{ "license": "CC BY 4.0 — https://creativecommons.org/licenses/by/4.0/", "attribution": "Wheel Cue (wheelcue.com)", "source": "https://wheelcue.com/research/random-partners-week-after-week/", "slug": "random-partners-week-after-week", "generatedAt": "2026-10-10T14:51:54.733Z", "node": "v24.21.0", "randomJsSha256": "946e82a3c426d698779d3246c37c732f771db3873c93239ef3952aea39be1e2d", "totalSpins": 80818074, "rawDraws": 80818251, "totalPresses": 3682151, "samplerPicks": 897044, "checksTotal": 189, "checksPassed": 189, "checksSimulatedVsExact": 186, "checksSanity": 3, "runtimeSeconds": 143.9, "params": { "evenSizes": [ 16, 20, 24, 30 ], "mainSize": 24, "oddSize": 25, "checkpoints": [ 4, 8, 12, 18 ], "maxWeeks": 18, "terms": { "note": "One term = maxWeeks weekly presses of Generate on the same class. 'size' = People per team 2; 'teams' = Number of teams n/2 (both modes are run so their results can be compared).", "size": { "16": 18000, "20": 18000, "24": 26000, "25": 10000, "30": 13000 }, "teams": { "16": 5000, "20": 5000, "24": 12000, "25": 10000, "30": 4000 } }, "regenerateLastWeek": { "note": "Last week = one press. Then press until no pair from last week is together again.", "experiments": { "16": 15000, "20": 15000, "24": 40000, "25": 12000, "30": 15000 } }, "regenerateAllWeeks": { "note": "Every week, press until no pair has met in ANY earlier week. Two kinds of simulated class. Detail classes (the first detailClasses): weeks 2..pressUpTo are pressed for real through random.js, and the exact number of repeat-free pairings left is counted in every week from week 2, so each week's expected presses is known for each class's own history. Fast classes (the rest, there to measure the dead-end share precisely): weeks 2..fastPressUpTo are pressed for real (fastPressUpTo <= n/2, where a repeat-free pairing always exists by Dirac's theorem), and from week fastPressUpTo + 1 the exact count is made every week. In both kinds, after the pressed weeks the week's pairing is drawn with CueRandom.pickWeighted from the exact count of repeat-free pairings (the same distribution pressing until success would give, without millions of presses); a week whose count is above 2^32 (too large for one pickWeighted draw) is pressed for real instead.", "sizes": { "16": { "classes": 6000, "detailClasses": 300, "pressUpTo": 9, "fastPressUpTo": 5 }, "20": { "classes": 3000, "detailClasses": 200, "pressUpTo": 10, "fastPressUpTo": 8 }, "24": { "classes": 1000, "detailClasses": 100, "pressUpTo": 10, "fastPressUpTo": 9 } } }, "circle": { "randomStarts": { "16": 40000, "24": 100000 }, "fullScheduleChecks": 2000, "oddExamples": [ 25 ], "tableSizes": { "from": 4, "to": 40 } }, "tableSizes": { "from": 4, "to": 40 } }, "notes": { "model": "The tool (app.js initTeams) shuffles with CueRandom.shuffle (Fisher–Yates, n-1 draws for n names). People per team 2 cuts the shuffled list into consecutive pairs (odd class: the last person is a single). Number of teams floor(n/2) deals round-robin: Team j gets shuffled positions j, j+k, j+2k, ... (odd class: Team 1 gets three). Either way every pairing is equally likely, so which students are 'student 1' and 'student 2' does not matter. A partner pair = two students in the same group (all three pairs in a trio).", "totalSpins": "totalSpins = CueRandom draws that place a name (n-1 per shuffle) plus samplerPicks (one pickWeighted per pair in the exact repeat-free sampler of section 3b). rawDraws also counts draws rejected for modulo bias. totalPresses = presses of Generate simulated (each one a full shuffle of the class). In the article quote totalPresses as simulated presses of Generate and call totalSpins 'random draws', not spins.", "simulatedVsExact": "results holds simulated pairings (never site usage); theory holds exact values only and is the same on every run. Statements in the article use theory; simulated values are called 'simulated'. Quantities marked simulationOnly (P(some pair met 3+ times), the first-repeat week beyond week 3 (beyond week 2 for odd classes), everything in results.regenerateAllWeeks except the checked rows, including the dead-end share, the class-average columns) have no exact counterpart computed here; the class averages have the same expectation as the exact student-level values.", "regenerateAllWeeks": "Pressing until a week is all-new: early weeks were pressed for real (through random.js); later weeks were drawn with CueRandom.pickWeighted from the exact number of repeat-free completions, which is the distribution pressing until success gives. expectedPresses is exact for each class's own history (1/p) and summarized across the simulated classes. A dead end = a week in which no repeat-free pairing exists at all. The dead-end share is simulated: quote it loosely, with its range and the number of classes (for example 'roughly 4 in 10 of 1,000 simulated classes of 24'), never as an exact or a rounded-up 'about half'. Most dead ends come in week n-2, when the unmet pairs form loops; earlier ones are possible but rare, so describe when they happen as what the simulations showed (deadEnd.byWeek), not as a rule.", "odd": "Odd classes: 'size' = People per team 2 leaves one student single each week (the tool's FAQ: place them by hand); 'teams' = Number of teams (n-1)/2 makes one trio (Team 1).", "rounding": "Probabilities are rounded to 6 decimals. Use the display strings for percentages; never print a share as 100% or 0% unless it is exactly that.", "checks": "Every check of kind 'simulated vs exact' allows 4 standard errors of the simulated share or average (se from the exact value, never below one sample's worth for a share); shares within 0.0001 of 0 or 1 are not checked. 'simulated vs exact (simulation se)' uses the sample sd across independent terms. 'simulated vs exact (given each history)' compares presses actually made with 1/p computed exactly for each simulated class's history (se from the geometric variance). 'sanity' checks (se 0) must hold exactly." }, "display": { "pairTogether24": "1/23 (4.3%)", "atLeastOneRepeatNextWeek24": "40.6%", "noRepeatNextWeek24": "59.4%", "expectedRepeatsNextWeek24": "0.52", "expectedPressesNoRepeat24": "1.68", "distinctAfter12Weeks24": "9.5", "distinctAfter18Weeks24": "12.7", "studentRepeatedBy4Weeks24": "24.1%", "studentRepeatedBy8Weeks24": "74.8%", "studentRepeatedBy12Weeks24": "97.0%", "pairsMetTwiceAfter12Weeks24": "25.8", "pairsMetThreeAfter18Weeks24": "11.35", "atLeastOneRepeatNextWeek25Single": "38.1%", "atLeastOneRepeatNextWeek25Trio": "48.4%", "firstRepeatByWeek3_24": "79.6%", "byeSeatWeeks25": "25", "trioGreedyRuleWeeks25": "11", "allNewMedianPressesWeek10_24": "325", "allNewMedianPressesWeek15_24": "50,626", "allNewDeadEndShare24": "39%", "allNewDeadEndRange24": "36% to 42%", "allNewDeadEndClasses24": "1,000", "allNewDeadEndShare20": "39%", "allNewDeadEndShare16": "35%", "allNewCompletedShare24": "61%", "allNewDeadEndWeek24": "22", "allNewLastWeekPresses24": "316,234,143,225", "allNewWeekMedianOver10_24": "6", "allNewWeekMedianOver100_24": "9", "allNewWeekMedianOver1000_24": "12", "allNewWeekMedianOver1000000_24": "18", "roundRobinWeeks24": "23" }, "theory": { "nextWeek": { "note": "Last week's groups vs this week's, both from the generator (any fixed last week gives the same answer). A 'repeat' = two students together this week who were together last week (in a trio all three pairs count). Even classes: People per team 2 and Number of teams n/2 give the same uniformly random pairing. Odd classes: 'size' = People per team 2 (pairs + one student left single), 'teams' = Number of teams (n-1)/2 (pairs + one trio, Team 1). Exact by inclusion–exclusion (formulas in the script), verified against a full listing of every arrangement for classes of 4-11. expectedPresses = presses of Generate needed on average until nobody repeats a partner from last week (1 / pNone).", "bySize": { "16": { "size": { "classSize": 16, "mode": "size", "partnerPairsPerWeek": 8, "pPairTogether": 0.066667, "pPairTogetherFraction": "1/15", "expectedRepeats": 0.5333, "expectedRepeatsFraction": "8/15", "sdRepeats": 0.7322, "pAtLeastOneRepeat": 0.412601, "pNoRepeat": 0.587399, "pNoRepeatFraction": "170096/289575", "expectedPressesForNoRepeat": 1.7024, "distribution": [ { "repeats": 0, "exact": 0.587399 }, { "repeats": 1, "exact": 0.311819 }, { "repeats": 2, "exact": 0.083433 }, { "repeats": 3, "exact": 0.015029 }, { "repeats": 4, "exact": 0.002072 }, { "repeats": 5, "exact": 0.000221 }, { "repeats": 6, "exact": 0.000028 } ], "display": { "pAtLeastOneRepeat": "41.3%", "pNoRepeat": "58.7%", "pPairTogether": "6.7%", "expectedRepeats": "0.53" } } }, "20": { "size": { "classSize": 20, "mode": "size", "partnerPairsPerWeek": 10, "pPairTogether": 0.052632, "pPairTogetherFraction": "1/19", "expectedRepeats": 0.5263, "expectedRepeatsFraction": "10/19", "sdRepeats": 0.7266, "pAtLeastOneRepeat": 0.408763, "pNoRepeat": 0.591237, "pNoRepeatFraction": "43011104/72747675", "expectedPressesForNoRepeat": 1.6914, "distribution": [ { "repeats": 0, "exact": 0.591237 }, { "repeats": 1, "exact": 0.310279 }, { "repeats": 2, "exact": 0.081836 }, { "repeats": 3, "exact": 0.014481 }, { "repeats": 4, "exact": 0.001937 }, { "repeats": 5, "exact": 0.000209 }, { "repeats": 6, "exact": 0.000019 }, { "repeats": 7, "exact": 0.000001 } ], "display": { "pAtLeastOneRepeat": "40.9%", "pNoRepeat": "59.1%", "pPairTogether": "5.3%", "expectedRepeats": "0.53" } } }, "24": { "size": { "classSize": 24, "mode": "size", "partnerPairsPerWeek": 12, "pPairTogether": 0.043478, "pPairTogetherFraction": "1/23", "expectedRepeats": 0.5217, "expectedRepeatsFraction": "12/23", "sdRepeats": 0.7231, "pAtLeastOneRepeat": 0.406204, "pNoRepeat": 0.593796, "pNoRepeatFraction": "17070792512/28748558475", "expectedPressesForNoRepeat": 1.6841, "distribution": [ { "repeats": 0, "exact": 0.593796 }, { "repeats": 1, "exact": 0.3092 }, { "repeats": 2, "exact": 0.08079 }, { "repeats": 3, "exact": 0.014133 }, { "repeats": 4, "exact": 0.001864 }, { "repeats": 5, "exact": 0.000198 }, { "repeats": 6, "exact": 0.000018 }, { "repeats": 7, "exact": 0.000001 } ], "display": { "pAtLeastOneRepeat": "40.6%", "pNoRepeat": "59.4%", "pPairTogether": "4.3%", "expectedRepeats": "0.52" } } }, "25": { "size": { "classSize": 25, "mode": "size", "partnerPairsPerWeek": 12, "pPairTogether": 0.04, "pPairTogetherFraction": "1/25", "expectedRepeats": 0.48, "expectedRepeatsFraction": "12/25", "sdRepeats": 0.6922, "pAtLeastOneRepeat": 0.381468, "pNoRepeat": 0.618532, "pNoRepeatFraction": "978005410496/1581170716125", "expectedPressesForNoRepeat": 1.6167, "distribution": [ { "repeats": 0, "exact": 0.618532 }, { "repeats": 1, "exact": 0.29739 }, { "repeats": 2, "exact": 0.071256 }, { "repeats": 3, "exact": 0.011337 }, { "repeats": 4, "exact": 0.001347 }, { "repeats": 5, "exact": 0.000127 }, { "repeats": 6, "exact": 0.00001 } ], "display": { "pAtLeastOneRepeat": "38.1%", "pNoRepeat": "61.9%", "pPairTogether": "4.0%", "expectedRepeats": "0.48" } }, "teams": { "classSize": 25, "mode": "teams", "partnerPairsPerWeek": 14, "pPairTogether": 0.046667, "pPairTogetherFraction": "7/150", "expectedRepeats": 0.6533, "expectedRepeatsFraction": "49/75", "sdRepeats": 0.7983, "pAtLeastOneRepeat": 0.484385, "pNoRepeat": 0.515615, "pNoRepeatFraction": "24705336928/47914264125", "expectedPressesForNoRepeat": 1.9394, "distribution": [ { "repeats": 0, "exact": 0.515615 }, { "repeats": 1, "exact": 0.346787 }, { "repeats": 2, "exact": 0.110731 }, { "repeats": 3, "exact": 0.022901 }, { "repeats": 4, "exact": 0.003495 }, { "repeats": 5, "exact": 0.000423 }, { "repeats": 6, "exact": 0.000043 }, { "repeats": 7, "exact": 0.000004 } ], "display": { "pAtLeastOneRepeat": "48.4%", "pNoRepeat": "51.6%", "pPairTogether": "4.7%", "expectedRepeats": "0.65" } } }, "30": { "size": { "classSize": 30, "mode": "size", "partnerPairsPerWeek": 15, "pPairTogether": 0.034483, "pPairTogetherFraction": "1/29", "expectedRepeats": 0.5172, "expectedRepeatsFraction": "15/29", "sdRepeats": 0.7197, "pAtLeastOneRepeat": 0.403646, "pNoRepeat": 0.596354, "pNoRepeatFraction": "527371806797312/884326193375625", "expectedPressesForNoRepeat": 1.6769, "distribution": [ { "repeats": 0, "exact": 0.596354 }, { "repeats": 1, "exact": 0.308081 }, { "repeats": 2, "exact": 0.07976 }, { "repeats": 3, "exact": 0.013802 }, { "repeats": 4, "exact": 0.001797 }, { "repeats": 5, "exact": 0.000188 }, { "repeats": 6, "exact": 0.000016 }, { "repeats": 7, "exact": 0.000001 } ], "display": { "pAtLeastOneRepeat": "40.4%", "pNoRepeat": "59.6%", "pPairTogether": "3.4%", "expectedRepeats": "0.52" } } } } }, "nextWeekTable": { "note": "Every class size from 4 to 40. Even sizes: one row (both modes). Odd sizes: 'single' = People per team 2 (pairs + a single), 'trio' = Number of teams (n-1)/2 (pairs + a trio). noRepeatPossible false (class of 5, pairs + trio): every arrangement repeats someone from last week, so expectedPresses is null.", "rows": [ { "classSize": 4, "arrangement": "pairs", "pPairTogether": 0.333333, "expectedRepeats": 0.6667, "pAtLeastOneRepeat": 0.333333, "expectedPresses": 1.5, "noRepeatPossible": true }, { "classSize": 5, "arrangement": "pairs + single", "pPairTogether": 0.2, "expectedRepeats": 0.4, "pAtLeastOneRepeat": 0.333333, "expectedPresses": 1.5, "noRepeatPossible": true }, { "classSize": 5, "arrangement": "pairs + trio", "pPairTogether": 0.4, "expectedRepeats": 1.6, "pAtLeastOneRepeat": 1, "expectedPresses": null, "noRepeatPossible": false }, { "classSize": 6, "arrangement": "pairs", "pPairTogether": 0.2, "expectedRepeats": 0.6, "pAtLeastOneRepeat": 0.466667, "expectedPresses": 1.875, "noRepeatPossible": true }, { "classSize": 7, "arrangement": "pairs + single", "pPairTogether": 0.142857, "expectedRepeats": 0.4286, "pAtLeastOneRepeat": 0.352381, "expectedPresses": 1.5441, "noRepeatPossible": true }, { "classSize": 7, "arrangement": "pairs + trio", "pPairTogether": 0.238095, "expectedRepeats": 1.1905, "pAtLeastOneRepeat": 0.771429, "expectedPresses": 4.375, "noRepeatPossible": true }, { "classSize": 8, "arrangement": "pairs", "pPairTogether": 0.142857, "expectedRepeats": 0.5714, "pAtLeastOneRepeat": 0.428571, "expectedPresses": 1.75, "noRepeatPossible": true }, { "classSize": 9, "arrangement": "pairs + single", "pPairTogether": 0.111111, "expectedRepeats": 0.4444, "pAtLeastOneRepeat": 0.360847, "expectedPresses": 1.5646, "noRepeatPossible": true }, { "classSize": 9, "arrangement": "pairs + trio", "pPairTogether": 0.166667, "expectedRepeats": 1, "pAtLeastOneRepeat": 0.67619, "expectedPresses": 3.0882, "noRepeatPossible": true }, { "classSize": 10, "arrangement": "pairs", "pPairTogether": 0.111111, "expectedRepeats": 0.5556, "pAtLeastOneRepeat": 0.424339, "expectedPresses": 1.7371, "noRepeatPossible": true }, { "classSize": 11, "arrangement": "pairs + single", "pPairTogether": 0.090909, "expectedRepeats": 0.4545, "pAtLeastOneRepeat": 0.366619, "expectedPresses": 1.5788, "noRepeatPossible": true }, { "classSize": 11, "arrangement": "pairs + trio", "pPairTogether": 0.127273, "expectedRepeats": 0.8909, "pAtLeastOneRepeat": 0.617662, "expectedPresses": 2.6155, "noRepeatPossible": true }, { "classSize": 12, "arrangement": "pairs", "pPairTogether": 0.090909, "expectedRepeats": 0.5455, "pAtLeastOneRepeat": 0.418951, "expectedPresses": 1.721, "noRepeatPossible": true }, { "classSize": 13, "arrangement": "pairs + single", "pPairTogether": 0.076923, "expectedRepeats": 0.4615, "pAtLeastOneRepeat": 0.370644, "expectedPresses": 1.5889, "noRepeatPossible": true }, { "classSize": 13, "arrangement": "pairs + trio", "pPairTogether": 0.102564, "expectedRepeats": 0.8205, "pAtLeastOneRepeat": 0.579088, "expectedPresses": 2.3758, "noRepeatPossible": true }, { "classSize": 14, "arrangement": "pairs", "pPairTogether": 0.076923, "expectedRepeats": 0.5385, "pAtLeastOneRepeat": 0.41534, "expectedPresses": 1.7104, "noRepeatPossible": true }, { "classSize": 15, "arrangement": "pairs + single", "pPairTogether": 0.066667, "expectedRepeats": 0.4667, "pAtLeastOneRepeat": 0.373624, "expectedPresses": 1.5965, "noRepeatPossible": true }, { "classSize": 15, "arrangement": "pairs + trio", "pPairTogether": 0.085714, "expectedRepeats": 0.7714, "pAtLeastOneRepeat": 0.551737, "expectedPresses": 2.2308, "noRepeatPossible": true }, { "classSize": 16, "arrangement": "pairs", "pPairTogether": 0.066667, "expectedRepeats": 0.5333, "pAtLeastOneRepeat": 0.412601, "expectedPresses": 1.7024, "noRepeatPossible": true }, { "classSize": 17, "arrangement": "pairs + single", "pPairTogether": 0.058824, "expectedRepeats": 0.4706, "pAtLeastOneRepeat": 0.375917, "expectedPresses": 1.6024, "noRepeatPossible": true }, { "classSize": 17, "arrangement": "pairs + trio", "pPairTogether": 0.073529, "expectedRepeats": 0.7353, "pAtLeastOneRepeat": 0.531364, "expectedPresses": 2.1339, "noRepeatPossible": true }, { "classSize": 18, "arrangement": "pairs", "pPairTogether": 0.058824, "expectedRepeats": 0.5294, "pAtLeastOneRepeat": 0.41047, "expectedPresses": 1.6963, "noRepeatPossible": true }, { "classSize": 19, "arrangement": "pairs + single", "pPairTogether": 0.052632, "expectedRepeats": 0.4737, "pAtLeastOneRepeat": 0.377735, "expectedPresses": 1.607, "noRepeatPossible": true }, { "classSize": 19, "arrangement": "pairs + trio", "pPairTogether": 0.064327, "expectedRepeats": 0.7076, "pAtLeastOneRepeat": 0.515612, "expectedPresses": 2.0645, "noRepeatPossible": true }, { "classSize": 20, "arrangement": "pairs", "pPairTogether": 0.052632, "expectedRepeats": 0.5263, "pAtLeastOneRepeat": 0.408763, "expectedPresses": 1.6914, "noRepeatPossible": true }, { "classSize": 21, "arrangement": "pairs + single", "pPairTogether": 0.047619, "expectedRepeats": 0.4762, "pAtLeastOneRepeat": 0.379213, "expectedPresses": 1.6109, "noRepeatPossible": true }, { "classSize": 21, "arrangement": "pairs + trio", "pPairTogether": 0.057143, "expectedRepeats": 0.6857, "pAtLeastOneRepeat": 0.503075, "expectedPresses": 2.0124, "noRepeatPossible": true }, { "classSize": 22, "arrangement": "pairs", "pPairTogether": 0.047619, "expectedRepeats": 0.5238, "pAtLeastOneRepeat": 0.407367, "expectedPresses": 1.6874, "noRepeatPossible": true }, { "classSize": 23, "arrangement": "pairs + single", "pPairTogether": 0.043478, "expectedRepeats": 0.4783, "pAtLeastOneRepeat": 0.380437, "expectedPresses": 1.614, "noRepeatPossible": true }, { "classSize": 23, "arrangement": "pairs + trio", "pPairTogether": 0.051383, "expectedRepeats": 0.668, "pAtLeastOneRepeat": 