pGapAtLeast10pctOfFair": 0.702825,
       "gap10pct": 13
      }
     ]
    },
    {
     "people": 4,
     "series": [
      {
       "days": 7,
       "fairShare": 1.75,
       "sdPerson": 1.1456,
       "expectedGap": 2.6729,
       "gapPerFairShare": 1.5273,
       "pGapAtLeast7": 0.000244,
       "pGapAtLeast20pctOfFair": 1,
       "gap20pct": 1,
       "pGapAtLeast10pctOfFair": 1,
       "gap10pct": 1
      },
      {
       "days": 14,
       "fairShare": 3.5,
       "sdPerson": 1.6202,
       "expectedGap": 3.8088,
       "gapPerFairShare": 1.0882,
       "pGapAtLeast7": 0.056619,
       "pGapAtLeast20pctOfFair": 1,
       "gap20pct": 1,
       "pGapAtLeast10pctOfFair": 1,
       "gap10pct": 1
      },
      {
       "days": 30,
       "fairShare": 7.5,
       "sdPerson": 2.3717,
       "expectedGap": 5.6114,
       "gapPerFairShare": 0.7482,
       "pGapAtLeast7": 0.334739,
       "pGapAtLeast20pctOfFair": 0.966572,
       "gap20pct": 2,
       "pGapAtLeast10pctOfFair": 1,
       "gap10pct": 1
      },
      {
       "days": 60,
       "fairShare": 15,
       "sdPerson": 3.3541,
       "expectedGap": 7.9564,
       "gapPerFairShare": 0.5304,
       "pGapAtLeast7": 0.63392,
       "pGapAtLeast20pctOfFair": 0.962486,
       "gap20pct": 3,
       "pGapAtLeast10pctOfFair": 0.997859,
       "gap10pct": 2
      },
      {
       "days": 90,
       "fairShare": 22.5,
       "sdPerson": 4.1079,
       "expectedGap": 9.7508,
       "gapPerFairShare": 0.4334,
       "pGapAtLeast7": 0.768666,
       "pGapAtLeast20pctOfFair": 0.90795,
       "gap20pct": 5,
       "pGapAtLeast10pctOfFair": 0.984316,
       "gap10pct": 3
      },
      {
       "days": 180,
       "fairShare": 45,
       "sdPerson": 5.8095,
       "expectedGap": 13.8005,
       "gapPerFairShare": 0.3067,
       "pGapAtLeast7": 0.901919,
       "pGapAtLeast20pctOfFair": 0.806942,
       "gap20pct": 9,
       "pGapAtLeast10pctOfFair": 0.964288,
       "gap10pct": 5
      },
      {
       "days": 365,
       "fairShare": 91.25,
       "sdPerson": 8.2727,
       "expectedGap": 19.6591,
       "gapPerFairShare": 0.2154,
       "pGapAtLeast7": 0.963206,
       "pGapAtLeast20pctOfFair": 0.51866,
       "gap20pct": 19,
       "pGapAtLeast10pctOfFair": 0.895787,
       "gap10pct": 10
      }
     ]
    },
    {
     "people": 5,
     "series": [
      {
       "days": 7,
       "fairShare": 1.4,
       "sdPerson": 1.0583,
       "expectedGap": 2.6544,
       "gapPerFairShare": 1.896,
       "pGapAtLeast7": 0.000064,
       "pGapAtLeast20pctOfFair": 1,
       "gap20pct": 1,
       "pGapAtLeast10pctOfFair": 1,
       "gap10pct": 1
      },
      {
       "days": 14,
       "fairShare": 2.8,
       "sdPerson": 1.4967,
       "expectedGap": 3.8332,
       "gapPerFairShare": 1.369,
       "pGapAtLeast7": 0.034427,
       "pGapAtLeast20pctOfFair": 1,
       "gap20pct": 1,
       "pGapAtLeast10pctOfFair": 1,
       "gap10pct": 1
      },
      {
       "days": 30,
       "fairShare": 6,
       "sdPerson": 2.1909,
       "expectedGap": 5.6575,
       "gapPerFairShare": 0.9429,
       "pGapAtLeast7": 0.32412,
       "pGapAtLeast20pctOfFair": 0.998528,
       "gap20pct": 2,
       "pGapAtLeast10pctOfFair": 0.998528,
       "gap10pct": 1
      },
      {
       "days": 60,
       "fairShare": 12,
       "sdPerson": 3.0984,
       "expectedGap": 8.0293,
       "gapPerFairShare": 0.6691,
       "pGapAtLeast7": 0.674314,
       "pGapAtLeast20pctOfFair": 0.982871,
       "gap20pct": 3,
       "pGapAtLeast10pctOfFair": 0.99962,
       "gap10pct": 2
      },
      {
       "days": 90,
       "fairShare": 18,
       "sdPerson": 3.7947,
       "expectedGap": 9.8453,
       "gapPerFairShare": 0.547,
       "pGapAtLeast7": 0.81529,
       "pGapAtLeast20pctOfFair": 0.977757,
       "gap20pct": 4,
       "pGapAtLeast10pctOfFair": 0.999829,
       "gap10pct": 2
      },
      {
       "days": 180,
       "fairShare": 36,
       "sdPerson": 5.3666,
       "expectedGap": 13.9395,
       "gapPerFairShare": 0.3872,
       "pGapAtLeast7": 0.940205,
       "pGapAtLeast20pctOfFair": 0.902619,
       "gap20pct": 8,
       "pGapAtLeast10pctOfFair": 0.99395,
       "gap10pct": 4
      },
      {
       "days": 365,
       "fairShare": 73,
       "sdPerson": 7.642,
       "expectedGap": 19.8615,
       "gapPerFairShare": 0.2721,
       "pGapAtLeast7": 0.983321,
       "pGapAtLeast20pctOfFair": 0.751378,
       "gap20pct": 15,
       "pGapAtLeast10pctOfFair": 0.971647,
       "gap10pct": 8
      }
     ]
    }
   ],
   "yearFourPeople": {
    "expectedGap": 19.6591,
    "sdGap": 8.3994,
    "pGapAtLeast20": 0.472118,
    "displayGapAtLeast20": "47.2%"
   }
  },
  "threeChores": {
   "kids": 3,
   "chores": [
    "Dishes",
    "Trash",
    "Laundry"
   ],
   "days": 30,
   "oneDay": {
    "spin": {
     "pSomeoneTwoOrMore": 0.777778,
     "fractionSomeoneTwoOrMore": "7/9",
     "display": "77.8%",
     "pOneKidAll": 0.111111,
     "fractionOneKidAll": "1/9",
     "displayOneKidAll": "11.1%",
     "pEachOne": 0.222222,
     "fractionEachOne": "2/9",
     "pParticularKidNone": 0.296296,
     "fractionParticularKidNone": "8/27",
     "displayParticularKidNone": "29.6%",
     "pSomeKidNone": 0.777778,
     "fractionSomeKidNone": "7/9",
     "displaySomeKidNone": "77.8%",
     "note": "pParticularKidNone = the chance that ONE PARTICULAR kid (say, yours) gets no chore that day; pSomeKidNone = the chance that at least one of the 3 kids gets none, the same event as some kid getting 2+ when there are as many chores as kids"
    },
    "roundsOrTeams": {
     "pSomeoneTwoOrMore": 0,
     "pEachOne": 1
    }
   },
   "monthTotals": {
    "spin": {
     "chores": 90,
     "fairShare": 30,
     "sdPerson": 4.4721,
     "gapPmf": [
      0.009121,
      0,
      0.052961,
      0.049597,
      0.047996,
      0.086983,
      0.07762,
      0.071401,
      0.09093,
      0.077337,
      0.067543,
      0.071702,
      0.05812,
      0.048132,
      0.044985,
      0.034739,
      0.027247,
      0.023003,
      0.016913,
      0.012552,
      0.009716,
      0.006795,
      0.004768,
      0.003418,
      0.002271,
      0.001506,
      0.001007,
      0.000635,
      0.000398,
      0.000249,
      0.000149,
      0.000088,
      0.000052,
      0.000029,
      0.000016,
      0.000009,
      0.000005,
      0.000003,
      0.000001,
      0.000001
     ],
     "expectedGap": 9.2642,
     "sdGap": 4.8595,
     "medianGap": 9,
     "p95Gap": 18,
     "threshold": 7,
     "pGapAtLeastThreshold": 0.675722,
     "display": "67.6%",
     "pSomeoneDoubleSomeone": 0.028789
    },
    "roundsOrTeams": {
     "eachKid": 30,
     "gap": 0
    }
   },
   "perChore": {
    "note": "How often each kid gets one particular chore (say the dishes) in the month. It is the same under all three methods: every day the dishes go to a uniformly random kid, independently of other days. So rounds and the team generator even out the number of chores, not who gets which one.",
    "fairShare": 10,
    "expectedGap": 5.3414,
    "threshold": 7,
    "pGapAtLeastThreshold": 0.310655,
    "display": "31.1%",
    "fixedRotation": {
     "eachKidEachChore": 10,
     "note": "a fixed rotation (kid A dishes, kid B trash, kid C laundry, shifted one place each day) gives every kid each chore exactly D/k times"
    }
   }
  },
  "fiveChores": {
   "kids": 3,
   "chores": [
    "Dishes",
    "Trash",
    "Laundry",
    "Vacuum",
    "Feed the dog"
   ],
   "days": 30,
   "totalChores": 150,
   "fairShare": 50,
   "spin": {
    "expectedGap": 11.9633,
    "sdGap": 6.2767,
    "medianGap": 11,
    "p95Gap": 23,
    "pGapAtLeast7": 0.789911,
    "displayGapAtLeast7": "79.0%",
    "pGapAtLeast10": 0.607118,
    "displayGapAtLeast10": "60.7%",
    "sdPerson": 5.7735
   },
   "teamFixed": {
    "totals": [
     60,
     60,
     30
    ],
    "gap": 30,
    "perDay": [
     2,
     2,
     1
    ],
    "pDishesByKid": [
     0.4,
     0.4,
     0.2
    ],
    "note": "Deterministic: the team generator deals round-robin, so with 5 chores and 3 teams the first two team names always get 2 chores and the third gets 1. Typed in the same order every day, the same kid gets the light day every day."
   },
   "teamRotated": {
    "totals": [
     50,
     50,
     50
    ],
    "gap": 0,
    "note": "Team names rotated one place each day: every kid gets the 1-chore day once every 3 days."
   },
   "roundsDaily": {
    "expectedGap": 5.3414,
    "sdGap": 2.7995,
    "pGapAtLeast7": 0.310655,
    "displayGapAtLeast7": "31.1%",
    "pGapAtLeast4": 0.704545,
    "displayGapAtLeast4": "70.5%",
    "note": "Removal on, Reset every morning: one full round (one chore each) plus 2 picks from a second round. Which kid is left with 1 chore is uniform each day, so the month-total gap has the same distribution as one name spun daily on a 3-name wheel for 30 days."
   },
   "roundsCarried": {
    "totals": [
     50,
     50,
     50
    ],
    "gap": 0,
    "tripleDays": 10,
    "pTriplePerSuchDay": 0.333333,
    "expectedTripleDays": 3.3333,
    "note": "Removal on and the round carried over to the next day (Reset only when the wheel is used up): 150 chores = 50 complete rounds, so every kid ends the month on exactly 50. The price: on days that span three rounds, the kid who ended one round can start the round after next, and gets 3 of the 5 chores (chance 1/3 on each such day, independently). On the site this needs the page left open from day to day (or the remaining list saved and loaded), because the wheel does not keep a round between visits."
   }
  },
  "weighted": {
   "families": [
    {
     "kids": 2,
     "weights": [
      2,
      1
     ],
     "lines": [
      "Older *2",
      "Younger"
     ],
     "olderShare": 0.666667,
     "olderShareFraction": "2/3",
     "olderShareDisplay": "66.7%",
     "youngerShare": 0.333333,
     "olderExpected": 20,
     "olderSd": 2.582,
     "olderShareSd": 0.0861,
     "olderP5": 16,
     "olderMedian": 20,
     "olderP95": 24,
     "olderShareP5": 0.5333,
     "olderShareP95": 0.8,
     "pOlderP5ToP95": 0.921064,
     "displayOlderP5ToP95": "92.11%",
     "youngerExpected": 10,
     "pOlderFewerThanAYounger": 0.018795,
     "displayOlderFewer": "1.88%",
     "pOlderNoMoreThanAYounger": 0.043482,
     "displayOlderNoMore": "4.35%",
     "pShareOff10Points": 0.332794,
     "displayShareOff10Points": "33.3%",
     "olderPmf": [
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0.000001,
      0.000007,
      0.000036,
      0.000149,
      0.000543,
      0.001721,
      0.004765,
      0.011572,
      0.024687,
      0.046289,
      0.07624,
      0.110125,
      0.139105,
      0.153015,
      0.145729,
      0.119233,
      0.082944,
      0.048384,
      0.023224,
      0.008932,
      0.002647,
      0.000567,
      0.000078,
      0.000005
     ]
    },
    {
     "kids": 3,
     "weights": [
      2,
      1,
      1
     ],
     "lines": [
      "Older *2",
      "Younger 1",
      "Younger 2"
     ],
     "olderShare": 0.5,
     "olderShareFraction": "1/2",
     "olderShareDisplay": "50.0%",
     "youngerShare": 0.25,
     "olderExpected": 15,
     "olderSd": 2.7386,
     "olderShareSd": 0.0913,
     "olderP5": 11,
     "olderMedian": 15,
     "olderP95": 19,
     "olderShareP5": 0.3667,
     "olderShareP95": 0.6333,
     "pOlderP5ToP95": 0.901263,
     "displayOlderP5ToP95": "90.13%",
     "youngerExpected": 7.5,
     "pOlderFewerThanAYounger": 0.07196,
     "displayOlderFewer": "7.20%",
     "pOlderNoMoreThanAYounger": 0.107523,
     "displayOlderNoMore": "10.8%",
     "pShareOff10Points": 0.361595,
     "displayShareOff10Points": "36.2%",
     "olderPmf": [
      0,
      0,
      0,
      0.000004,
      0.000026,
      0.000133,
      0.000553,
      0.001896,
      0.005451,
      0.013325,
      0.027982,
      0.050876,
      0.080553,
      0.111535,
      0.135435,
      0.144464,
      0.135435,
      0.111535,
      0.080553,
      0.050876,
      0.027982,
      0.013325,
      0.005451,
      0.001896,
      0.000553,
      0.000133,
      0.000026,
      0.000004
     ]
    }
   ],
   "roundOrder": {
    "weights": [
     2,
     1,
     1
    ],
    "turnsPerRoundEach": 1,
    "pPosition": [
     0.5,
     0.333333,
     0.166667
    ],
    "fractions": [
     "1/2",
     "1/3",
     "1/6"
    ],
    "note": "With removal on, a weighted line leaves whole when it wins, so the *2 kid still has exactly one turn per round: the weight only moves the turn earlier in the round (pPosition[j] = chance of going (j+1)-th)."
   },
   "lastTimeLighter": {
    "rule": "re-weighting before every spin: whoever had it last time *1, everyone else *2 (the first spin is unweighted). The chore wheel page's tip is for a weekly job such as the bathroom, with the weights edited by hand; applying it before every one of 30 daily spins is this study's test, not the page's recommendation",
    "byPeople": [
     {
      "people": 3,
      "days": 30,
      "pSameAsLastTime": 0.2,
      "fraction": "1/5",
      "display": "20.0%",
      "plainPSameAsLastTime": 0.333333,
      "plainFraction": "1/3",
      "pAnyBackToBack": 0.998453,
      "displayAnyBackToBack": "99.85%",
      "plainPAnyBackToBack": 0.999992,
      "pThreeInARow": 0.625708,
      "displayThreeInARow": "62.6%",
      "plainPThreeInARow": 0.928548,
      "plainDisplayThreeInARow": "92.85%",
      "sdPerson": 2.1228,
      "plainSdPerson": 2.582,
      "expectedGap": 4.3796,
      "plainExpectedGap": 5.3414,
      "pGapAtLeast7": 0.176401,
      "displayGapAtLeast7": "17.6%",
      "plainPGapAtLeast7": 0.310655,
      "plainDisplayGapAtLeast7": "31.1%",
      "gapPmf": [
       0.040305,
       0,
       0.209269,
       0.156597,
       0.13541,
       0.17485,
       0.107169,
       0.072365,
       0.05288,
       0.026442,
       0.013659,
       0.00677,
       0.002705,
       0.001049,
       0.000374,
       0.000115,
       0.000033,
       0.000008,
       0.000002
      ]
     },
     {
      "people": 4,
      "days": 30,
      "pSameAsLastTime": 0.142857,
      "fraction": "1/7",
      "display": "14.3%",
      "plainPSameAsLastTime": 0.25,
      "plainFraction": "1/4",
      "pAnyBackToBack": 0.988557,
      "displayAnyBackToBack": "98.86%",
      "plainPAnyBackToBack": 0.999762,
      "pThreeInARow": 0.402368,
      "displayThreeInARow": "40.2%",
      "plainPThreeInARow": 0.778986,
      "plainDisplayThreeInARow": "77.9%",
      "sdPerson": 2.0639,
      "plainSdPerson": 2.3717,
      "expectedGap": 4.874,
      "plainExpectedGap": 5.6114,
      "pGapAtLeast7": 0.213196,
      "displayGapAtLeast7": "21.3%",
      "plainPGapAtLeast7": 0.334739,
      "plainDisplayGapAtLeast7": "33.5%",
      "gapPmf": [
       0,
       0.050166,
       0.056466,
       0.168507,
       0.18727,
       0.180845,
       0.143549,
       0.101198,
       0.059522,
       0.030495,
       0.013797,
       0.005481,
       0.001911,
       0.000586,
       0.000159,
       0.000038,
       0.000008,
       0.000001
      ]
     }
    ],
    "note": "Exact. The chore wheel page suggests, for the assign-to-people version and a weekly job such as the bathroom, giving whoever had the job last time *1 and everyone else *2 (the weights are edited by hand). Here it is applied as if you re-weight before every one of 30 daily spins: the chance of the same person twice running falls from 1/n to 1/(2n-1); a 30-day month still almost always has at least one; three in a row becomes much rarer; the spread of the month's counts shrinks noticeably but stays far from even (sdPerson, expectedGap, pGapAtLeast7, computed by an exact DP over count vectors with integer weights, BigInt). Compare with remove-the-winner rounds, where the gap is never more than 1. 'plain' values are the unweighted wheel for comparison."
   },
   "note": "Exact. With Weighted choices on and removal off, a line 'Older *2' among n-1 plain lines wins each spin with chance 2/(n+1), so over D days the older kid's count is Binomial(D, 2/(n+1)). pOlderFewerThanAYounger = P(the older kid ends the month with fewer chores than at least one younger sibling), by exact enumeration (BigInt). olderP5..olderP95 is the 5th to 95th percentile range and covers more than 90% of months (pOlderP5ToP95). pShareOff10Points = P(the older kid's share of the month is 10 or more percentage points away from the target share)."