0.492862, "expectedPresses": 1.9719, "noRepeatPossible": true }, { "classSize": 24, "arrangement": "pairs", "pPairTogether": 0.043478, "expectedRepeats": 0.5217, "pAtLeastOneRepeat": 0.406204, "expectedPresses": 1.6841, "noRepeatPossible": true }, { "classSize": 25, "arrangement": "pairs + single", "pPairTogether": 0.04, "expectedRepeats": 0.48, "pAtLeastOneRepeat": 0.381468, "expectedPresses": 1.6167, "noRepeatPossible": true }, { "classSize": 25, "arrangement": "pairs + trio", "pPairTogether": 0.046667, "expectedRepeats": 0.6533, "pAtLeastOneRepeat": 0.484385, "expectedPresses": 1.9394, "noRepeatPossible": true }, { "classSize": 26, "arrangement": "pairs", "pPairTogether": 0.04, "expectedRepeats": 0.52, "pAtLeastOneRepeat": 0.405219, "expectedPresses": 1.6813, "noRepeatPossible": true }, { "classSize": 27, "arrangement": "pairs + single", "pPairTogether": 0.037037, "expectedRepeats": 0.4815, "pAtLeastOneRepeat": 0.382347, "expectedPresses": 1.619, "noRepeatPossible": true }, { "classSize": 27, "arrangement": "pairs + trio", "pPairTogether": 0.042735, "expectedRepeats": 0.641, "pAtLeastOneRepeat": 0.477235, "expectedPresses": 1.9129, "noRepeatPossible": true }, { "classSize": 28, "arrangement": "pairs", "pPairTogether": 0.037037, "expectedRepeats": 0.5185, "pAtLeastOneRepeat": 0.404376, "expectedPresses": 1.6789, "noRepeatPossible": true }, { "classSize": 29, "arrangement": "pairs + single", "pPairTogether": 0.034483, "expectedRepeats": 0.4828, "pAtLeastOneRepeat": 0.383107, "expectedPresses": 1.621, "noRepeatPossible": true }, { "classSize": 29, "arrangement": "pairs + trio", "pPairTogether": 0.039409, "expectedRepeats": 0.6305, "pAtLeastOneRepeat": 0.471126, "expectedPresses": 1.8908, "noRepeatPossible": true }, { "classSize": 30, "arrangement": "pairs", "pPairTogether": 0.034483, "expectedRepeats": 0.5172, "pAtLeastOneRepeat": 0.403646, "expectedPresses": 1.6769, "noRepeatPossible": true }, { "classSize": 31, "arrangement": "pairs + single", "pPairTogether": 0.032258, "expectedRepeats": 0.4839, "pAtLeastOneRepeat": 0.383769, "expectedPresses": 1.6228, "noRepeatPossible": true }, { "classSize": 31, "arrangement": "pairs + trio", "pPairTogether": 0.036559, "expectedRepeats": 0.6215, "pAtLeastOneRepeat": 0.465845, "expectedPresses": 1.8721, "noRepeatPossible": true }, { "classSize": 32, "arrangement": "pairs", "pPairTogether": 0.032258, "expectedRepeats": 0.5161, "pAtLeastOneRepeat": 0.403007, "expectedPresses": 1.6751, "noRepeatPossible": true }, { "classSize": 33, "arrangement": "pairs + single", "pPairTogether": 0.030303, "expectedRepeats": 0.4848, "pAtLeastOneRepeat": 0.384352, "expectedPresses": 1.6243, "noRepeatPossible": true }, { "classSize": 33, "arrangement": "pairs + trio", "pPairTogether": 0.034091, "expectedRepeats": 0.6136, "pAtLeastOneRepeat": 0.461235, "expectedPresses": 1.8561, "noRepeatPossible": true }, { "classSize": 34, "arrangement": "pairs", "pPairTogether": 0.030303, "expectedRepeats": 0.5152, "pAtLeastOneRepeat": 0.402443, "expectedPresses": 1.6735, "noRepeatPossible": true }, { "classSize": 35, "arrangement": "pairs + single", "pPairTogether": 0.028571, "expectedRepeats": 0.4857, "pAtLeastOneRepeat": 0.384869, "expectedPresses": 1.6257, "noRepeatPossible": true }, { "classSize": 35, "arrangement": "pairs + trio", "pPairTogether": 0.031933, "expectedRepeats": 0.6067, "pAtLeastOneRepeat": 0.457177, "expectedPresses": 1.8422, "noRepeatPossible": true }, { "classSize": 36, "arrangement": "pairs", "pPairTogether": 0.028571, "expectedRepeats": 0.5143, "pAtLeastOneRepeat": 0.401942, "expectedPresses": 1.6721, "noRepeatPossible": true }, { "classSize": 37, "arrangement": "pairs + single", "pPairTogether": 0.027027, "expectedRepeats": 0.4865, "pAtLeastOneRepeat": 0.385331, "expectedPresses": 1.6269, "noRepeatPossible": true }, { "classSize": 37, "arrangement": "pairs + trio", "pPairTogether": 0.03003, "expectedRepeats": 0.6006, "pAtLeastOneRepeat": 0.453576, "expectedPresses": 1.8301, "noRepeatPossible": true }, { "classSize": 38, "arrangement": "pairs", "pPairTogether": 0.027027, "expectedRepeats": 0.5135, "pAtLeastOneRepeat": 0.401494, "expectedPresses": 1.6708, "noRepeatPossible": true }, { "classSize": 39, "arrangement": "pairs + single", "pPairTogether": 0.025641, "expectedRepeats": 0.4872, "pAtLeastOneRepeat": 0.385745, "expectedPresses": 1.628, "noRepeatPossible": true }, { "classSize": 39, "arrangement": "pairs + trio", "pPairTogether": 0.02834, "expectedRepeats": 0.5951, "pAtLeastOneRepeat": 0.45036, "expectedPresses": 1.8194, "noRepeatPossible": true }, { "classSize": 40, "arrangement": "pairs", "pPairTogether": 0.025641, "expectedRepeats": 0.5128, "pAtLeastOneRepeat": 0.401091, "expectedPresses": 1.6697, "noRepeatPossible": true } ] }, "term": { "note": "Weekly independent random pairings. Student-level values are exact (recursion over the student's distinct partners, also checked against closed forms: E[distinct] = (n-1)(1 - (1-p)^W) with p = P(a given pair together in a week); even classes P(repeated) = 1 - (n-1)(n-2)...(n-W)/(n-1)^W). pairsMetTwice / pairsMetThree = expected number of pairs (of all C(n,2)) who have worked together at least 2 / 3 times by week W, exact with exact sd (joint counts of two pairs, see the script); even classes only. expectedRepeatsInWeek[w] = expected number of week w's pairs who already worked together in an earlier week = pairsPerWeek * (1 - (1-p)^(w-1)). pFirstRepeatAtWeek2 = P(week 2 already repeats a week-1 pair) = nextWeek pAtLeastOneRepeat. pFirstRepeatByWeek3 (even classes) = P(some pair has worked together twice by the end of week 3), exact from the loops formed by weeks 1 + 2 (formula in the script, checked by listing every week-2 and week-3 pairing for classes of 4-10). lostPartners (even classes only) = partners a round-robin gives in W weeks minus the expected different partners with random pairing; it is not given for odd classes, where a trio week brings two partners. repeatForced = more weeks than classmates, so a repeat is certain (pStudentRepeated is exactly 1, not a rounding). circleDistinct = W: a round-robin schedule gives W different partners in W weeks (W <= n-1).", "bySize": { "16": { "size": { "classSize": 16, "mode": "size", "pPairTogether": 0.066667, "pFirstRepeatAtWeek2": 0.412601, "pFirstRepeatByWeek3": 0.804836, "displayFirstRepeatByWeek3": "80.5%", "checkpoints": { "4": { "weeks": 4, "meanDistinctPartners": 3.6175, "pStudentRepeated": 0.352889, "lostPartners": 0.3825, "pairsMetTwice": { "mean": 2.9227, "sd": 1.4766 }, "pairsMetThree": { "mean": 0.1351, "sd": 0.3685, "pGivenPair": 0.001126 }, "display": { "pStudentRepeated": "35.3%", "meanDistinctPartners": "3.6" } }, "8": { "weeks": 8, "meanDistinctPartners": 6.3626, "pStudentRepeated": 0.898763, "lostPartners": 1.6374, "pairsMetTwice": { "mean": 11.4149, "sd": 2.2156 }, "pairsMetThree": { "mean": 1.5436, "sd": 1.1706, "pGivenPair": 0.012863 }, "display": { "pStudentRepeated": "89.9%", "meanDistinctPartners": "6.4" } }, "12": { "weeks": 12, "meanDistinctPartners": 8.4456, "pStudentRepeated": 0.99832, "lostPartners": 3.5544, "pairsMetTwice": { "mean": 22.6204, "sd": 2.5093 }, "pairsMetThree": { "mean": 4.9637, "sd": 1.8684, "pGivenPair": 0.041364 }, "display": { "pStudentRepeated": "99.83%", "meanDistinctPartners": "8.4" } }, "18": { "weeks": 18, "meanDistinctPartners": 10.6674, "pStudentRepeated": 1, "lostPartners": 4.3326, "repeatForced": true, "pairsMetTwice": { "mean": 40.7745, "sd": 2.818 }, "pairsMetThree": { "mean": 13.7175, "sd": 2.5059, "pGivenPair": 0.114313 }, "display": { "pStudentRepeated": "100%", "meanDistinctPartners": "10.7" } } }, "byWeek": [ { "week": 1, "meanDistinctPartners": 1, "sdDistinctPartners": 0, "pStudentRepeated": 0, "shareOfClassMet": 0.066667, "circleDistinct": 1, "expectedRepeatsInWeek": 0, "expectedPairsMetTwice": 0 }, { "week": 2, "meanDistinctPartners": 1.9333, "sdDistinctPartners": 0.2494, "pStudentRepeated": 0.066667, "shareOfClassMet": 0.128889, "circleDistinct": 2, "expectedRepeatsInWeek": 0.5333, "expectedPairsMetTwice": 0.5333 }, { "week": 3, "meanDistinctPartners": 2.8044, "sdDistinctPartners": 0.4077, "pStudentRepeated": 0.191111, "shareOfClassMet": 0.186963, "circleDistinct": 3, "expectedRepeatsInWeek": 1.0311, "expectedPairsMetTwice": 1.5289 }, { "week": 4, "meanDistinctPartners": 3.6175, "sdDistinctPartners": 0.5441, "pStudentRepeated": 0.352889, "shareOfClassMet": 0.241165, "circleDistinct": 4, "expectedRepeatsInWeek": 1.4957, "expectedPairsMetTwice": 2.9227 }, { "week": 5, "meanDistinctPartners": 4.3763, "sdDistinctPartners": 0.663, "pStudentRepeated": 0.525452, "shareOfClassMet": 0.291754, "circleDistinct": 5, "expectedRepeatsInWeek": 1.9293, "expectedPairsMetTwice": 4.6571 }, { "week": 6, "meanDistinctPartners": 5.0846, "sdDistinctPartners": 0.7666, "pStudentRepeated": 0.683635, "shareOfClassMet": 0.338971, "circleDistinct": 6, "expectedRepeatsInWeek": 2.334, "expectedPairsMetTwice": 6.6807 }, { "week": 7, "meanDistinctPartners": 5.7456, "sdDistinctPartners": 0.8563, "pStudentRepeated": 0.810181, "shareOfClassMet": 0.383039, "circleDistinct": 7, "expectedRepeatsInWeek": 2.7118, "expectedPairsMetTwice": 8.9471 }, { "week": 8, "meanDistinctPartners": 6.3626, "sdDistinctPartners": 