  },
  "widgetGrid": {
   "note": "Exact anchors for the widget, one spin a day with removal off: gapCdf[g] = P(gap <= g), cut once P(gap > g) < 1e-6 (expectedGap uses the cut CDF, error < 1e-5). roundsGap and roundsPAnyBackToBack are for remove-the-winner rounds started on day 1.",
   "rows": [
    {
     "people": 2,
     "days": 7,
     "fairShare": 3.5,
     "sdPerson": 1.3229,
     "expectedGap": 2.1875,
     "gapCdf": [
      0,
      0.546875,
      0.546875,
      0.875,
      0.875,
      0.984375,
      0.984375,
      1
     ],
     "pThreeInARow": 0.671875,
     "roundsGap": 1,
     "roundsPAnyBackToBack": 0.875
    },
    {
     "people": 2,
     "days": 14,
     "fairShare": 7,
     "sdPerson": 1.8708,
     "expectedGap": 2.9326,
     "gapCdf": [
      0.209473,
      0.209473,
      0.57605,
      0.57605,
      0.820435,
      0.820435,
      0.942627,
      0.942627,
      0.987061,
      0.987061,
      0.998169,
      0.998169,
      0.999878,
      0.999878,
      1
     ],
     "pThreeInARow": 0.925537,
     "roundsGap": 0,
     "roundsPAnyBackToBack": 0.984375
    },
    {
     "people": 2,
     "days": 21,
     "fairShare": 10.5,
     "sdPerson": 2.2913,
     "expectedGap": 3.7001,
     "gapCdf": [
      0,
      0.336376,
      0.336376,
      0.61669,
      0.61669,
      0.810753,
      0.810753,
      0.921646,
      0.921646,
      0.973396,
      0.973396,
      0.992803,
      0.992803,
      0.99851,
      0.99851,
      0.999779,
      0.999779,
      0.999979,
      0.999979,
      0.999999
     ],
     "pThreeInARow": 0.983109,
     "roundsGap": 1,
     "roundsPAnyBackToBack": 0.999023
    },
    {
     "people": 2,
     "days": 30,
     "fairShare": 15,
     "sdPerson": 2.7386,
     "expectedGap": 4.3339,
     "gapCdf": [
      0.144464,
      0.144464,
      0.415335,
      0.415335,
      0.638405,
      0.638405,
      0.799512,
      0.799512,
      0.901263,
      0.901263,
      0.957226,
      0.957226,
      0.983875,
      0.983875,
      0.994777,
      0.994777,
      0.998569,
      0.998569,
      0.999675,
      0.999675,
      0.999941,
      0.999941,
      0.999992,
      0.999992,
      0.999999
     ],
     "pThreeInARow": 0.997492,
     "roundsGap": 0,
     "roundsPAnyBackToBack": 0.999939
    },
    {
     "people": 2,
     "days": 45,
     "fairShare": 22.5,
     "sdPerson": 3.3541,
     "expectedGap": 5.3822,
     "gapCdf": [
      0,
      0.234008,
      0.234008,
      0.448516,
      0.448516,
      0.628702,
      0.628702,
      0.767307,
      0.767307,
      0.864844,
      0.864844,
      0.927546,
      0.927546,
      0.964302,
      0.964302,
      0.983906,
      0.983906,
      0.993391,
      0.993391,
      0.997541,
      0.997541,
      0.999176,
      0.999176,
      0.999753,
      0.999753,
      0.999934,
      0.999934,
      0.999985,
      0.999985,
      0.999997,
      0.999997,
      0.999999
     ],
     "pThreeInARow": 0.999896,
     "roundsGap": 1,
     "roundsPAnyBackToBack": 1
    },
    {
     "people": 2,
     "days": 60,
     "fairShare": 30,
     "sdPerson": 3.873,
     "expectedGap": 6.1547,
     "gapCdf": [
      0.102578,
      0.102578,
      0.301117,
      0.301117,
      0.481042,
      0.481042,
      0.633706,
      0.633706,
      0.754939,
      0.754939,
      0.844998,
      0.844998,
      0.907539,
      0.907539,
      0.948106,
      0.948106,
      0.97266,
      0.97266,
      0.986511,
      0.986511,
      0.993782,
      0.993782,
      0.99733,
      0.99733,
      0.998934,
      0.998934,
      0.999606,
      0.999606,
      0.999865,
      0.999865,
      0.999958,
      0.999958,
      0.999988,
      0.999988,
      0.999997,
      0.999997,
      0.999999
     ],
     "pThreeInARow": 0.999996,
     "roundsGap": 0,
     "roundsPAnyBackToBack": 1
    },
    {
     "people": 3,
     "days": 7,
     "fairShare": 2.3333,
     "sdPerson": 1.2472,
     "expectedGap": 2.5638,
     "gapCdf": [
      0,
      0.288066,
      0.48011,
      0.768176,
      0.921811,
      0.979424,
      0.998628,
      1
     ],
     "pThreeInARow": 0.38546,
     "roundsGap": 1,
     "roundsPAnyBackToBack": 0.555556
    },
    {
     "people": 3,
     "days": 14,
     "fairShare": 4.6667,
     "sdPerson": 1.7638,
     "expectedGap": 3.6405,
     "gapCdf": [
      0,
      0.158219,
      0.290068,
      0.501026,
      0.704451,
      0.832533,
      0.919176,
      0.969046,
      0.989137,
      0.996671,
      0.999297,
      0.999868,
      0.999982,
      0.999999
     ],
     "pThreeInARow": 0.680747,
     "roundsGap": 1,
     "roundsPAnyBackToBack": 0.802469
    },
    {
     "people": 3,
     "days": 21,
     "fairShare": 7,
     "sdPerson": 2.1602,
     "expectedGap": 4.465,
     "gapCdf": [
      0.038151,
      0.038151,
      0.238444,
      0.391445,
      0.524974,
      0.701899,
      0.812701,
      0.888569,
      0.945218,
      0.973682,
      0.988311,
      0.995633,
      0.998447,
      0.999498,
      0.999868,
      0.999968,
      0.999993,
      0.999999,
      1
     ],
     "pThreeInARow": 0.834153,
     "roundsGap": 0,
     "roundsPAnyBackToBack": 0.912209
    },
    {
     "people": 3,
     "days": 30,
     "fairShare": 10,
     "sdPerson": 2.582,
     "expectedGap": 5.3414,
     "gapCdf": [
      0.026961,
      0.026961,
      0.17402,
      0.295455,
      0.405749,
      0.570805,
      0.689345,
      0.781018,
      0.86564,
      0.9182,
      0.952214,
      0.975231,
      0.98744,
      0.993949,
      0.997384,
      0.998907,
      0.99957,
      0.999849,
      0.999949,
      0.999984,
      0.999996,
      0.999999,
      1
     ],
     "pThreeInARow": 0.928548,
     "roundsGap": 0,
     "roundsPAnyBackToBack": 0.973988
    },
    {
     "people": 3,
     "days": 45,
     "fairShare": 15,
     "sdPerson": 3.1623,
     "expectedGap": 6.5463,
     "gapCdf": [
      0.018107,
      0.018107,
      0.119962,
      0.209459,
      0.293339,
      0.431391,
      0.541777,
      0.635039,
      0.736177,
      0.809706,
      0.865353,
      0.912578,
      0.943705,
      0.964675,
      0.979429,
      0.988202,
      0.993438,
      0.996585,
      0.99826,
      0.999144,
      0.999604,
      0.999822,
      0.999923,
      0.999969,
      0.999988,
      0.999995,
      0.999998,
      0.999999
     ],
     "pThreeInARow": 0.98244,
     "roundsGap": 0,
     "roundsPAnyBackToBack": 0.996575
    },
    {
     "people": 3,
     "days": 60,
     "fairShare": 20,
     "sdPerson": 3.6515,
     "expectedGap": 7.5616,
     "gapCdf": [
      0.013631,
      0.013631,
      0.091522,
      0.162163,
      0.229433,
      0.345588,
      0.443666,
      0.530155,
      0.631783,
      0.711676,
      0.776715,
      0.838446,
      0.883588,
      0.917403,
      0.944821,
      0.963439,
      0.976237,
      0.98535,
      0.99108,
      0.994688,
      0.996982,
      0.998313,
      0.99908,
      0.99952,
      0.999754,
      0.999877,
      0.999941,
      0.999973,
      0.999988,
      0.999995,
      0.999998,
      0.999999
     ],
     "pThreeInARow": 0.995684,
     "roundsGap": 0,
     "roundsPAnyBackToBack": 0.999549
    },
    {
     "people": 4,
     "days": 7,
     "fairShare": 1.75,
     "sdPerson": 1.1456,
     "expectedGap": 2.6729,
     "gapCdf": [
      0,
      0.153809,
      0.461426,
      0.769043,
      0.948486,
      0.994629,
      0.999756,
      1
     ],
     "pThreeInARow": 0.241943,
     "roundsGap": 1,
     "roundsPAnyBackToBack": 0.25
    },
    {
     "people": 4,
     "days": 14,
     "fairShare": 3.5,
     "sdPerson": 1.6202,
     "expectedGap": 3.8088,
     "gapCdf": [
      0,
      0.093971,
      0.191075,
      0.450435,
      0.683484,
      0.851021,
      0.943381,
      0.982926,
      0.995858,
      0.999169,
      0.999873,
      0.999987,
      0.999999
     ],
     "pThreeInARow": 0.479057,
     "roundsGap": 1,
     "roundsPAnyBackToBack": 0.578125
    },
    {
     "people": 4,
     "days": 21,
     "fairShare": 5.25,
     "sdPerson": 1.9843,
     "expectedGap": 4.6877,
     "gapCdf": [
      0,
      0.037348,
      0.130718,
      0.298192,
      0.49303,
      0.6776,
      0.820249,
      0.91295,
      0.962698,
      0.985936,
      0.995344,
      0.998648,
      0.999653,
      0.999923,
      0.999986,
      0.999998,
      1
     ],
     "pThreeInARow": 0.642004,
     "roundsGap": 1,
     "roundsPAnyBackToBack": 0.762695
    },
    {
     "people": 4,
     "days": 30,
     "fairShare": 7.5,
     "sdPerson": 2.3717,
     "expectedGap": 5.6114,
     "gapCdf": [
      0,
      0.033428,
      0.072737,
      0.196957,
      0.34862,
      0.51497,
      0.665261,
      0.79109,
      0.880529,
      0.937205,
      0.969702,
      0.986601,
      0.994554,
      0.997952,
      0.999291,
      0.999775,
      0.999935,
      0.999983,
      0.999996,
      0.999999
     ],
     "pThreeInARow": 0.778986,
     "roundsGap": 1,
     "roundsPAnyBackToBack": 0.866516
    },
    {
     "people": 4,
     "days": 45,
     "fairShare": 11.25,
     "sdPerson": 2.9047,
     "expectedGap": 6.8851,
     "gapCdf": [
      0,
      0.012687,
      0.047577,
      0.118997,
      0.220689,
      0.346984,
      0.481301,
      0.611575,
      0.724797,
      0.815934,
      0.883706,
      0.930654,
      0.960801,
      0.979012,
      0.989354,
      0.99488,
      0.997659,
      0.998983,
      0.999581,
      0.999836,
      0.999939,
      0.999979,
      0.999993,
      0.999998,
      0.999999
     ],
     "pThreeInARow": 0.901072,
     "roundsGap": 1,
     "roundsPAnyBackToBack": 0.957765
    },
    {
     "people": 4,
     "days": 60,
     "fairShare": 15,
     "sdPerson": 3.3541,
     "expectedGap": 7.9564,
     "gapCdf": [
      0.002141,
      0.002141,
      0.037514,
      0.079838,
      0.156128,
      0.250096,
      0.36608,
      0.480828,
      0.593882,
      0.695068,
      0.781393,
      0.849134,
      0.900244,
      0.936705,
      0.961481,
      0.977438,
      0.987295,
      0.993119,
      0.996415,
      0.9982,
      0.999129,
      0.999595,
      0.999818,
      0.999922,
      0.999967,
      0.999987,
      0.999995,
      0.999998,
      0.999999
     ],
     "pThreeInARow": 0.955719,
     "roundsGap": 0,
     "roundsPAnyBackToBack": 0.982182
    },
    {
     "people": 5,
     "days": 7,
     "fairShare": 1.4,
     "sdPerson": 1.0583,
     "expectedGap": 2.6544,
     "gapCdf": [
      0,
      0.16128,
      0.37632,
      0.83328,
      0.97664,
      0.998144,
      0.999936,
      1
     ],
     "pThreeInARow": 0.164416,
     "roundsGap": 1,
     "roundsPAnyBackToBack": 0.2
    },
    {
     "people": 5,
     "days": 14,
     "fairShare": 2.8,
     "sdPerson": 1.4967,
     "expectedGap": 3.8332,
     "gapCdf": [
      0,
      0.027553,
      0.182536,
      0.421555,
      0.696806,
      0.882649,
      0.965573,
      0.991852,
      0.998484,
      0.999789,
      0.99998,
      0.999999,
      1
     ],
     "pThreeInARow": 0.345605,
     "roundsGap": 1,
     "roundsPAnyBackToBack": 0.36
    },
    {
     "people": 5,
     "days": 21,
     "fairShare": 4.2,
     "sdPerson": 1.833,
     "expectedGap": 4.7187,
     "gapCdf": [
      0,
      0.013456,
      0.095269,
      0.252675,
      0.474656,
      0.690202,
      0.847891,
      0.937728,
      0.978257,
      0.993415,
      0.998272,
      0.99961,
      0.999925,
      0.999988,
      0.999998,
      1
     ],
     "pThreeInARow": 0.487505,
     "roundsGap": 1,
     "roundsPAnyBackToBack": 0.5904
    },
    {
     "people": 5,
     "days": 30,
     "fairShare": 6,
     "sdPerson": 2.1909,
     "expectedGap": 5.6575,
     "gapCdf": [
      0.001472,
      0.001472,
      0.059149,
      0.146244,
      0.308404,
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       "pSomeoneDoubleSomeone": 0.85555,
       "pThreeInARow": 0.478135,
       "longestRunMean": 2.6213,
       "longestWaitAnyoneMean": 9.3271,
       "pWaitBeyondRoundsMax": 0.91437,
       "pWaitAnyoneAtLeast10": 0.4174,
       "longestWaitOnePersonMean": 6.1192,
       "pSomeoneDoubleSomeoneAllHadOne": 0.784355,
       "longestGapBetweenTurnsMean": 6.2782,
       "pGapBetweenTurnsAtLeast7": 0.42107,
       "pGapBetweenTurnsAtLeast10": 0.0707,
       "pGapBetweenTurnsBeyondRoundsMax": 0.42107
      },
      {
       "days": 30,
       "gapPmf": [
        0,
        0.03379,
        0.038735,
        0.12342,
        0.153215,
        0.16657,
        0.1492,
        0.12661,
        0.09026,
        0.056775,
        0.032185,
        0.01642,
        0.00766,
        0.00326,
        0.00119,
        0.000485,
        0.00018,
        0.000035,
        0.00001
       ],
       "gapMean": 5.6061,
       "pGapAtLeastThreshold": 0.33507,
       "onePersonMean": 7.499,
       "pSomeoneNever": 0.000765,
       "pSomeoneDoubleSomeone": 0.624045,
       "pThreeInARow": 0.77823,
       "longestRunMean": 3.1613,
       "longestWaitAnyoneMean": 12.6358,
       "pWaitBeyondRoundsMax": 0.998915,
       "pWaitAnyoneAtLeast10": 0.840175,
       "longestWaitOnePersonMean": 8.6377,
       "pSomeoneDoubleSomeoneAllHadOne": 0.62328,
       "longestGapBetweenTurnsMean": 11.2623,
       "pGapBetweenTurnsAtLeast7": 0.97931,
       "pGapBetweenTurnsAtLeast10": 0.67834,
       "pGapBetweenTurnsBeyondRoundsMax": 0.97931
      }
     ]
    },
    {
     "people": 5,
     "byDays": [
      {
       "days": 7,
       "gapPmf": [
        0,
        0.161135,
        0.215395,
        0.45793,
        0.14254,
        0.021205,
        0.001745,
        0.00005
       ],
       "gapMean": 2.6527,
       "pGapAtLeastThreshold": 0.62347,
       "onePersonMean": 1.3984,
       "pSomeoneNever": 0.78545,
       "pSomeoneDoubleSomeone": 1,
       "pThreeInARow": 0.16416,
       "longestRunMean": 1.9322,
       "longestWaitAnyoneMean": 6.7302,
       "pWaitBeyondRoundsMax": 0,
       "pWaitAnyoneAtLeast10": 0,
       "longestWaitOnePersonMean": 4.4932,
       "pSomeoneDoubleSomeoneAllHadOne": 0.21455,
       "longestGapBetweenTurnsMean": 2.4374,
       "pGapBetweenTurnsAtLeast7": 0,
       "pGapBetweenTurnsAtLeast10": 0,
       "pGapBetweenTurnsBeyondRoundsMax": 0
      },
      {
       "days": 14,
       "gapPmf": [
        0,
        0.027255,
        0.15586,
        0.239175,
        0.275595,
        0.186175,
        0.08166,
        0.02602,
        0.006825,
        0.00127,
        0.000145,
        0.00002
       ],
       "gapMean": 3.8296,
       "pGapAtLeastThreshold": 0.57771,
       "onePersonMean": 2.7987,
       "pSomeoneNever": 0.210965,
       "pSomeoneDoubleSomeone": 0.972745,
       "pThreeInARow": 0.34617,
       "longestRunMean": 2.3781,
       "longestWaitAnyoneMean": 11.1046,
       "pWaitBeyondRoundsMax": 0.876635,
       "pWaitAnyoneAtLeast10": 0.73669,
       "longestWaitOnePersonMean": 7.0494,
       "pSomeoneDoubleSomeoneAllHadOne": 0.76178,
       "longestGapBetweenTurnsMean": 6.7916,
       "pGapBetweenTurnsAtLeast7": 0.52877,
       "pGapBetweenTurnsAtLeast10": 0.11096,
       "pGapBetweenTurnsBeyondRoundsMax": 0.21143
      },
      {
       "days": 30,
       "gapPmf": [
        0.00137,
        0,
        0.05789,
        0.086455,
        0.16249,
        0.189235,
        0.179505,
        0.139195,
        0.091725,
        0.050495,
        0.024135,
        0.011105,
        0.004275,
        0.00148,
        0.0005,
        0.000095,
        0.00004,
        0.00001
       ],
       "gapMean": 5.6542,
       "pGapAtLeastThreshold": 0.323055,
       "onePersonMean": 5.9977,
       "pSomeoneNever": 0.00622,
       "pSomeoneDoubleSomeone": 0.841605,
       "pThreeInARow": 0.62663,
       "longestRunMean": 2.8295,
       "longestWaitAnyoneMean": 15.8555,
       "pWaitBeyondRoundsMax": 0.99855,
       "pWaitAnyoneAtLeast10": 0.9887,
       "longestWaitOnePersonMean": 10.2653,
       "pSomeoneDoubleSomeoneAllHadOne": 0.835385,
       "longestGapBetweenTurnsMean": 13.3989,
       "pGapBetweenTurnsAtLeast7": 0.997245,
       "pGapBetweenTurnsAtLeast10": 0.88775,
       "pGapBetweenTurnsBeyondRoundsMax": 0.95352
      }
     ]
    }
   ],
   "note": "Simulated: each month is 30 daily spins of an n-name wheel with removal off; the 7- and 14-day values are the first 7 and 14 days of the same months, so the three rows are not independent of each other."
  },
  "rounds": {
   "months": 150000,
   "byPeople": [
    {
     "people": 2,
     "byDays": [
      {
       "days": 7,
       "largestGapSeen": 1,
       "averageGap": 1,
       "pAnyBackToBack": 0.875127,
       "backToBackPerMonth": 1.5001,
       "longestWaitMean": 1.8751,
       "longestRunSeen": 2,
       "pExtraTurnPerson1": 0.500173
      },
      {
       "days": 14,
       "largestGapSeen": 0,
       "averageGap": 0,
       "pAnyBackToBack": 0.98396,
       "backToBackPerMonth": 2.998,
       "longestWaitMean": 1.984,
       "longestRunSeen": 2,
       "pExtraTurnPerson1": 0
      },
      {
       "days": 30,
       "largestGapSeen": 0,
       "averageGap": 0,
       "pAnyBackToBack": 0.999953,
       "backToBackPerMonth": 6.9992,
       "longestWaitMean": 2,
       "longestRunSeen": 2,
       "pExtraTurnPerson1": 0
      }
     ],
     "sameNameEndsAndStarts": 0.500253,
     "daysOffFirstGapMean": 0.9979,
     "daysOffFirstGapZero": 0.25116
    },
    {
     "people": 3,
     "byDays": [
      {
       "days": 7,
       "largestGapSeen": 1,
       "averageGap": 1,
       "pAnyBackToBack": 0.556233,
       "backToBackPerMonth": 0.6673,
       "longestWaitMean": 3.277,
       "longestRunSeen": 2,
       "pExtraTurnPerson1": 0.33416
      },
      {
       "days": 14,
       "largestGapSeen": 1,
       "averageGap": 1,
       "pAnyBackToBack": 0.803267,
       "backToBackPerMonth": 1.3331,
       "longestWaitMean": 3.8019,
       "longestRunSeen": 2,
       "pExtraTurnPerson1": 0.66884
      },
      {
       "days": 30,
       "largestGapSeen": 0,
       "averageGap": 0,
       "pAnyBackToBack": 0.97448,
       "backToBackPerMonth": 3.0016,
       "longestWaitMean": 3.9734,
       "longestRunSeen": 2,
       "pExtraTurnPerson1": 0
      }
     ],
     "sameNameEndsAndStarts": 0.3342,
     "daysOffFirstGapMean": 2.003,
     "daysOffFirstGapZero": 0.111013
    },
    {
     "people": 4,
     "byDays": [
      {
       "days": 7,
       "largestGapSeen": 1,
       "averageGap": 1,
       "pAnyBackToBack": 0.2481,
       "backToBackPerMonth": 0.2481,
       "longestWaitMean": 4.8755,
       "longestRunSeen": 2,
       "pExtraTurnPerson1": 0.750547
      },
      {
       "days": 14,
       "largestGapSeen": 1,
       "averageGap": 1,
       "pAnyBackToBack": 0.57748,
       "backToBackPerMonth": 0.7485,
       "longestWaitMean": 5.3811,
       "longestRunSeen": 2,
       "pExtraTurnPerson1": 0.502547
      },
      {
       "days": 30,
       "largestGapSeen": 1,
       "averageGap": 1,
       "pAnyBackToBack": 0.8668,
       "backToBackPerMonth": 1.7481,
       "longestWaitMean": 5.8213,
       "longestRunSeen": 2,
       "pExtraTurnPerson1": 0.500127
      }
     ],
     "sameNameEndsAndStarts": 0.2481,
     "daysOffFirstGapMean": 3.0009,
     "daysOffFirstGapZero": 0.061953
    },
    {
     "people": 5,
     "byDays": [
      {
       "days": 7,
       "largestGapSeen": 1,
       "averageGap": 1,
       "pAnyBackToBack": 0.197633,
       "backToBackPerMonth": 0.1976,
       "longestWaitMean": 5.553,
       "longestRunSeen": 2,
       "pExtraTurnPerson1": 0.399593
      },
      {
       "days": 14,
       "largestGapSeen": 1,
       "averageGap": 1,
       "pAnyBackToBack": 0.357333,
       "backToBackPerMonth": 0.3971,
       "longestWaitMean": 7.1444,
       "longestRunSeen": 2,
       "pExtraTurnPerson1": 0.800127
      },
      {
       "days": 30,
       "largestGapSeen": 0,
       "averageGap": 0,
       "pAnyBackToBack": 0.67096,
       "backToBackPerMonth": 0.9984,
       "longestWaitMean": 7.6554,
       "longestRunSeen": 2,
       "pExtraTurnPerson1": 0
      }
     ],
     "sameNameEndsAndStarts": 0.197633,
     "daysOffFirstGapMean": 3.9988,
     "daysOffFirstGapZero": 0.039747
    }
   ],
   "note": "Simulated. largestGapSeen and longestRunSeen are the largest values seen in any simulated month. sameNameEndsAndStarts = share of months in which the person who ended round 1 also started round 2. daysOffFirstGapMean = average days between person 1's first and second turns."