0.9337, "pStudentRepeated": 0.898763, "shareOfClassMet": 0.42417, "circleDistinct": 8, "expectedRepeatsInWeek": 3.0643, "expectedPairsMetTwice": 11.4149 }, { "week": 9, "meanDistinctPartners": 6.9384, "sdDistinctPartners": 0.9999, "pStudentRepeated": 0.952756, "shareOfClassMet": 0.462559, "circleDistinct": 9, "expectedRepeatsInWeek": 3.3934, "expectedPairsMetTwice": 14.0473 }, { "week": 10, "meanDistinctPartners": 7.4758, "sdDistinctPartners": 1.056, "pStudentRepeated": 0.981102, "shareOfClassMet": 0.498388, "circleDistinct": 10, "expectedRepeatsInWeek": 3.7005, "expectedPairsMetTwice": 16.8113 }, { "week": 11, "meanDistinctPartners": 7.9774, "sdDistinctPartners": 1.1029, "pStudentRepeated": 0.993701, "shareOfClassMet": 0.531829, "circleDistinct": 11, "expectedRepeatsInWeek": 3.9871, "expectedPairsMetTwice": 19.6776 }, { "week": 12, "meanDistinctPartners": 8.4456, "sdDistinctPartners": 1.1416, "pStudentRepeated": 0.99832, "shareOfClassMet": 0.56304, "circleDistinct": 12, "expectedRepeatsInWeek": 4.2546, "expectedPairsMetTwice": 22.6204 }, { "week": 13, "meanDistinctPartners": 8.8826, "sdDistinctPartners": 1.1728, "pStudentRepeated": 0.999664, "shareOfClassMet": 0.592171, "circleDistinct": 13, "expectedRepeatsInWeek": 4.5043, "expectedPairsMetTwice": 25.6167 }, { "week": 14, "meanDistinctPartners": 9.2904, "sdDistinctPartners": 1.1973, "pStudentRepeated": 0.999955, "shareOfClassMet": 0.61936, "circleDistinct": 14, "expectedRepeatsInWeek": 4.7374, "expectedPairsMetTwice": 28.6463 }, { "week": 15, "meanDistinctPartners": 9.671, "sdDistinctPartners": 1.2158, "pStudentRepeated": 0.999997, "shareOfClassMet": 0.644736, "circleDistinct": 15, "expectedRepeatsInWeek": 4.9549, "expectedPairsMetTwice": 31.6914 }, { "week": 16, "meanDistinctPartners": 10.0263, "sdDistinctPartners": 1.2289, "pStudentRepeated": 1, "shareOfClassMet": 0.66842, "circleDistinct": 15, "expectedRepeatsInWeek": 5.1579, "expectedPairsMetTwice": 34.7366 }, { "week": 17, "meanDistinctPartners": 10.3579, "sdDistinctPartners": 1.2371, "pStudentRepeated": 1, "shareOfClassMet": 0.690525, "circleDistinct": 15, "expectedRepeatsInWeek": 5.3474, "expectedPairsMetTwice": 37.7681 }, { "week": 18, "meanDistinctPartners": 10.6674, "sdDistinctPartners": 1.241, "pStudentRepeated": 1, "shareOfClassMet": 0.711157, "circleDistinct": 15, "expectedRepeatsInWeek": 5.5242, "expectedPairsMetTwice": 40.7745 } ] } }, "20": { "size": { "classSize": 20, "mode": "size", "pPairTogether": 0.052632, "pFirstRepeatAtWeek2": 0.408763, "pFirstRepeatByWeek3": 0.799252, "displayFirstRepeatByWeek3": "79.9%", "checkpoints": { "4": { "weeks": 4, "meanDistinctPartners": 3.6951, "pStudentRepeated": 0.286193, "lostPartners": 0.3049, "pairsMetTwice": { "mean": 2.9407, "sd": 1.5311 }, "pairsMetThree": { "mean": 0.1064, "sd": 0.3267, "pGivenPair": 0.00056 }, "display": { "pStudentRepeated": "28.6%", "meanDistinctPartners": "3.7" } }, "8": { "weeks": 8, "meanDistinctPartners": 6.6717, "pStudentRepeated": 0.820564, "lostPartners": 1.3283, "pairsMetTwice": { "mean": 11.9239, "sd": 2.4792 }, "pairsMetThree": { "mean": 1.2698, "sd": 1.0853, "pGivenPair": 0.006683 }, "display": { "pStudentRepeated": "82.1%", "meanDistinctPartners": "6.7" } }, "12": { "weeks": 12, "meanDistinctPartners": 9.0693, "pStudentRepeated": 0.989095, "lostPartners": 2.9307, "pairsMetTwice": { "mean": 24.4881, "sd": 2.9374 }, "pairsMetThree": { "mean": 4.2589, "sd": 1.8391, "pGivenPair": 0.022415 }, "display": { "pStudentRepeated": "98.9%", "meanDistinctPartners": "9.1" } }, "18": { "weeks": 18, "meanDistinctPartners": 11.8205, "pStudentRepeated": 0.999999, "lostPartners": 6.1795, "pairsMetTwice": { "mean": 46.4101, "sd": 3.296 }, "pairsMetThree": { "mean": 12.5069, "sd": 2.703, "pGivenPair": 0.065826 }, "display": { "pStudentRepeated": ">99.99%", "meanDistinctPartners": "11.8" } } }, "byWeek": [ { "week": 1, "meanDistinctPartners": 1, "sdDistinctPartners": 0, "pStudentRepeated": 0, "shareOfClassMet": 0.052632, "circleDistinct": 1, "expectedRepeatsInWeek": 0, "expectedPairsMetTwice": 0 }, { "week": 2, "meanDistinctPartners": 1.9474, "sdDistinctPartners": 0.2233, "pStudentRepeated": 0.052632, "shareOfClassMet": 0.102493, "circleDistinct": 2, "expectedRepeatsInWeek": 0.5263, "expectedPairsMetTwice": 0.5263 }, { "week": 3, "meanDistinctPartners": 2.8449, "sdDistinctPartners": 0.3696, "pStudentRepeated": 0.152355, "shareOfClassMet": 0.14973, "circleDistinct": 3, "expectedRepeatsInWeek": 1.0249, "expectedPairsMetTwice": 1.5235 }, { "week": 4, "meanDistinctPartners": 3.6951, "sdDistinctPartners": 0.4995, "pStudentRepeated": 0.286193, "shareOfClassMet": 0.194481, "circleDistinct": 4, "expectedRepeatsInWeek": 1.4973, "expectedPairsMetTwice": 2.9407 }, { "week": 5, "meanDistinctPartners": 4.5007, "sdDistinctPartners": 0.6164, "pStudentRepeated": 0.436468, "shareOfClassMet": 0.236877, "circleDistinct": 5, "expectedRepeatsInWeek": 1.9448, "expectedPairsMetTwice": 4.7307 }, { "week": 6, "meanDistinctPartners": 5.2638, "sdDistinctPartners": 0.7216, "pStudentRepeated": 0.584766, "shareOfClassMet": 0.277041, "circleDistinct": 6, "expectedRepeatsInWeek": 2.3688, "expectedPairsMetTwice": 6.8505 }, { "week": 7, "meanDistinctPartners": 5.9867, "sdDistinctPartners": 0.8162, "pStudentRepeated": 0.715893, "shareOfClassMet": 0.315092, "circleDistinct": 7, "expectedRepeatsInWeek": 2.7704, "expectedPairsMetTwice": 9.2604 }, { "week": 8, "meanDistinctPartners": 6.6717, "sdDistinctPartners": 0.901, "pStudentRepeated": 0.820564, "shareOfClassMet": 0.35114, "circleDistinct": 8, "expectedRepeatsInWeek": 3.1509, "expectedPairsMetTwice": 11.9239 }, { "week": 9, "meanDistinctPartners": 7.3205, "sdDistinctPartners": 0.9769, "pStudentRepeated": 0.896116, "shareOfClassMet": 0.38529, "circleDistinct": 9, "expectedRepeatsInWeek": 3.5114, "expectedPairsMetTwice": 14.8077 }, { "week": 10, "meanDistinctPartners": 7.9352, "sdDistinctPartners": 1.0443, "pStudentRepeated": 0.945324, "shareOfClassMet": 0.417643, "circleDistinct": 10, "expectedRepeatsInWeek": 3.8529, "expectedPairsMetTwice": 17.8813 }, { "week": 11, "meanDistinctPartners": 8.5176, "sdDistinctPartners": 1.1041, "pStudentRepeated": 0.974101, "shareOfClassMet": 0.448294, "circleDistinct": 11, "expectedRepeatsInWeek": 4.1764, "expectedPairsMetTwice": 21.1166 }, { "week": 12, "meanDistinctPartners": 9.0693, "sdDistinctPartners": 1.1567, "pStudentRepeated": 0.989095, "shareOfClassMet": 0.477331, "circleDistinct": 12, "expectedRepeatsInWeek": 4.4829, "expectedPairsMetTwice": 24.4881 }, { "week": 13, "meanDistinctPartners": 9.592, "sdDistinctPartners": 1.2028, "pStudentRepeated": 0.995982, "shareOfClassMet": 0.50484, "circleDistinct": 13, "expectedRepeatsInWeek": 4.7733, "expectedPairsMetTwice": 27.9726 }, { "week": 14, "meanDistinctPartners": 10.0871, "sdDistinctPartners": 1.2427, "pStudentRepeated": 0.998731, "shareOfClassMet": 0.530901, "circleDistinct": 14, "expectedRepeatsInWeek": 5.0484, "expectedPairsMetTwice": 31.5487 }, { "week": 15, "meanDistinctPartners": 10.5562, "sdDistinctPartners": 1.2771, "pStudentRepeated": 0.999666, "shareOfClassMet": 0.55559, "circleDistinct": 15, "expectedRepeatsInWeek": 5.309, "expectedPairsMetTwice": 35.1973 }, { "week": 16, "meanDistinctPartners": 11.0006, "sdDistinctPartners": 1.3062, "pStudentRepeated": 0.99993, "shareOfClassMet": 0.57898, "circleDistinct": 16, "expectedRepeatsInWeek": 5.5559, "expectedPairsMetTwice": 38.9007 }, { "week": 17, "meanDistinctPartners": 11.4216, "sdDistinctPartners": 1.3305, "pStudentRepeated": 0.999989, "shareOfClassMet": 0.601139, "circleDistinct": 17, "expectedRepeatsInWeek": 5.7898, "expectedPairsMetTwice": 42.6431 }, { "week": 18, "meanDistinctPartners": 11.8205, "sdDistinctPartners": 1.3504, "pStudentRepeated": 0.999999, "shareOfClassMet": 0.622132, "circleDistinct": 18, "expectedRepeatsInWeek": 6.0114, "expectedPairsMetTwice": 46.4101 } ] } }, "24": { "size": { "classSize": 24, "mode": "size", "pPairTogether": 0.043478, "pFirstRepeatAtWeek2": 0.406204, "pFirstRepeatByWeek3": 0.795521, "displayFirstRepeatByWeek3": "79.6%", "checkpoints": { "4": { "weeks": 4, "meanDistinctPartners": 3.7466, "pStudentRepeated": 0.240569, "lostPartners": 0.2534, "pairsMetTwice": { "mean": 2.9519, "sd": 1.5665 }, "pairsMetThree": { "mean": 0.0878, "sd": 0.2966, "pGivenPair": 0.000318 }, "display": { "pStudentRepeated": "24.1%", "meanDistinctPartners": "3.7" } }, "8": { "weeks": 8, "meanDistinctPartners": 6.8829, "pStudentRepeated": 0.747552, "lostPartners": 1.1171, "pairsMetTwice": { "mean": 12.2658, "sd": 2.6678 }, "pairsMetThree": { "mean": 1.0771, "sd": 1.0114, "pGivenPair": 0.003903 }, "display": { "pStudentRepeated": "74.8%", "meanDistinctPartners": "6.9" } }, "12": { "weeks": 12, "meanDistinctPartners": 9.5083, "pStudentRepeated": 0.970447, "lostPartners": 2.4917, "pairsMetTwice": { "mean": 25.7907, "sd": 3.2828 }, "pairsMetThree": { "mean": 3.7134, "sd": 1.7763, "pGivenPair": 0.013454 }, "display": { "pStudentRepeated": "97.0%", "meanDistinctPartners": "9.5" } }, "18": { "weeks": 18, "meanDistinctPartners": 12.6668, "pStudentRepeated": 0.999934, "lostPartners": 5.3332, "pairsMetTwice": { "mean": 50.5483, "sd": 3.7642 }, "pairsMetThree": { "mean": 11.3504, "sd": 2.7695, "pGivenPair": 0.041125 }, "display": { "pStudentRepeated": ">99.99%", "meanDistinctPartners": "12.7" } } }, "byWeek": [ { "week": 1, "meanDistinctPartners": 1, "sdDistinctPartners": 0, "pStudentRepeated": 0, "shareOfClassMet": 0.043478, "circleDistinct": 1, "expectedRepeatsInWeek": 0, "expectedPairsMetTwice": 0 }, { "week": 2, "meanDistinctPartners": 1.9565, "sdDistinctPartners": 0.2039, "pStudentRepeated": 0.043478, "shareOfClassMet": 0.085066, "circleDistinct": 2, "expectedRepeatsInWeek": 0.5217, "expectedPairsMetTwice": 0.5217 }, { "week": 3, "meanDistinctPartners": 2.8715, "sdDistinctPartners": 0.3403, "pStudentRepeated": 0.126654, "shareOfClassMet": 0.124846, "circleDistinct": 3, "expectedRepeatsInWeek": 1.0208, "expectedPairsMetTwice": 1.5198 }, { "week": 4, "meanDistinctPartners": 3.7466, "sdDistinctPartners": 0.4637, "pStudentRepeated": 0.240569, "shareOfClassMet": 0.162896, "circleDistinct": 4, "expectedRepeatsInWeek": 1.4982, "expectedPairsMetTwice": 2.9519 }, { "week": 5, "meanDistinctPartners": 4.5837, "sdDistinctPartners": 0.5768, "pStudentRepeated": 0.372644, "shareOfClassMet": 0.199292, "circleDistinct": 5, "expectedRepeatsInWeek": 1.9548, "expectedPairsMetTwice": 4.7783 }, { "week": 6, "meanDistinctPartners": 5.3844, "sdDistinctPartners": 0.6807, "pStudentRepeated": 0.509026, "shareOfClassMet": 0.234105, "circleDistinct": 6, "expectedRepeatsInWeek": 2.3915, "expectedPairsMetTwice": 6.9621 }, { "week": 7, "meanDistinctPartners": 6.1503, "sdDistinctPartners": 0.7761, "pStudentRepeated": 0.637106, "shareOfClassMet": 0.267405, "circleDistinct": 7, "expectedRepeatsInWeek": 2.8093, "expectedPairsMetTwice": 9.4686 }, { "week": 8, "meanDistinctPartners": 6.8829, "sdDistinctPartners": 0.8636, "pStudentRepeated": 0.747552, "shareOfClassMet": 0.299257, "circleDistinct": 8, "expectedRepeatsInWeek": 3.2089, "expectedPairsMetTwice": 12.2658 }, { "week": 9, "meanDistinctPartners": 7.5837, "sdDistinctPartners": 0.9438, "pStudentRepeated": 0.83536, "shareOfClassMet": 0.329724, "circleDistinct": 9, "expectedRepeatsInWeek": 3.5911, "expectedPairsMetTwice": 15.3236 }, { "week": 10, "meanDistinctPartners": 8.2539, "sdDistinctPartners": 1.017, "pStudentRepeated": 0.899784, "shareOfClassMet": 0.358867, "circleDistinct": 10, "expectedRepeatsInWeek": 3.9567, "expectedPairsMetTwice": 18.6141 }, { "week": 11, "meanDistinctPartners": 8.8951, "sdDistinctPartners": 1.0837, "pStudentRepeated": 0.943356, "shareOfClassMet": 0.386742, "circleDistinct": 11, "expectedRepeatsInWeek": 4.3064, "expectedPairsMetTwice": 22.1111 }, { "week": 12, "meanDistinctPartners": 9.5083, "sdDistinctPartners": 1.1443, "pStudentRepeated": 0.970447, "shareOfClassMet": 0.413405, "circleDistinct": 12, "expectedRepeatsInWeek": 4.6409, "expectedPairsMetTwice": 25.7907 }, { "week": 13, "meanDistinctPartners": 10.0949, "sdDistinctPartners": 1.1992, "pStudentRepeated": 0.985866, "shareOfClassMet": 0.438909, "circleDistinct": 13, "expectedRepeatsInWeek": 4.9609, "expectedPairsMetTwice": 29.6302 }, { "week": 14, "meanDistinctPartners": 10.656, "sdDistinctPartners": 1.2487, "pStudentRepeated": 0.993855, "shareOfClassMet": 0.463305, "circleDistinct": 14, "expectedRepeatsInWeek": 5.2669, "expectedPairsMetTwice": 33.6089 }, { "week": 15, "meanDistinctPartners": 11.1927, "sdDistinctPartners": 1.2932, "pStudentRepeated": 0.997595, "shareOfClassMet": 0.486639, "circleDistinct": 15, "expectedRepeatsInWeek": 5.5597, "expectedPairsMetTwice": 37.7073 }, { "week": 16, "meanDistinctPartners": 11.7061, "sdDistinctPartners": 1.333, "pStudentRepeated": 0.999164, "shareOfClassMet": 0.508959, "circleDistinct": 16, "expectedRepeatsInWeek": 5.8397, "expectedPairsMetTwice": 41.9075 }, { "week": 17, "meanDistinctPartners": 12.1971, "sdDistinctPartners": 1.3683, "pStudentRepeated": 0.999745, "shareOfClassMet": 0.530309, "circleDistinct": 17, "expectedRepeatsInWeek": 6.1075, "expectedPairsMetTwice": 46.1929 }, { "week": 18, "meanDistinctPartners": 12.6668, "sdDistinctPartners": 1.3995, "pStudentRepeated": 0.999934, "shareOfClassMet": 0.55073, "circleDistinct": 18, "expectedRepeatsInWeek": 6.3637, "expectedPairsMetTwice": 50.5483 } ] } }, "25": { "size": { "classSize": 25, "mode": "size", "pPairTogether": 0.04, "pFirstRepeatAtWeek2": 0.381468, "checkpoints": { "4": { "weeks": 4, "meanDistinctPartners": 3.6157, "pStudentRepeated": 0.214057, "pStudentSingleAtLeastOnce": 0.150653, "display": { "pStudentRepeated": "21.4%", "meanDistinctPartners": "3.6" } }, "8": { "weeks": 8, "meanDistinctPartners": 6.6867, "pStudentRepeated": 0.694427, "pStudentSingleAtLeastOnce": 0.27861, "display": { "pStudentRepeated": "69.4%", "meanDistinctPartners": "6.7" } }, "12": { "weeks": 12, "meanDistinctPartners": 9.295, "pStudentRepeated": 0.948306, "pStudentSingleAtLeastOnce": 0.38729, "display": { "pStudentRepeated": "94.8%", "meanDistinctPartners": "9.3" } }, "18": { "weeks": 18, "meanDistinctPartners": 12.4895, "pStudentRepeated": 0.999484, "pStudentSingleAtLeastOnce": 0.520397, "display": { "pStudentRepeated": "99.95%", "meanDistinctPartners": "12.5" } } }, "byWeek": [ { "week": 1, "meanDistinctPartners": 0.96, "sdDistinctPartners": 0.196, "pStudentRepeated": 0, "shareOfClassMet": 0.04, "expectedRepeatsInWeek": 0 }, { "week": 2, "meanDistinctPartners": 1.8816, "sdDistinctPartners": 0.328, "pStudentRepeated": 0.0384, "shareOfClassMet": 0.0784, "expectedRepeatsInWeek": 0.48 }, { "week": 3, "meanDistinctPartners": 2.7663, "sdDistinctPartners": 0.4483, "pStudentRepeated": 0.112128, "shareOfClassMet": 0.115264, "expectedRepeatsInWeek": 0.9408 }, { "week": 4, "meanDistinctPartners": 3.6157, "sdDistinctPartners": 0.5593, "pStudentRepeated": 0.214057, "shareOfClassMet": 0.150653, "expectedRepeatsInWeek": 1.3832 }, { "week": 5, "meanDistinctPartners": 4.4311, "sdDistinctPartners": 0.6621, "pStudentRepeated": 0.334125, "shareOfClassMet": 0.184627, "expectedRepeatsInWeek": 1.8078 }, { "week": 6, "meanDistinctPartners": 5.2138, "sdDistinctPartners": 0.7572, "pStudentRepeated": 0.461013, "shareOfClassMet": 0.217242, "expectedRepeatsInWeek": 2.2155 }, { "week": 7, "meanDistinctPartners": 5.9653, "sdDistinctPartners": 0.8451, "pStudentRepeated": 0.583977, "shareOfClassMet": 0.248553, "expectedRepeatsInWeek": 2.6069 }, { "week": 8, "meanDistinctPartners": 6.6867, "sdDistinctPartners": 0.9263, "pStudentRepeated": 0.694427, "shareOfClassMet": 0.27861, "expectedRepeatsInWeek": 2.9826 }, { "week": 9, "meanDistinctPartners": 7.3792, "sdDistinctPartners": 1.0012, "pStudentRepeated": 0.786885, "shareOfClassMet": 0.307466, "expectedRepeatsInWeek": 3.3433 }, { "week": 10, "meanDistinctPartners": 8.044, "sdDistinctPartners": 1.0701, "pStudentRepeated": 0.859206, "shareOfClassMet": 0.335167, "expectedRepeatsInWeek": 3.6896 }, { "week": 11, "meanDistinctPartners": 8.6823, "sdDistinctPartners": 1.1333, "pStudentRepeated": 0.912114, "shareOfClassMet": 0.361761, "expectedRepeatsInWeek": 4.022 }, { "week": 12, "meanDistinctPartners": 9.295, "sdDistinctPartners": 1.1912, "pStudentRepeated": 0.948306, "shareOfClassMet": 0.38729, "expectedRepeatsInWeek": 4.3411 }, { "week": 13, "meanDistinctPartners": 9.8832, "sdDistinctPartners": 1.244, "pStudentRepeated": 0.971432, "shareOfClassMet": 0.411799, "expectedRepeatsInWeek": 4.6475 }, { "week": 14, "meanDistinctPartners": 10.4478, "sdDistinctPartners": 1.2921, "pStudentRepeated": 0.985212, "shareOfClassMet": 0.435327, "expectedRepeatsInWeek": 4.9416 }, { "week": 15, "meanDistinctPartners": 10.9899, "sdDistinctPartners": 1.3358, "pStudentRepeated": 0.992853, "shareOfClassMet": 0.457914, "expectedRepeatsInWeek": 5.2239 }, { "week": 16, "meanDistinctPartners": 11.5103, "sdDistinctPartners": 1.3752, "pStudentRepeated": 0.996786, "shareOfClassMet": 0.479597, "expectedRepeatsInWeek": 5.495 }, { "week": 17, "meanDistinctPartners": 12.0099, "sdDistinctPartners": 1.4106, "pStudentRepeated": 0.99866, "shareOfClassMet": 0.500413, "expectedRepeatsInWeek": 5.7552 }, { "week": 18, "meanDistinctPartners": 12.4895, "sdDistinctPartners": 1.4423, "pStudentRepeated": 0.999484, "shareOfClassMet": 0.520397, "expectedRepeatsInWeek": 6.005 } ] }, "teams": { "classSize": 25, "mode": "teams", "pPairTogether": 0.046667, "pFirstRepeatAtWeek2": 0.484385, "checkpoints": { "4": { "weeks": 4, "meanDistinctPartners": 4.176, "pStudentRepeated": 0.280759, "pStudentInTrioAtLeastOnce": 0.400305, "display": { "pStudentRepeated": "28.1%", "meanDistinctPartners": "4.2" } }, "8": { "weeks": 8, "meanDistinctPartners": 7.6254, "pStudentRepeated": 0.802517, "pStudentInTrioAtLeastOnce": 0.640365, "display": { "pStudentRepeated": "80.3%", "meanDistinctPartners": "7.6" } }, "12": { "weeks": 12, "meanDistinctPartners": 10.4746, "pStudentRepeated": 0.982954, "pStudentInTrioAtLeastOnce": 0.784329, "display": { "pStudentRepeated": "98.3%", "meanDistinctPartners": "10.5" } }, "18": { "weeks": 18, "meanDistinctPartners": 13.8465, "pStudentRepeated": 0.999977, "pStudentInTrioAtLeastOnce": 0.899841, "display": { "pStudentRepeated": ">99.99%", "meanDistinctPartners": "13.8" } } }, "byWeek": [ { "week": 1, "meanDistinctPartners": 1.12, "sdDistinctPartners": 0.325, "pStudentRepeated": 0, "shareOfClassMet": 0.046667, "expectedRepeatsInWeek": 0 }, { "week": 2, "meanDistinctPartners": 2.1877, "sdDistinctPartners": 0.491, "pStudentRepeated": 