  },
  "longRun": {
   "people": 4,
   "days": 365,
   "years": 20000,
   "averageGap": 19.5258,
   "pGapAtLeast20": 0.4651,
   "note": "Simulated years of 365 daily spins of a 4-name wheel."
  },
  "threeChores": {
   "spin": {
    "months": 150000,
    "pSomeoneTwoOrMore": 0.777898,
    "pOneKidAll": 0.111175,
    "monthGapPmf": [
     0.00924,
     0,
     0.052613,
     0.049427,
     0.047733,
     0.085887,
     0.078053,
     0.07178,
     0.090893,
     0.077907,
     0.067787,
     0.07136,
     0.057133,
     0.047733,
     0.045287,
     0.034927,
     0.027947,
     0.023187,
     0.016793,
     0.012567,
     0.009793,
     0.006853,
     0.004967,
     0.003287,
     0.002473,
     0.001467,
     0.00128,
     0.00068,
     0.000373,
     0.000227,
     0.000127,
     0.000093,
     0.000053,
     0.00004,
     0.00002,
     0.000013
    ],
    "monthAverageGap": 9.2824,
    "monthPGapAtLeastThreshold": 0.677047,
    "dishesAverageGap": 5.3395
   },
   "roundsDaily": {
    "months": 100000,
    "largestTotalGapSeen": 0,
    "dishesPGapAtLeastThreshold": 0.30908,
    "dishesAverageGap": 5.3278,
    "laundryAverageGap": 5.3392
   },
   "teamGenerator": {
    "months": 50000,
    "presses": 1500000,
    "pKid1Dishes": 0.334247,
    "dishesAverageGap": 5.3598,
    "largestTotalGapSeen": 0
   }
  },
  "fiveChores": {
   "spin": {
    "months": 40000,
    "averageGap": 11.9641,
    "pGapAtLeast7": 0.79195,
    "pGapAtLeast10": 0.608225
   },
   "teamFixed": {
    "months": 20000,
    "presses": 600000,
    "shareOfMonthsWithTotals": 1,
    "pDishesByKid": [
     0.399502,
     0.40113,
     0.199368
    ]
   },
   "teamRotated": {
    "largestGapSeen": 0,
    "note": "the same simulated presses as teamFixed, with the team names rotated one place each day"
   },
   "roundsDaily": {
    "months": 40000,
    "averageGap": 5.3343,
    "pGapAtLeast4": 0.70365,
    "pGapAtLeast7": 0.308725
   },
   "roundsCarried": {
    "months": 40000,
    "largestGapSeen": 0,
    "tripleDaysPerMonth": 3.342
   }
  },
  "weighted": {
   "months": 200000,
   "families": [
    {
     "kids": 2,
     "olderAverage": 19.9999,
     "olderAverageShare": 0.6667,
     "pOlderFewerThanAYounger": 0.019005
    },
    {
     "kids": 3,
     "olderAverage": 14.9937,
     "olderAverageShare": 0.4998,
     "pOlderFewerThanAYounger": 0.071525
    }
   ],
   "roundOrder": {
    "rounds": 200000,
    "pPosition": [
     0.49744,
     0.336035,
     0.166525
    ]
   },
   "lastTimeLighter": {
    "months": 200000,
    "byPeople": [
     {
      "people": 3,
      "pSameOnDays1And2": 0.200425,
      "pAnyBackToBack": 0.99843,
      "pThreeInARow": 0.62323,
      "averageGap": 4.3746,
      "sdPersonSimulated": 2.1138
     },
     {
      "people": 4,
      "pSameOnDays1And2": 0.14422,
      "pAnyBackToBack": 0.98909,
      "pThreeInARow": 0.40195,
      "averageGap": 4.8681,
      "sdPersonSimulated": 2.1107
     }
    ]
   }
  }
 },
 "checks": [
  {
   "name": "daily spins, 2 people, 7 days: P(someone never gets the chore)",
   "kind": "simulated vs exact",
   "simulated": 0.01558,
   "exact": 0.015625,
   "se": 0.000277,
   "z": -0.16,
   "tolerance": 0.00111,
   "pass": true
  },
  {
   "name": "daily spins, 2 people, 7 days: P(someone has 3+ days off between two turns)",
   "kind": "simulated vs exact",
   "simulated": 0.266235,
   "exact": 0.265625,
   "se": 0.000988,
   "z": 0.62,
   "tolerance": 0.00395,
   "pass": true
  },
  {
   "name": "daily spins, 2 people, 7 days: P(the same name 3+ days in a row)",
   "kind": "simulated vs exact",
   "simulated": 0.672025,
   "exact": 0.671875,
   "se": 0.00105,
   "z": 0.14,
   "tolerance": 0.0042,
   "pass": true
  },
  {
   "name": "daily spins, 2 people, 14 days: P(gap >= 4)",
   "kind": "simulated vs exact",
   "simulated": 0.42318,
   "exact": 0.42395,
   "se": 0.00111,
   "z": -0.7,
   "tolerance": 0.00442,
   "pass": true
  },
  {
   "name": "daily spins, 2 people, 30 days: P(gap >= 7)",
   "kind": "simulated vs exact",
   "simulated": 0.19958,
   "exact": 0.200488,
   "se": 0.000895,
   "z": -1.01,
   "tolerance": 0.00358,
   "pass": true
  },
  {
   "name": "daily spins, 2 people, 30 days: average gap",
   "kind": "simulated vs exact",
   "simulated": 4.32972,
   "exact": 4.333933,
   "se": 0.00749,
   "z": -0.56,
   "tolerance": 0.03,
   "pass": true
  },
  {
   "name": "daily spins, 2 people, 30 days: P(someone has at least twice someone else's count)",
   "kind": "simulated vs exact",
   "simulated": 0.09807,
   "exact": 0.098737,
   "se": 0.000667,
   "z": -1,
   "tolerance": 0.00267,
   "pass": true
  },
  {
   "name": "daily spins, 2 people, 30 days: P(the same name 3+ days in a row)",
   "kind": "simulated vs exact",
   "simulated": 0.997675,
   "exact": 0.997492,
   "se": 0.000112,
   "z": 1.63,
   "tolerance": 0.000447,
   "pass": true
  },
  {
   "name": "daily spins, 2 people, 30 days: one person's longest wait, average",
   "kind": "simulated vs exact",
   "simulated": 4.29304,
   "exact": 4.289496,
   "se": 0.00372,
   "z": 0.95,
   "tolerance": 0.0149,
   "pass": true
  },
  {
   "name": "daily spins, 2 people, 30 days: P(busiest >= 2 x luckiest, everyone had at least one)",
   "kind": "simulated vs exact",
   "simulated": 0.09807,
   "exact": 0.098737,
   "se": 0.000667,
   "z": -1,
   "tolerance": 0.00267,
   "pass": true
  },
  {
   "name": "daily spins, 2 people, 30 days: P(someone has 10+ days off between two turns)",
   "kind": "simulated vs exact",
   "simulated": 0.0176,
   "exact": 0.017543,
   "se": 0.000294,
   "z": 0.19,
   "tolerance": 0.00117,
   "pass": true
  },
  {
   "name": "daily spins, 2 people, 30 days: longest days off between two turns (anyone), average",
   "kind": "simulated vs exact",
   "simulated": 5.030755,
   "exact": 5.031683,
   "se": 0.00366,
   "z": -0.25,
   "tolerance": 0.0146,
   "pass": true
  },
  {
   "name": "daily spins, 3 people, 7 days: P(someone never gets the chore)",
   "kind": "simulated vs exact",
   "simulated": 0.173715,
   "exact": 0.174211,
   "se": 0.000848,
   "z": -0.59,
   "tolerance": 0.00339,
   "pass": true
  },
  {
   "name": "daily spins, 3 people, 7 days: P(someone has 3+ days off between two turns)",
   "kind": "simulated vs exact",
   "simulated": 0.427585,
   "exact": 0.427984,
   "se": 0.00111,
   "z": -0.36,
   "tolerance": 0.00443,
   "pass": true
  },
  {
   "name": "daily spins, 3 people, 7 days: P(the same name 3+ days in a row)",
   "kind": "simulated vs exact",
   "simulated": 0.383085,
   "exact": 0.38546,
   "se": 0.00109,
   "z": -2.18,
   "tolerance": 0.00435,
   "pass": true
  },
  {
   "name": "daily spins, 3 people, 14 days: P(gap >= 4)",
   "kind": "simulated vs exact",
   "simulated": 0.49894,
   "exact": 0.498974,
   "se": 0.00112,
   "z": -0.03,
   "tolerance": 0.00447,
   "pass": true
  },
  {
   "name": "daily spins, 3 people, 30 days: P(gap >= 7)",
   "kind": "simulated vs exact",
   "simulated": 0.31083,
   "exact": 0.310655,
   "se": 0.00103,
   "z": 0.17,
   "tolerance": 0.00414,
   "pass": true
  },
  {
   "name": "daily spins, 3 people, 30 days: average gap",
   "kind": "simulated vs exact",
   "simulated": 5.346895,
   "exact": 5.341374,
   "se": 0.00626,
   "z": 0.88,
   "tolerance": 0.025,
   "pass": true
  },
  {
   "name": "daily spins, 3 people, 30 days: P(someone has at least twice someone else's count)",
   "kind": "simulated vs exact",
   "simulated": 0.334095,
   "exact": 0.334051,
   "se": 0.00105,
   "z": 0.04,
   "tolerance": 0.00422,
   "pass": true
  },
  {
   "name": "daily spins, 3 people, 30 days: P(the same name 3+ days in a row)",
   "kind": "simulated vs exact",
   "simulated": 0.929445,
   "exact": 0.928548,
   "se": 0.000576,
   "z": 1.56,
   "tolerance": 0.0023,
   "pass": true
  },
  {
   "name": "daily spins, 3 people, 30 days: P(someone waits 5+ days, longer than a round ever allows)",
   "kind": "simulated vs exact",
   "simulated": 0.99874,
   "exact": 0.998778,
   "se": 0.0000781,
   "z": -0.49,
   "tolerance": 0.000312,
   "pass": true
  },
  {
   "name": "daily spins, 3 people, 30 days: P(someone waits 10+ days)",
   "kind": "simulated vs exact",
   "simulated": 0.358845,
   "exact": 0.35974,
   "se": 0.00107,
   "z": -0.83,
   "tolerance": 0.00429,
   "pass": true
  },
  {
   "name": "daily spins, 3 people, 30 days: one person's longest wait, average",
   "kind": "simulated vs exact",
   "simulated": 6.683575,
   "exact": 6.686017,
   "se": 0.00587,
   "z": -0.42,
   "tolerance": 0.0235,
   "pass": true
  },
  {
   "name": "daily spins, 3 people, 30 days: P(busiest >= 2 x luckiest, everyone had at least one)",
   "kind": "simulated vs exact",
   "simulated": 0.334085,
   "exact": 0.334035,
   "se": 0.00105,
   "z": 0.05,
   "tolerance": 0.00422,
   "pass": true
  },
  {
   "name": "daily spins, 3 people, 30 days: P(someone has 10+ days off between two turns)",
   "kind": "simulated vs exact",
   "simulated": 0.276565,
   "exact": 0.277205,
   "se": 0.001,
   "z": -0.64,
   "tolerance": 0.004,
   "pass": true
  },
  {
   "name": "daily spins, 3 people, 30 days: P(someone has 5+ days off between two turns)",
   "kind": "simulated vs exact",
   "simulated": 0.991405,
   "exact": 0.991189,
   "se": 0.000209,
   "z": 1.03,
   "tolerance": 0.000836,
   "pass": true
  },
  {
   "name": "daily spins, 3 people, 30 days: longest days off between two turns (anyone), average",
   "kind": "simulated vs exact",
   "simulated": 8.4674,
   "exact": 8.467974,
   "se": 0.00567,
   "z": -0.1,
   "tolerance": 0.0227,
   "pass": true
  },
  {
   "name": "daily spins, 4 people, 7 days: P(someone never gets the chore)",
   "kind": "simulated vs exact",
   "simulated": 0.486555,
   "exact": 0.487305,
   "se": 0.00112,
   "z": -0.67,
   "tolerance": 0.00447,
   "pass": true
  },
  {
   "name": "daily spins, 4 people, 7 days: P(someone has 3+ days off between two turns)",
   "kind": "simulated vs exact",
   "simulated": 0.470265,
   "exact": 0.469482,
   "se": 0.00112,
   "z": 0.7,
   "tolerance": 0.00446,
   "pass": true
  },
  {
   "name": "daily spins, 4 people, 7 days: P(the same name 3+ days in a row)",
   "kind": "simulated vs exact",
   "simulated": 0.241895,
   "exact": 0.241943,
   "se": 0.000958,
   "z": -0.05,
   "tolerance": 0.00383,
   "pass": true
  },
  {
   "name": "daily spins, 4 people, 14 days: P(gap >= 4)",
   "kind": "simulated vs exact",
   "simulated": 0.54968,
   "exact": 0.549565,
   "se": 0.00111,
   "z": 0.1,
   "tolerance": 0.00445,
   "pass": true
  },
  {
   "name": "daily spins, 4 people, 30 days: P(gap >= 7)",
   "kind": "simulated vs exact",
   "simulated": 0.33507,
   "exact": 0.334739,
   "se": 0.00106,
   "z": 0.31,
   "tolerance": 0.00422,
   "pass": true
  },
  {
   "name": "daily spins, 4 people, 30 days: average gap",
   "kind": "simulated vs exact",
   "simulated": 5.606115,
   "exact": 5.611418,
   "se": 0.00536,
   "z": -0.99,
   "tolerance": 0.0214,
   "pass": true
  },
  {
   "name": "daily spins, 4 people, 30 days: P(someone has at least twice someone else's count)",
   "kind": "simulated vs exact",
   "simulated": 0.624045,
   "exact": 0.624908,
   "se": 0.00108,
   "z": -0.8,
   "tolerance": 0.00433,
   "pass": true
  },
  {
   "name": "daily spins, 4 people, 30 days: P(the same name 3+ days in a row)",
   "kind": "simulated vs exact",
   "simulated": 0.77823,
   "exact": 0.778986,
   "se": 0.000928,
   "z": -0.82,
   "tolerance": 0.00371,
   "pass": true
  },
  {
   "name": "daily spins, 4 people, 30 days: P(someone waits 7+ days, longer than a round ever allows)",
   "kind": "simulated vs exact",
   "simulated": 0.998915,
   "exact": 0.998799,
   "se": 0.0000774,
   "z": 1.5,
   "tolerance": 0.00031,
   "pass": true
  },
  {
   "name": "daily spins, 4 people, 30 days: P(someone waits 10+ days)",
   "kind": "simulated vs exact",
   "simulated": 0.840175,
   "exact": 0.839401,
   "se": 0.000821,
   "z": 0.94,
   "tolerance": 0.00328,
   "pass": true
  },
  {
   "name": "daily spins, 4 people, 30 days: one person's longest wait, average",
   "kind": "simulated vs exact",
   "simulated": 8.637725,
   "exact": 8.627074,
   "se": 0.00768,
   "z": 1.39,
   "tolerance": 0.0307,
   "pass": true
  },
  {
   "name": "daily spins, 4 people, 30 days: P(busiest >= 2 x luckiest, everyone had at least one)",
   "kind": "simulated vs exact",
   "simulated": 0.62328,
   "exact": 0.624193,
   "se": 0.00108,
   "z": -0.84,
   "tolerance": 0.00433,
   "pass": true
  },
  {
   "name": "daily spins, 4 people, 30 days: P(someone has 10+ days off between two turns)",
   "kind": "simulated vs exact",
   "simulated": 0.67834,
   "exact": 0.676832,
   "se": 0.00105,
   "z": 1.44,
   "tolerance": 0.00418,
   "pass": true
  },
  {
   "name": "daily spins, 4 people, 30 days: P(someone has 7+ days off between two turns)",
   "kind": "simulated vs exact",
   "simulated": 0.97931,
   "exact": 0.979401,
   "se": 0.000318,
   "z": -0.29,
   "tolerance": 0.00127,
   "pass": true
  },
  {
   "name": "daily spins, 4 people, 30 days: longest days off between two turns (anyone), average",
   "kind": "simulated vs exact",
   "simulated": 11.262275,
   "exact": 11.257035,
   "se": 0.00709,
   "z": 0.74,
   "tolerance": 0.0283,
   "pass": true
  },
  {
   "name": "daily spins, 5 people, 7 days: P(someone never gets the chore)",
   "kind": "simulated vs exact",
   "simulated": 0.78545,
   "exact": 0.78496,
   "se": 0.000919,
   "z": 0.53,
   "tolerance": 0.00367,
   "pass": true
  },
  {
   "name": "daily spins, 5 people, 7 days: P(someone has 3+ days off between two turns)",
   "kind": "simulated vs exact",
   "simulated": 0.471675,
   "exact": 0.470528,
   "se": 0.00112,
   "z": 1.03,
   "tolerance": 0.00446,
   "pass": true
  },
  {
   "name": "daily spins, 5 people, 7 days: P(the same name 3+ days in a row)",
   "kind": "simulated vs exact",
   "simulated": 0.16416,
   "exact": 0.164416,
   "se": 0.000829,
   "z": -0.31,
   "tolerance": 0.00332,
   "pass": true
  },
  {
   "name": "daily spins, 5 people, 14 days: P(gap >= 4)",
   "kind": "simulated vs exact",
   "simulated": 0.57771,
   "exact": 0.578445,
   "se": 0.0011,
   "z": -0.67,
   "tolerance": 0.00442,
   "pass": true
  },
  {
   "name": "daily spins, 5 people, 30 days: P(gap >= 7)",
   "kind": "simulated vs exact",
   "simulated": 0.323055,
   "exact": 0.32412,
   "se": 0.00105,
   "z": -1.02,
   "tolerance": 0.00419,
   "pass": true
  },
  {
   "name": "daily spins, 5 people, 30 days: average gap",
   "kind": "simulated vs exact",
   "simulated": 5.65421,
   "exact": 5.657484,
   "se": 0.00468,
   "z": -0.7,
   "tolerance": 0.0187,
   "pass": true
  },
  {
   "name": "daily spins, 5 people, 30 days: P(someone has at least twice someone else's count)",
   "kind": "simulated vs exact",
   "simulated": 0.841605,
   "exact": 0.841139,
   "se": 0.000817,
   "z": 0.57,
   "tolerance": 0.00327,
   "pass": true
  },
  {
   "name": "daily spins, 5 people, 30 days: P(the same name 3+ days in a row)",
   "kind": "simulated vs exact",
   "simulated": 0.62663,
   "exact": 0.625708,
   "se": 0.00108,
   "z": 0.85,
   "tolerance": 0.00433,
   "pass": true
  },
  {
   "name": "daily spins, 5 people, 30 days: P(someone waits 9+ days, longer than a round ever allows)",
   "kind": "simulated vs exact",
   "simulated": 0.99855,
   "exact": 0.998529,
   "se": 0.0000857,
   "z": 0.24,
   "tolerance": 0.000343,
   "pass": true
  },
  {
   "name": "daily spins, 5 people, 30 days: P(someone waits 10+ days)",
   "kind": "simulated vs exact",
   "simulated": 0.9887,
   "exact": 0.988793,
   "se": 0.000235,
   "z": -0.39,
   "tolerance": 0.000942,
   "pass": true
  },
  {
   "name": "daily spins, 5 people, 30 days: one person's longest wait, average",
   "kind": "simulated vs exact",
   "simulated": 10.26527,
   "exact": 10.266601,
   "se": 0.0092,
   "z": -0.14,
   "tolerance": 0.0368,
   "pass": true
  },
  {
   "name": "daily spins, 5 people, 30 days: P(busiest >= 2 x luckiest, everyone had at least one)",