0.052214, "shareOfClassMet": 0.091156, "expectedRepeatsInWeek": 0.6533 }, { "week": 3, "meanDistinctPartners": 3.2056, "sdDistinctPartners": 0.6308, "pStudentRepeated": 0.150227, "shareOfClassMet": 0.133568, "expectedRepeatsInWeek": 1.2762 }, { "week": 4, "meanDistinctPartners": 4.176, "sdDistinctPartners": 0.7541, "pStudentRepeated": 0.280759, "shareOfClassMet": 0.174002, "expectedRepeatsInWeek": 1.87 }, { "week": 5, "meanDistinctPartners": 5.1012, "sdDistinctPartners": 0.8645, "pStudentRepeated": 0.42663, "shareOfClassMet": 0.212548, "expectedRepeatsInWeek": 2.436 }, { "week": 6, "meanDistinctPartners": 5.9831, "sdDistinctPartners": 0.9639, "pStudentRepeated": 0.570569, "shareOfClassMet": 0.249296, "expectedRepeatsInWeek": 2.9757 }, { "week": 7, "meanDistinctPartners": 6.8239, "sdDistinctPartners": 1.0535, "pStudentRepeated": 0.698672, "shareOfClassMet": 0.284329, "expectedRepeatsInWeek": 3.4901 }, { "week": 8, "meanDistinctPartners": 7.6254, "sdDistinctPartners": 1.1343, "pStudentRepeated": 0.802517, "shareOfClassMet": 0.317727, "expectedRepeatsInWeek": 3.9806 }, { "week": 9, "meanDistinctPartners": 8.3896, "sdDistinctPartners": 1.207, "pStudentRepeated": 0.879536, "shareOfClassMet": 0.349566, "expectedRepeatsInWeek": 4.4482 }, { "week": 10, "meanDistinctPartners": 9.1181, "sdDistinctPartners": 1.2722, "pStudentRepeated": 0.931873, "shareOfClassMet": 0.37992, "expectedRepeatsInWeek": 4.8939 }, { "week": 11, "meanDistinctPartners": 9.8126, "sdDistinctPartners": 1.3304, "pStudentRepeated": 0.964439, "shareOfClassMet": 0.408857, "expectedRepeatsInWeek": 5.3189 }, { "week": 12, "meanDistinctPartners": 10.4746, "sdDistinctPartners": 1.3823, "pStudentRepeated": 0.982954, "shareOfClassMet": 0.436444, "expectedRepeatsInWeek": 5.724 }, { "week": 13, "meanDistinctPartners": 11.1058, "sdDistinctPartners": 1.4282, "pStudentRepeated": 0.992542, "shareOfClassMet": 0.462743, "expectedRepeatsInWeek": 6.1102 }, { "week": 14, "meanDistinctPartners": 11.7076, "sdDistinctPartners": 1.4685, "pStudentRepeated": 0.997042, "shareOfClassMet": 0.487815, "expectedRepeatsInWeek": 6.4784 }, { "week": 15, "meanDistinctPartners": 12.2812, "sdDistinctPartners": 1.5037, "pStudentRepeated": 0.998945, "shareOfClassMet": 0.511717, "expectedRepeatsInWeek": 6.8294 }, { "week": 16, "meanDistinctPartners": 12.8281, "sdDistinctPartners": 1.5341, "pStudentRepeated": 0.999665, "shareOfClassMet": 0.534503, "expectedRepeatsInWeek": 7.164 }, { "week": 17, "meanDistinctPartners": 13.3494, "sdDistinctPartners": 1.5601, "pStudentRepeated": 0.999907, "shareOfClassMet": 0.556227, "expectedRepeatsInWeek": 7.483 }, { "week": 18, "meanDistinctPartners": 13.8465, "sdDistinctPartners": 1.5819, "pStudentRepeated": 0.999977, "shareOfClassMet": 0.576936, "expectedRepeatsInWeek": 7.7872 } ] } }, "30": { "size": { "classSize": 30, "mode": "size", "pPairTogether": 0.034483, "pFirstRepeatAtWeek2": 0.403646, "pFirstRepeatByWeek3": 0.791787, "displayFirstRepeatByWeek3": "79.2%", "checkpoints": { "4": { "weeks": 4, "meanDistinctPartners": 3.7978, "pStudentRepeated": 0.194063, "lostPartners": 0.2022, "pairsMetTwice": { "mean": 2.9626, "sd": 1.6011 }, "pairsMetThree": { "mean": 0.0695, "sd": 0.2638, "pGivenPair": 0.00016 }, "display": { "pStudentRepeated": "19.4%", "meanDistinctPartners": "3.8" } }, "8": { "weeks": 8, "meanDistinctPartners": 7.0983, "pStudentRepeated": 0.654052, "lostPartners": 0.9017, "pairsMetTwice": { "mean": 12.6096, "sd": 2.8659 }, "pairsMetThree": { "mean": 0.8766, "sd": 0.921, "pGivenPair": 0.002015 }, "display": { "pStudentRepeated": "65.4%", "meanDistinctPartners": "7.1" } }, "12": { "weeks": 12, "meanDistinctPartners": 9.9665, "pStudentRepeated": 0.929742, "lostPartners": 2.0335, "pairsMetTwice": { "mean": 27.1395, "sd": 3.6772 }, "pairsMetThree": { "mean": 3.1049, "sd": 1.6709, "pGivenPair": 0.007138 }, "display": { "pStudentRepeated": "93.0%", "meanDistinctPartners": "10.0" } }, "18": { "weeks": 18, "meanDistinctPartners": 13.5802, "pStudentRepeated": 0.998948, "lostPartners": 4.4198, "pairsMetTwice": { "mean": 55.0122, "sd": 4.3833 }, "pairsMetThree": { "mean": 9.8739, "sd": 2.7535, "pGivenPair": 0.022699 }, "display": { "pStudentRepeated": "99.89%", "meanDistinctPartners": "13.6" } } }, "byWeek": [ { "week": 1, "meanDistinctPartners": 1, "sdDistinctPartners": 0, "pStudentRepeated": 0, "shareOfClassMet": 0.034483, "circleDistinct": 1, "expectedRepeatsInWeek": 0, "expectedPairsMetTwice": 0 }, { "week": 2, "meanDistinctPartners": 1.9655, "sdDistinctPartners": 0.1825, "pStudentRepeated": 0.034483, "shareOfClassMet": 0.067776, "circleDistinct": 2, "expectedRepeatsInWeek": 0.5172, "expectedPairsMetTwice": 0.5172 }, { "week": 3, "meanDistinctPartners": 2.8977, "sdDistinctPartners": 0.3069, "pStudentRepeated": 0.10107, "shareOfClassMet": 0.099922, "circleDistinct": 3, "expectedRepeatsInWeek": 1.0166, "expectedPairsMetTwice": 1.5161 }, { "week": 4, "meanDistinctPartners": 3.7978, "sdDistinctPartners": 0.4215, "pStudentRepeated": 0.194063, "shareOfClassMet": 0.130959, "circleDistinct": 4, "expectedRepeatsInWeek": 1.4988, "expectedPairsMetTwice": 2.9626 }, { "week": 5, "meanDistinctPartners": 4.6669, "sdDistinctPartners": 0.5284, "pStudentRepeated": 0.305227, "shareOfClassMet": 0.160926, "circleDistinct": 5, "expectedRepeatsInWeek": 1.9644, "expectedPairsMetTwice": 4.8248 }, { "week": 6, "meanDistinctPartners": 5.5059, "sdDistinctPartners": 0.6285, "pStudentRepeated": 0.425015, "shareOfClassMet": 0.18986, "circleDistinct": 6, "expectedRepeatsInWeek": 2.4139, "expectedPairsMetTwice": 7.0724 }, { "week": 7, "meanDistinctPartners": 6.3161, "sdDistinctPartners": 0.7222, "pStudentRepeated": 0.543978, "shareOfClassMet": 0.217796, "circleDistinct": 7, "expectedRepeatsInWeek": 2.8479, "expectedPairsMetTwice": 9.6764 }, { "week": 8, "meanDistinctPartners": 7.0983, "sdDistinctPartners": 0.8099, "pStudentRepeated": 0.654052, "shareOfClassMet": 0.244768, "circleDistinct": 8, "expectedRepeatsInWeek": 3.2669, "expectedPairsMetTwice": 12.6096 }, { "week": 9, "meanDistinctPartners": 7.8535, "sdDistinctPartners": 0.8919, "pStudentRepeated": 0.749486, "shareOfClassMet": 0.270811, "circleDistinct": 9, "expectedRepeatsInWeek": 3.6715, "expectedPairsMetTwice": 15.8464 }, { "week": 10, "meanDistinctPartners": 8.5827, "sdDistinctPartners": 0.9686, "pStudentRepeated": 0.827232, "shareOfClassMet": 0.295955, "circleDistinct": 10, "expectedRepeatsInWeek": 4.0622, "expectedPairsMetTwice": 19.3621 }, { "week": 11, "meanDistinctPartners": 9.2867, "sdDistinctPartners": 1.0401, "pStudentRepeated": 0.886807, "shareOfClassMet": 0.320233, "circleDistinct": 11, "expectedRepeatsInWeek": 4.4393, "expectedPairsMetTwice": 23.1338 }, { "week": 12, "meanDistinctPartners": 9.9665, "sdDistinctPartners": 1.1067, "pStudentRepeated": 0.929742, "shareOfClassMet": 0.343673, "circleDistinct": 12, "expectedRepeatsInWeek": 4.8035, "expectedPairsMetTwice": 27.1395 }, { "week": 13, "meanDistinctPartners": 10.6228, "sdDistinctPartners": 1.1688, "pStudentRepeated": 0.958814, "shareOfClassMet": 0.366305, "circleDistinct": 13, "expectedRepeatsInWeek": 5.1551, "expectedPairsMetTwice": 31.3588 }, { "week": 14, "meanDistinctPartners": 11.2565, "sdDistinctPartners": 1.2263, "pStudentRepeated": 0.977277, "shareOfClassMet": 0.388156, "circleDistinct": 14, "expectedRepeatsInWeek": 5.4946, "expectedPairsMetTwice": 35.772 }, { "week": 15, "meanDistinctPartners": 11.8684, "sdDistinctPartners": 1.2797, "pStudentRepeated": 0.988247, "shareOfClassMet": 0.409254, "circleDistinct": 15, "expectedRepeatsInWeek": 5.8223, "expectedPairsMetTwice": 40.3608 }, { "week": 16, "meanDistinctPartners": 12.4591, "sdDistinctPartners": 1.3291, "pStudentRepeated": 0.994326, "shareOfClassMet": 0.429625, "circleDistinct": 16, "expectedRepeatsInWeek": 6.1388, "expectedPairsMetTwice": 45.1079 }, { "week": 17, "meanDistinctPartners": 13.0295, "sdDistinctPartners": 1.3747, "pStudentRepeated": 0.997456, "shareOfClassMet": 0.449293, "circleDistinct": 17, "expectedRepeatsInWeek": 6.4444, "expectedPairsMetTwice": 49.9968 }, { "week": 18, "meanDistinctPartners": 13.5802, "sdDistinctPartners": 1.4166, "pStudentRepeated": 0.998948, "shareOfClassMet": 0.468283, "circleDistinct": 18, "expectedRepeatsInWeek": 6.7394, "expectedPairsMetTwice": 55.0122 } ] } } } }, "regenerateLastWeek": { "note": "Press Generate until no pair from last week is together again. Presses are geometric with success chance p = pNoRepeat per press: mean 1/p, P(done in 1 press) = p, P(more than 3 presses) = (1-p)^3.", "bySize": { "16": { "size": { "pPerPress": 0.587399, "meanPresses": 1.7024, "sdPresses": 1.0935, "pDoneFirstPress": 0.587399, "pMoreThan3": 0.070241, "display": { "meanPresses": "1.70", "pMoreThan3": "7.0%" } } }, "20": { "size": { "pPerPress": 0.591237, "meanPresses": 1.6914, "sdPresses": 1.0814, "pDoneFirstPress": 0.591237, "pMoreThan3": 0.068299, "display": { "meanPresses": "1.69", "pMoreThan3": "6.8%" } } }, "24": { "size": { "pPerPress": 0.593796, "meanPresses": 1.6841, "sdPresses": 1.0733, "pDoneFirstPress": 0.593796, "pMoreThan3": 0.067024, "display": { "meanPresses": "1.68", "pMoreThan3": "6.7%" } } }, "25": { "size": { "pPerPress": 0.618532, "meanPresses": 1.6167, "sdPresses": 0.9985, "pDoneFirstPress": 0.618532, "pMoreThan3": 