   "kind": "simulated vs exact",
   "simulated": 0.835385,
   "exact": 0.834952,
   "se": 0.00083,
   "z": 0.52,
   "tolerance": 0.00332,
   "pass": true
  },
  {
   "name": "daily spins, 5 people, 30 days: P(someone has 10+ days off between two turns)",
   "kind": "simulated vs exact",
   "simulated": 0.88775,
   "exact": 0.888023,
   "se": 0.000705,
   "z": -0.39,
   "tolerance": 0.00282,
   "pass": true
  },
  {
   "name": "daily spins, 5 people, 30 days: P(someone has 9+ days off between two turns)",
   "kind": "simulated vs exact",
   "simulated": 0.95352,
   "exact": 0.95358,
   "se": 0.00047,
   "z": -0.13,
   "tolerance": 0.00188,
   "pass": true
  },
  {
   "name": "daily spins, 5 people, 30 days: longest days off between two turns (anyone), average",
   "kind": "simulated vs exact",
   "simulated": 13.39891,
   "exact": 13.403686,
   "se": 0.00793,
   "z": -0.6,
   "tolerance": 0.0317,
   "pass": true
  },
  {
   "name": "rounds, 2 people, 30 days: P(at least one back-to-back turn)",
   "kind": "simulated vs exact",
   "simulated": 0.999953,
   "exact": 0.999939,
   "se": 0.0000202,
   "z": 0.7,
   "tolerance": 0.0000807,
   "pass": true
  },
  {
   "name": "rounds, 2 people, 30 days: longest wait for anyone, average",
   "kind": "simulated vs exact",
   "simulated": 1.999953,
   "exact": 1.999939,
   "se": 0.0000202,
   "z": 0.71,
   "tolerance": 0.0000807,
   "pass": true
  },
  {
   "name": "rounds, 2 people, 30 days: largest gap in any simulated month (exact: 0)",
   "kind": "deterministic",
   "simulated": 0,
   "exact": 0,
   "se": 0,
   "z": 0,
   "tolerance": 0,
   "pass": true
  },
  {
   "name": "rounds, 2 people, 30 days: longest run of one name in any simulated month (exact maximum: 2)",
   "kind": "deterministic",
   "simulated": 2,
   "exact": 2,
   "se": 0,
   "z": 0,
   "tolerance": 0,
   "pass": true
  },
  {
   "name": "rounds, 2 people: P(the name that ends round 1 starts round 2)",
   "kind": "simulated vs exact",
   "simulated": 0.500253,
   "exact": 0.5,
   "se": 0.00129,
   "z": 0.2,
   "tolerance": 0.00516,
   "pass": true
  },
  {
   "name": "rounds, 2 people: days off between person 1's first two turns, average",
   "kind": "simulated vs exact",
   "simulated": 0.997933,
   "exact": 1,
   "se": 0.00183,
   "z": -1.13,
   "tolerance": 0.0073,
   "pass": true
  },
  {
   "name": "rounds, 3 people, 30 days: P(at least one back-to-back turn)",
   "kind": "simulated vs exact",
   "simulated": 0.97448,
   "exact": 0.973988,
   "se": 0.000411,
   "z": 1.2,
   "tolerance": 0.00164,
   "pass": true
  },
  {
   "name": "rounds, 3 people, 30 days: longest wait for anyone, average",
   "kind": "simulated vs exact",
   "simulated": 3.9734,
   "exact": 3.973988,
   "se": 0.000411,
   "z": -1.43,
   "tolerance": 0.00164,
   "pass": true
  },
  {
   "name": "rounds, 3 people, 30 days: largest gap in any simulated month (exact: 0)",
   "kind": "deterministic",
   "simulated": 0,
   "exact": 0,
   "se": 0,
   "z": 0,
   "tolerance": 0,
   "pass": true
  },
  {
   "name": "rounds, 3 people, 30 days: longest run of one name in any simulated month (exact maximum: 2)",
   "kind": "deterministic",
   "simulated": 2,
   "exact": 2,
   "se": 0,
   "z": 0,
   "tolerance": 0,
   "pass": true
  },
  {
   "name": "rounds, 3 people: P(the name that ends round 1 starts round 2)",
   "kind": "simulated vs exact",
   "simulated": 0.3342,
   "exact": 0.333333,
   "se": 0.00122,
   "z": 0.71,
   "tolerance": 0.00487,
   "pass": true
  },
  {
   "name": "rounds, 3 people: days off between person 1's first two turns, average",
   "kind": "simulated vs exact",
   "simulated": 2.00298,
   "exact": 2,
   "se": 0.00298,
   "z": 1,
   "tolerance": 0.0119,
   "pass": true
  },
  {
   "name": "rounds, 4 people, 30 days: P(at least one back-to-back turn)",
   "kind": "simulated vs exact",
   "simulated": 0.8668,
   "exact": 0.866516,
   "se": 0.000878,
   "z": 0.32,
   "tolerance": 0.00351,
   "pass": true
  },
  {
   "name": "rounds, 4 people, 30 days: longest wait for anyone, average",
   "kind": "simulated vs exact",
   "simulated": 5.821267,
   "exact": 5.821336,
   "se": 0.000994,
   "z": -0.07,
   "tolerance": 0.00397,
   "pass": true
  },
  {
   "name": "rounds, 4 people, 30 days: largest gap in any simulated month (exact: 1)",
   "kind": "deterministic",
   "simulated": 1,
   "exact": 1,
   "se": 0,
   "z": 0,
   "tolerance": 0,
   "pass": true
  },
  {
   "name": "rounds, 4 people, 30 days: longest run of one name in any simulated month (exact maximum: 2)",
   "kind": "deterministic",
   "simulated": 2,
   "exact": 2,
   "se": 0,
   "z": 0,
   "tolerance": 0,
   "pass": true
  },
  {
   "name": "rounds, 4 people, 30 days: P(person 1 gets the extra turn of the unfinished round)",
   "kind": "simulated vs exact",
   "simulated": 0.500127,
   "exact": 0.5,
   "se": 0.00129,
   "z": 0.1,
   "tolerance": 0.00516,
   "pass": true
  },
  {
   "name": "rounds, 4 people: P(the name that ends round 1 starts round 2)",
   "kind": "simulated vs exact",
   "simulated": 0.2481,
   "exact": 0.25,
   "se": 0.00112,
   "z": -1.7,
   "tolerance": 0.00447,
   "pass": true
  },
  {
   "name": "rounds, 4 people: days off between person 1's first two turns, average",
   "kind": "simulated vs exact",
   "simulated": 3.000913,
   "exact": 3,
   "se": 0.00408,
   "z": 0.22,
   "tolerance": 0.0163,
   "pass": true
  },
  {
   "name": "rounds, 5 people, 30 days: P(at least one back-to-back turn)",
   "kind": "simulated vs exact",
   "simulated": 0.67096,
   "exact": 0.67232,
   "se": 0.00121,
   "z": -1.12,
   "tolerance": 0.00485,
   "pass": true
  },
  {
   "name": "rounds, 5 people, 30 days: longest wait for anyone, average",
   "kind": "simulated vs exact",
   "simulated": 7.65542,
   "exact": 7.653825,
   "se": 0.00133,
   "z": 1.2,
   "tolerance": 0.0053,
   "pass": true
  },
  {
   "name": "rounds, 5 people, 30 days: largest gap in any simulated month (exact: 0)",
   "kind": "deterministic",
   "simulated": 0,
   "exact": 0,
   "se": 0,
   "z": 0,
   "tolerance": 0,
   "pass": true
  },
  {
   "name": "rounds, 5 people, 30 days: longest run of one name in any simulated month (exact maximum: 2)",
   "kind": "deterministic",
   "simulated": 2,
   "exact": 2,
   "se": 0,
   "z": 0,
   "tolerance": 0,
   "pass": true
  },
  {
   "name": "rounds, 5 people: P(the name that ends round 1 starts round 2)",
   "kind": "simulated vs exact",
   "simulated": 0.197633,
   "exact": 0.2,
   "se": 0.00103,
   "z": -2.29,
   "tolerance": 0.00413,
   "pass": true
  },
  {
   "name": "rounds, 5 people: days off between person 1's first two turns, average",
   "kind": "simulated vs exact",
   "simulated": 3.998833,
   "exact": 4,
   "se": 0.00516,
   "z": -0.23,
   "tolerance": 0.0207,
   "pass": true
  },
  {
   "name": "a year of daily spins, 4 people: average gap",
   "kind": "simulated vs exact",
   "simulated": 19.52585,
   "exact": 19.659087,
   "se": 0.0594,
   "z": -2.24,
   "tolerance": 0.238,
   "pass": true
  },
  {
   "name": "a year of daily spins, 4 people: P(gap >= 20)",
   "kind": "simulated vs exact",
   "simulated": 0.4651,
   "exact": 0.472118,
   "se": 0.00353,
   "z": -1.99,
   "tolerance": 0.0141,
   "pass": true
  },
  {
   "name": "3 chores a day, spun with repeats: P(a kid gets 2+ chores on a day) (pooled over 30 independent days)",
   "kind": "simulated vs exact",
   "simulated": 0.777898,
   "exact": 0.777778,
   "se": 0.000196,
   "z": 0.61,
   "tolerance": 0.000784,
   "pass": true
  },
  {
   "name": "3 chores a day, spun with repeats: P(one kid gets all 3)",
   "kind": "simulated vs exact",
   "simulated": 0.111175,
   "exact": 0.111111,
   "se": 0.000148,
   "z": 0.43,
   "tolerance": 0.000593,
   "pass": true
  },
  {
   "name": "3 chores a day, spun with repeats: month totals, P(gap >= 7)",
   "kind": "simulated vs exact",
   "simulated": 0.677047,
   "exact": 0.675722,
   "se": 0.00121,
   "z": 1.1,
   "tolerance": 0.00483,
   "pass": true
  },
  {
   "name": "3 chores a day, spun with repeats: month totals, average gap",
   "kind": "simulated vs exact",
   "simulated": 9.282407,
   "exact": 9.264172,
   "se": 0.0125,
   "z": 1.45,
   "tolerance": 0.0502,
   "pass": true
  },
  {
   "name": "3 chores a day, rounds reset daily: largest month-total gap seen (exact: 0)",
   "kind": "deterministic",
   "simulated": 0,
   "exact": 0,
   "se": 0,
   "z": 0,
   "tolerance": 0,
   "pass": true
  },
  {
   "name": "3 chores a day, rounds reset daily: dishes (spun first), P(gap >= 7)",
   "kind": "simulated vs exact",
   "simulated": 0.30908,
   "exact": 0.310655,
   "se": 0.00146,
   "z": -1.08,
   "tolerance": 0.00585,
   "pass": true
  },
  {
   "name": "3 chores a day, rounds reset daily: laundry (left over, no spin), average gap",
   "kind": "simulated vs exact",
   "simulated": 5.33919,
   "exact": 5.341374,
   "se": 0.00885,
   "z": -0.25,
   "tolerance": 0.0354,
   "pass": true
  },
  {
   "name": "3 chores a day, team generator: P(kid 1 gets the dishes on a day) (pooled over days)",
   "kind": "simulated vs exact",
   "simulated": 0.334247,
   "exact": 0.333333,
   "se": 0.000385,
   "z": 2.37,
   "tolerance": 0.00154,
   "pass": true
  },
  {
   "name": "3 chores a day, team generator: dishes, average gap",
   "kind": "simulated vs exact",
   "simulated": 5.35982,
   "exact": 5.341374,
   "se": 0.0125,
   "z": 1.47,
   "tolerance": 0.0501,
   "pass": true
  },
  {
   "name": "3 chores a day, team generator: largest month-total gap seen (exact: 0)",
   "kind": "deterministic",
   "simulated": 0,
   "exact": 0,
   "se": 0,
   "z": 0,
   "tolerance": 0,
   "pass": true
  },
  {
   "name": "5 chores, 3 kids, spun with repeats: month totals, average gap",
   "kind": "simulated vs exact",
   "simulated": 11.96405,
   "exact": 11.963295,
   "se": 0.0314,
   "z": 0.02,
   "tolerance": 0.126,
   "pass": true
  },
  {
   "name": "5 chores, 3 kids, spun with repeats: month totals, P(gap >= 10)",
   "kind": "simulated vs exact",
   "simulated": 0.608225,
   "exact": 0.607118,
   "se": 0.00244,
   "z": 0.45,
   "tolerance": 0.00977,
   "pass": true
  },
  {
   "name": "5 chores, team generator, fixed team-name order: share of months with totals 60/60/30",
   "kind": "deterministic",
   "simulated": 1,
   "exact": 1,
   "se": 0,
   "z": 0,
   "tolerance": 0,
   "pass": true
  },
  {
   "name": "5 chores, team generator, team names rotated daily: largest month-total gap seen",
   "kind": "deterministic",
   "simulated": 0,
   "exact": 0,
   "se": 0,
   "z": 0,
   "tolerance": 0,
   "pass": true
  },
  {
   "name": "5 chores, team generator, fixed order: P(first-named kid gets the dishes on a day)",
   "kind": "simulated vs exact",
   "simulated": 0.399502,
   "exact": 0.4,
   "se": 0.000632,
   "z": -0.79,
   "tolerance": 0.00253,
   "pass": true
  },
  {
   "name": "5 chores, team generator, fixed order: P(third-named kid gets the dishes on a day)",
   "kind": "simulated vs exact",
   "simulated": 0.199368,
   "exact": 0.2,
   "se": 0.000516,
   "z": -1.22,
   "tolerance": 0.00207,
   "pass": true
  },
  {
   "name": "5 chores, rounds reset every morning: month totals, average gap",
   "kind": "simulated vs exact",
   "simulated": 5.33435,
   "exact": 5.341374,
   "se": 0.014,
   "z": -0.5,
   "tolerance": 0.056,
   "pass": true
  },
  {
   "name": "5 chores, rounds reset every morning: month totals, P(gap >= 4)",
   "kind": "simulated vs exact",
   "simulated": 0.70365,
   "exact": 0.704545,
   "se": 0.00228,
   "z": -0.39,
   "tolerance": 0.00912,
   "pass": true
  },
  {
   "name": "5 chores, rounds carried over: largest month-total gap seen",
   "kind": "deterministic",
   "simulated": 0,
   "exact": 0,
   "se": 0,
   "z": 0,
   "tolerance": 0,
   "pass": true
  },
  {
   "name": "5 chores, rounds carried over: days a kid gets 3 of the 5 chores, per month",
   "kind": "simulated vs exact",
   "simulated": 3.342,
   "exact": 3.333333,
   "se": 0.00745,
   "z": 1.16,
   "tolerance": 0.0298,
   "pass": true
  },
  {
   "name": "weighted, 2 kids, older *2: older kid's chores in 30 days, average",
   "kind": "simulated vs exact",
   "simulated": 19.99994,
   "exact": 20,
   "se": 0.00577,
   "z": -0.01,
   "tolerance": 0.0231,
   "pass": true
  },
  {
   "name": "weighted, 2 kids, older *2: P(older kid does fewer than a younger one)",
   "kind": "simulated vs exact",
   "simulated": 0.019005,
   "exact": 0.018795,
   "se": 0.000304,
   "z": 0.69,
   "tolerance": 0.00121,
   "pass": true
  },
  {
   "name": "weighted, 3 kids, older *2: older kid's chores in 30 days, average",
   "kind": "simulated vs exact",
   "simulated": 14.99374,
   "exact": 15,
   "se": 0.00612,
   "z": -1.02,
   "tolerance": 0.0245,
   "pass": true
  },
  {
   "name": "weighted, 3 kids, older *2: P(older kid does fewer than a younger one)",
   "kind": "simulated vs exact",
   "simulated": 0.071525,
   "exact": 0.07196,
   "se": 0.000578,
   "z": -0.75,
   "tolerance": 0.00231,
   "pass": true
  },
  {
   "name": "weighted *2 with removal on: P(the *2 kid goes first in the round)",
   "kind": "simulated vs exact",
   "simulated": 0.49744,
   "exact": 0.5,
   "se": 0.00112,
   "z": -2.29,
   "tolerance": 0.00447,
   "pass": true
  },
  {
   "name": "weighted *2 with removal on: P(the *2 kid goes last in the round)",
   "kind": "simulated vs exact",
   "simulated": 0.166525,
   "exact": 0.166667,
   "se": 0.000833,
   "z": -0.17,
   "tolerance": 0.00333,
   "pass": true
  },
  {
   "name": "\"last time *1, others *2\", 3 people, 30 days: P(same person on days 1 and 2)",
   "kind": "simulated vs exact",
   "simulated": 0.200425,
   "exact": 0.2,
   "se": 0.000894,
   "z": 0.48,
   "tolerance": 0.00358,
   "pass": true
  },
  {
   "name": "\"last time *1, others *2\", 3 people, 30 days: P(at least one back-to-back)",
   "kind": "simulated vs exact",
   "simulated": 0.99843,
   "exact": 0.998453,
   "se": 0.0000879,
   "z": -0.26,
   "tolerance": 0.000352,
   "pass": true
  },
  {
   "name": "\"last time *1, others *2\", 3 people, 30 days: P(3+ in a row)",
   "kind": "simulated vs exact",
   "simulated": 0.62323,
   "exact": 0.625708,
   "se": 0.00108,
   "z": -2.29,
   "tolerance": 0.00433,
   "pass": true
  },
  {
   "name": "\"last time *1, others *2\", 3 people, 30 days: average gap",
   "kind": "simulated vs exact",
   "simulated": 4.37457,
   "exact": 4.379613,
   "se": 0.00519,
   "z": -0.97,
   "tolerance": 0.0208,
   "pass": true
  },
  {
   "name": "\"last time *1, others *2\", 3 people, 30 days: E[(person 1's count)^2], i.e. the spread of one person's month",
   "kind": "simulated vs exact",
   "simulated": 104.4683,
   "exact": 104.506173,
   "se": 0.0962,
   "z": -0.39,
   "tolerance": 0.385,
   "pass": true
  },
  {
   "name": "\"last time *1, others *2\", 4 people, 30 days: P(same person on days 1 and 2)",
   "kind": "simulated vs exact",
   "simulated": 0.14422,
   "exact": 0.142857,
   "se": 0.000782,
   "z": 1.74,
   "tolerance": 0.00313,
   "pass": true
  },
  {
   "name": "\"last time *1, others *2\", 4 people, 30 days: P(at least one back-to-back)",
   "kind": "simulated vs exact",
   "simulated": 0.98909,
   "exact": 0.988557,
   "se": 0.000238,
   "z": 2.24,
   "tolerance": 0.000951,
   "pass": true
  },
  {
   "name": "\"last time *1, others *2\", 4 people, 30 days: P(3+ in a row)",
   "kind": "simulated vs exact",
   "simulated": 0.40195,
   "exact": 0.402368,
   "se": 0.0011,
   "z": -0.38,
   "tolerance": 0.00439,
   "pass": true
  },
  {
   "name": "\"last time *1, others *2\", 4 people, 30 days: average gap",
   "kind": "simulated vs exact",
   "simulated": 4.86806,
   "exact": 4.873996,
   "se": 0.0047,
   "z": -1.26,
   "tolerance": 0.0188,
   "pass": true
  },
  {
   "name": "\"last time *1, others *2\", 4 people, 30 days: E[(person 1's count)^2], i.e. the spread of one person's month",
   "kind": "simulated vs exact",
   "simulated": 60.70487,
   "exact": 60.509766,
   "se": 0.0715,
   "z": 2.73,
   "tolerance": 0.286,
   "pass": true
  }
 ]
}