0.05551, "display": { "meanPresses": "1.62", "pMoreThan3": "5.6%" } }, "teams": { "pPerPress": 0.515615, "meanPresses": 1.9394, "sdPresses": 1.3498, "pDoneFirstPress": 0.515615, "pMoreThan3": 0.11365, "display": { "meanPresses": "1.94", "pMoreThan3": "11.4%" } } }, "30": { "size": { "pPerPress": 0.596354, "meanPresses": 1.6769, "sdPresses": 1.0654, "pDoneFirstPress": 0.596354, "pMoreThan3": 0.065766, "display": { "meanPresses": "1.68", "pMoreThan3": "6.6%" } } } } }, "regenerateAllWeeks": { "note": "Week 2 is exact and equals regenerateLastWeek (only week 1's pairs to avoid). Later weeks depend on which pairs have already met, so the expected presses are computed exactly for each simulated class's own history (1/p, p = repeat-free pairings left / all pairings) and summarized in results.regenerateAllWeeks (simulation over histories). Two weeks are exact whatever the history: in week n-1 (if it can be reached) exactly one repeat-free pairing is left, so pressing takes (n-1)!! presses on average (lastWeekPresses = totalPairings); in week n-2 the pairs not yet met form loops (every student has exactly two unmet classmates), and a repeat-free pairing exists only if every loop has an even number of students, so a class can reach a dead end there however many times it presses. Up to week n/2 a dead end is impossible whatever the history (every student still has at least n/2 classmates not yet met, so by Dirac's theorem the not-yet-met graph has a Hamiltonian cycle and hence a repeat-free pairing): noDeadEndUpToWeek. Between week n/2 + 1 and week n-3 a dead end is also possible, but rare: the unmet pairs must then form one of the uncommon patterns that have no repeat-free pairing without being made of loops. How often dead ends happen, and in which weeks, is simulation only (results.regenerateAllWeeks.bySize[n].deadEnd). A round-robin schedule reaches n-1 weeks with no repeat by construction.", "bySize": { "16": { "totalPairings": 2027025, "totalPairingsDisplay": "2,027,025", "week2MeanPresses": 1.7024, "lastWeek": 15, "lastWeekPresses": 2027025, "noDeadEndUpToWeek": 8, "loopDeadEndWeek": 14, "roundRobinWeeks": 15 }, "20": { "totalPairings": 654729075, "totalPairingsDisplay": "654,729,075", "week2MeanPresses": 1.6914, "lastWeek": 19, "lastWeekPresses": 654729075, "noDeadEndUpToWeek": 10, "loopDeadEndWeek": 18, "roundRobinWeeks": 19 }, "24": { "totalPairings": 316234143225, "totalPairingsDisplay": "316,234,143,225", "week2MeanPresses": 1.6841, "lastWeek": 23, "lastWeekPresses": 316234143225, "noDeadEndUpToWeek": 12, "loopDeadEndWeek": 22, "roundRobinWeeks": 23 } } }, "circle": { "note": "Round-robin by the circle method. Even class of n: seat everyone, keep the last seat fixed and rotate the other n-1 seats one step each week; in week r (r = 0..n-2) seat n-1 pairs with seat r and seat (r+i) mod (n-1) pairs with seat (r-i) mod (n-1), i = 1..n/2-1. Every two students are partners exactly once in n-1 weeks (verified for every even class up to 64). Odd class: add an empty seat (the 'bye'); n weeks, each student has the bye exactly once (sits out, works with the teacher, or joins a pair as a trio). Random start: shuffle the names once (for example with Shuffle on a wheel page, or by reading the order off one press of Generate on the team generator, which has no Shuffle button), then apply the rotation to the shuffled order: every week on its own is a uniformly random pairing, each two students meet in a uniformly random week 1..n-1, and no one repeats a partner until week n-1 has passed. It is less random than pressing fresh each week: the shuffle only relabels one fixed round-robin, so the weeks are not independent of each other and not every repeat-free schedule is equally likely. trio = odd classes where the bye student joins a pair each week instead of sitting out: greedyRuleWeeksWithoutRepeat is how many weeks the simple rule in the script (trioHorizon) keeps every meeting new. It is NOT the most possible: the exhaustive search in the script finds an all-new 6-week trio schedule for 9 students (trioBetterThanRule9), where the rule gets 3; countingUpperBound = floor(C(n,2) / ((n+3)/2)) is a ceiling no trio schedule can pass. The safe statement for odd classes is the bye seat: n weeks with all-new partners, each student having the bye once.", "verifiedEvenSeatsUpTo": 64, "example8": [ { "week": 1, "pairs": [ [ "A", "H" ], [ "B", "G" ], [ "C", "F" ], [ "D", "E" ] ] }, { "week": 2, "pairs": [ [ "B", "H" ], [ "C", "A" ], [ "D", "G" ], [ "E", "F" ] ] }, { "week": 3, "pairs": [ [ "C", "H" ], [ "D", "B" ], [ "E", "A" ], [ "F", "G" ] ] }, { "week": 4, "pairs": [ [ "D", "H" ], [ "E", "C" ], [ "F", "B" ], [ "G", "A" ] ] }, { "week": 5, "pairs": [ [ "E", "H" ], [ "F", "D" ], [ "G", "C" ], [ "A", "B" ] ] }, { "week": 6, "pairs": [ [ "F", "H" ], [ "G", "E" ], [ "A", "D" ], [ "B", "C" ] ] }, { "week": 7, "pairs": [ [ "G", "H" ], [ "A", "F" ], [ "B", "E" ], [ "C", "D" ] ] } ], "example7": [ { "week": 1, "pairs": [ [ "A", "(bye)" ], [ "B", "G" ], [ "C", "F" ], [ "D", "E" ] ] }, { "week": 2, "pairs": [ [ "B", "(bye)" ], [ "C", "A" ], [ "D", "G" ], [ "E", "F" ] ] }, { "week": 3, "pairs": [ [ "C", "(bye)" ], [ "D", "B" ], [ "E", "A" ], [ "F", "G" ] ] }, { "week": 4, "pairs": [ [ "D", "(bye)" ], [ "E", "C" ], [ "F", "B" ], [ "G", "A" ] ] }, { "week": 5, "pairs": [ [ "E", "(bye)" ], [ "F", "D" ], [ "G", "C" ], [ "A", "B" ] ] }, { "week": 6, "pairs": [ [ "F", "(bye)" ], [ "G", "E" ], [ "A", "D" ], [ "B", "C" ] ] }, { "week": 7, "pairs": [ [ "G", "(bye)" ], [ "A", "F" ], [ "B", "E" ], [ "C", "D" ] ] } ], "trio": [ { "n": 5, "weeksWithBye": 5, "greedyRuleWeeksWithoutRepeat": 1, "countingUpperBound": 2 }, { "n": 7, "weeksWithBye": 7, "greedyRuleWeeksWithoutRepeat": 3, "countingUpperBound": 4 }, { "n": 9, "weeksWithBye": 9, "greedyRuleWeeksWithoutRepeat": 3, "countingUpperBound": 6 }, { "n": 11, "weeksWithBye": 11, "greedyRuleWeeksWithoutRepeat": 5, "countingUpperBound": 7 }, { "n": 13, "weeksWithBye": 13, "greedyRuleWeeksWithoutRepeat": 5, "countingUpperBound": 9 }, { "n": 15, "weeksWithBye": 15, "greedyRuleWeeksWithoutRepeat": 7, "countingUpperBound": 11 }, { "n": 17, "weeksWithBye": 17, "greedyRuleWeeksWithoutRepeat": 7, "countingUpperBound": 13 }, { "n": 19, "weeksWithBye": 19, "greedyRuleWeeksWithoutRepeat": 9, "countingUpperBound": 15 }, { "n": 21, "weeksWithBye": 21, "greedyRuleWeeksWithoutRepeat": 9, "countingUpperBound": 17 }, { "n": 23, "weeksWithBye": 23, "greedyRuleWeeksWithoutRepeat": 11, "countingUpperBound": 19 }, { "n": 25, "weeksWithBye": 25, "greedyRuleWeeksWithoutRepeat": 11, "countingUpperBound": 21 }, { "n": 27, "weeksWithBye": 27, "greedyRuleWeeksWithoutRepeat": 13, "countingUpperBound": 23 }, { "n": 29, "weeksWithBye": 29, "greedyRuleWeeksWithoutRepeat": 13, "countingUpperBound": 25 }, { "n": 31, "weeksWithBye": 31, "greedyRuleWeeksWithoutRepeat": 15, "countingUpperBound": 27 }, { "n": 33, "weeksWithBye": 33, "greedyRuleWeeksWithoutRepeat": 15, "countingUpperBound": 29 }, { "n": 35, "weeksWithBye": 35, "greedyRuleWeeksWithoutRepeat": 17, "countingUpperBound": 31 }, { "n": 37, "weeksWithBye": 37, "greedyRuleWeeksWithoutRepeat": 17, "countingUpperBound": 33 }, { "n": 39, "weeksWithBye": 39, "greedyRuleWeeksWithoutRepeat": 19, "countingUpperBound": 35 }, { "n": 41, "weeksWithBye": 41, "greedyRuleWeeksWithoutRepeat": 19, "countingUpperBound": 37 } ], "trioBetterThanRule9": { "note": "A 6-week all-new schedule (one trio + three pairs each week) for 9 students, found by exhaustive search in the script; the simple rule gets 3 weeks, and 6 is the counting ceiling for 9.", "n": 9, "weeks": 6, "schedule": [ { "week": 1, "groups": [ [ "A", "B", "C" ], [ "D", "E" ], [ "F", "G" ], [ "H", "I" ] ] }, { "week": 2, "groups": [ [ "A", "D", "F" ], [ "B", "H" ], [ "C", "I" ], [ "E", "G" ] ] }, { "week": 3, "groups": [ [ "B", "E", "I" ], [ "A", "G" ], [ "C", "F" ], [ "D", "H" ] ] }, { "week": 4, "groups": [ [ "C", "G", "H" ], [ "A", "E" ], [ "B", "D" ], [ "F", "I" ] ] }, { "week": 5, "groups": [ [ "D", "G", "I" ], [ "A", "H" ], [ "B", "F" ], [ "C", "E" ] ] }, { "week": 6, "groups": [ [ "E", "F", "H" ], [ "A", "I" ], [ "B", "G" ], [ "C", "D" ] ] } ] }, "pMeetInWeek1": { "16": { "exact": 0.066667, "fraction": "1/15" }, "24": { "exact": 0.043478, "fraction": "1/23" } }, "pMeetWithin12Weeks": { "16": { "exact": 0.8, "fraction": "4/5" }, "24": { "exact": 0.521739, "fraction": "12/23" } } }, "summaryTable": { "note": "Exact values. Even sizes, People per team 2 (same as Number of teams n/2). distinct12 = expected different partners after 12 weekly random pairings (a round-robin gives 12). pRepeated12 = P(a given student has had the same partner twice within 12 weeks). pairsMetTwice12 = expected number of pairs in the class who have worked together 2+ times after 12 weeks.", "rows": [ { "classSize": 16, "pAtLeastOneRepeatNextWeek": 0.412601, "expectedRepeatsNextWeek": 0.5333, "expectedPressesNoRepeat": 1.7024, "distinct12": 8.4456, "pRepeated8": 0.898763, "pRepeated12": 0.99832, "pairsMetTwice12": 22.6204, "roundRobinWeeks": 15, "display": { "pAtLeastOneRepeatNextWeek": "41.3%", "expectedRepeatsNextWeek": "0.53", "expectedPressesNoRepeat": "1.70", "distinct12": "8.4", "pRepeated8": "89.9%", "pRepeated12": "99.8%", "pairsMetTwice12": "22.6" } }, { "classSize": 20, "pAtLeastOneRepeatNextWeek": 0.408763, "expectedRepeatsNextWeek": 0.5263, "expectedPressesNoRepeat": 1.6914, "distinct12": 9.0693, "pRepeated8": 0.820564, "pRepeated12": 0.989095, "pairsMetTwice12": 24.4881, "roundRobinWeeks": 19, "display": { "pAtLeastOneRepeatNextWeek": "40.9%", "expectedRepeatsNextWeek": "0.53", "expectedPressesNoRepeat": "1.69", "distinct12": "9.1", "pRepeated8": "82.1%", "pRepeated12": "98.9%", "pairsMetTwice12": "24.5" } }, { "classSize": 24, "pAtLeastOneRepeatNextWeek": 0.406204, "expectedRepeatsNextWeek": 0.5217, "expectedPressesNoRepeat": 1.6841, "distinct12": 9.5083, "pRepeated8": 0.747552, "pRepeated12": 0.970447, "pairsMetTwice12": 25.7907, "roundRobinWeeks": 23, "display": { "pAtLeastOneRepeatNextWeek": "40.6%", "expectedRepeatsNextWeek": "0.52", "expectedPressesNoRepeat": "1.68", "distinct12": "9.5", "pRepeated8": "74.8%", "pRepeated12": "97.0%", "pairsMetTwice12": "25.8" } }, { "classSize": 30, "pAtLeastOneRepeatNextWeek": 0.403646, "expectedRepeatsNextWeek": 0.5172, "expectedPressesNoRepeat": 1.6769, "distinct12": 9.9665, "pRepeated8": 0.654052, "pRepeated12": 0.929742, "pairsMetTwice12": 27.1395, "roundRobinWeeks": 29, "display": { "pAtLeastOneRepeatNextWeek": "40.4%", "expectedRepeatsNextWeek": "0.52", "expectedPressesNoRepeat": "1.68", "distinct12": "10.0", "pRepeated8": "65.4%", "pRepeated12": "93.0%", "pairsMetTwice12": "27.1" } } ] }, "charts": { "distinctPartners": { "note": "Class of 24: expected different partners after w weeks, random every week (exact) vs a round-robin schedule (w). Simulated column in results.charts.", "rows": [ { "week": 1, "random": 1, "roundRobin": 1 }, { "week": 2, "random": 1.9565, "roundRobin": 2 }, { "week": 3, "random": 2.8715, "roundRobin": 3 }, { "week": 4, "random": 3.7466, "roundRobin": 4 }, { "week": 5, "random": 4.5837, "roundRobin": 5 }, { "week": 6, "random": 5.3844, "roundRobin": 6 }, { "week": 7, "random": 6.1503, "roundRobin": 7 }, { "week": 8, "random": 6.8829, "roundRobin": 8 }, { "week": 9, "random": 7.5837, "roundRobin": 9 }, { "week": 10, "random": 8.2539, "roundRobin": 10 }, { "week": 11, "random": 8.8951, "roundRobin": 11 }, { "week": 12, "random": 9.5083, "roundRobin": 12 }, { "week": 13, "random": 10.0949, "roundRobin": 13 }, { "week": 14, "random": 10.656, "roundRobin": 14 }, { "week": 15, "random": 11.1927, "roundRobin": 15 }, { "week": 16, "random": 11.7061, "roundRobin": 16 }, { "week": 17, "random": 12.1971, "roundRobin": 17 }, { "week": 18, "random": 12.6668, "roundRobin": 18 } ] }, "repeatsPerWeek": { "note": "Class of 24: expected number of this week's 12 pairs who already worked together in an earlier week (exact).", "rows": [ { "week": 1, "exact": 0 }, { "week": 2, "exact": 0.5217 }, { "week": 3, "exact": 1.0208 }, { "week": 4, "exact": 1.4982 }, { "week": 5, "exact": 1.9548 }, { "week": 6, "exact": 2.3915 }, { "week": 7, "exact": 2.8093 }, { "week": 8, "exact": 3.2089 }, { "week": 9, "exact": 3.5911 }, { "week": 10, "exact": 3.9567 }, { "week": 11, "exact": 4.3064 }, { "week": 12, "exact": 4.6409 }, { "week": 13, "exact": 4.9609 }, { "week": 14, "exact": 5.2669 }, { "week": 15, "exact": 5.5597 }, { "week": 16, "exact": 5.8397 }, { "week": 17, "exact": 6.1075 }, { "week": 18, "exact": 6.3637 } ] } } }, "results": { "nextWeek": { "bySize": { "16": { "size": { "weekPairs": 306000, "terms": 18000, "pAtLeastOneRepeat": 0.412725, "expectedRepeats": 0.5323, "pPairTogether": 0.066302, "distribution": [ { "repeats": 0, "simulated": 0.587275 }, { "repeats": 1, "simulated": 0.312493 }, { 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0.001967 }, { "repeats": 5, "simulated": 0.000209 }, { "repeats": 6, "simulated": 0.00001 }, { "repeats": 7, "simulated": 0.000007 } ] }, "teams": { "weekPairs": 85000, "terms": 5000, "pAtLeastOneRepeat": 0.411059, "expectedRepeats": 0.5306, "pPairTogether": 0.051889, "distribution": [ { "repeats": 0, "simulated": 0.588941 }, { "repeats": 1, "simulated": 0.311141 }, { "repeats": 2, "simulated": 0.082847 }, { "repeats": 3, "simulated": 0.014753 }, { "repeats": 4, "simulated": 0.002047 }, { "repeats": 5, "simulated": 0.000259 }, { "repeats": 6, "simulated": 0.000012 }, { "repeats": 7, "simulated": 0 } ] } }, "24": { "size": { "weekPairs": 442000, "terms": 26000, "pAtLeastOneRepeat": 0.407231, "expectedRepeats": 0.5221, "pPairTogether": 0.043271, "distribution": [ { "repeats": 0, "simulated": 0.592769 }, { "repeats": 1, "simulated": 0.310851 }, { "repeats": 2, "simulated": 0.080036 }, { "repeats": 3, "simulated": 0.014357 }, { "repeats": 4, "simulated": 0.001803 }, { "repeats": 5, 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"se": 0.0127 }, { "week": 7, "repeatsInWeek": 2.8317, "se": 0.0135 }, { "week": 8, "repeatsInWeek": 3.2689, "se": 0.0143 }, { "week": 9, "repeatsInWeek": 3.6479, "se": 0.0148 }, { "week": 10, "repeatsInWeek": 4.0812, "se": 0.0155 }, { "week": 11, "repeatsInWeek": 4.4513, "se": 0.0157 }, { "week": 12, "repeatsInWeek": 4.8079, "se": 0.0159 }, { "week": 13, "repeatsInWeek": 5.1684, "se": 0.0165 }, { "week": 14, "repeatsInWeek": 5.5161, "se": 0.0165 }, { "week": 15, "repeatsInWeek": 5.8398, "se": 0.0168 }, { "week": 16, "repeatsInWeek": 6.152, "se": 0.017 }, { "week": 17, "repeatsInWeek": 6.4578, "se": 0.017 }, { "week": 18, "repeatsInWeek": 6.7668, "se": 0.0171 } ], "firstRepeatWeek": { "simulationOnly": "beyond week 3", "rows": [ { "week": 2, "simulated": 0.396231, "cumulative": 0.396231 }, { "week": 3, "simulated": 0.389846, "cumulative": 0.786077 }, { "week": 4, "simulated": 0.171692, "cumulative": 0.957769 }, { "week": 5, "simulated": 0.036231, "cumulative": 0.994 }, { "week": 6, "simulated": 0.005538, "cumulative": 0.999538 }, { "week": 7, "simulated": 0.000462, "cumulative": 1 } ], "meanWeekGivenARepeat": 2.866, "pNoRepeatWithinTerm": 0 } }, "teams": { "terms": 4000, "checkpoints": { "4": { "weeks": 4, "meanDistinctPartnersStudent1": 3.7935, "meanDistinctPartnersClass": 3.795, "pStudentRepeatedStudent1": 0.2, "shareOfStudentsRepeated": 0.19675, "pairsMetTwice": 3.003, "pairsMetThree": 0.072, "pSomePairMetThreePlus": 0.07, "pSomePairMetThreePlusSimulationOnly": true }, "8": { "weeks": 8, "meanDistinctPartnersStudent1": 7.0697, "meanDistinctPartnersClass": 7.0963, "pStudentRepeatedStudent1": 0.6675, "shareOfStudentsRepeated": 0.655742, "pairsMetTwice": 12.638, "pairsMetThree": 0.8748, "pSomePairMetThreePlus": 0.59525, "pSomePairMetThreePlusSimulationOnly": true }, "12": { "weeks": 12, "meanDistinctPartnersStudent1": 9.95, "meanDistinctPartnersClass": 9.9606, "pStudentRepeatedStudent1": 0.92725, "shareOfStudentsRepeated": 0.930633, "pairsMetTwice": 27.1908, "pairsMetThree": 3.1225, "pSomePairMetThreePlus": 0.9625, "pSomePairMetThreePlusSimulationOnly": true }, "18": { "weeks": 18, "meanDistinctPartnersStudent1": 13.5898, "meanDistinctPartnersClass": 13.5761, "pStudentRepeatedStudent1": 0.99875, "shareOfStudentsRepeated": 0.99895, "pairsMetTwice": 55.0333, "pairsMetThree": 9.8745, "pSomePairMetThreePlus": 1, "pSomePairMetThreePlusSimulationOnly": true } }, "weekly": [ { "week": 1, "repeatsInWeek": 0, "se": 0 }, { "week": 2, "repeatsInWeek": 0.5323, "se": 0.0115 }, { "week": 3, "repeatsInWeek": 1.0353, "se": 0.0156 }, { "week": 4, "repeatsInWeek": 1.508, "se": 0.0184 }, { "week": 5, "repeatsInWeek": 1.9748, "se": 0.021 }, { "week": 6, "repeatsInWeek": 2.4453, "se": 0.0229 }, { "week": 7, "repeatsInWeek": 2.828, "se": 0.0246 }, { "week": 8, "repeatsInWeek": 3.2325, "se": 0.0253 }, { "week": 9, "repeatsInWeek": 3.6435, "se": 0.0268 }, { "week": 10, "repeatsInWeek": 4.078, "se": 0.0278 }, { "week": 11, "repeatsInWeek": 4.49, "se": 0.0282 }, { "week": 12, "repeatsInWeek": 4.8232, "se": 0.0289 }, { "week": 13, "repeatsInWeek": 5.1718, "se": 0.03 }, { "week": 14, "repeatsInWeek": 5.512, "se": 0.0296 }, { "week": 15, "repeatsInWeek": 5.7495, "se": 0.0302 }, { "week": 16, "repeatsInWeek": 6.1322, "se": 0.0303 }, { "week": 17, "repeatsInWeek": 6.4612, "se": 0.0305 }, { "week": 18, "repeatsInWeek": 6.7412, "se": 0.031 } ], "firstRepeatWeek": { "simulationOnly": "beyond week 3", "rows": [ { "week": 2, "simulated": 0.41325, "cumulative": 0.41325 }, { "week": 3, "simulated": 0.39075, "cumulative": 0.804 }, { "week": 4, "simulated": 0.15375, "cumulative": 0.95775 }, { "week": 5, "simulated": 0.036, "cumulative": 0.99375 }, { "week": 6, "simulated": 0.006, "cumulative": 0.99975 }, { "week": 8, "simulated": 0.00025, "cumulative": 1 } ], "meanWeekGivenARepeat": 2.832, "pNoRepeatWithinTerm": 0 } } } } }, "regenerateLastWeek": { "bySize": { "16": { "size": { "experiments": 15000, "meanPresses": 1.6961, "pDoneFirstPress": 0.593, "pMoreThan3": 0.071, "mostPressesSeen": 12 } }, "20": { "size": { "experiments": 15000, "meanPresses": 1.6786, "pDoneFirstPress": 0.595133, "pMoreThan3": 0.066, "mostPressesSeen": 13 } }, "24": { "size": { "experiments": 40000, "meanPresses": 1.6858, "pDoneFirstPress": 0.590975, "pMoreThan3": 0.0677, "mostPressesSeen": 15 } }, "25": { "size": { "experiments": 12000, "meanPresses": 1.6116, "pDoneFirstPress": 0.619333, "pMoreThan3": 0.05375, "mostPressesSeen": 9 }, "teams": { "experiments": 12000, "meanPresses": 1.9228, "pDoneFirstPress": 0.519833, "pMoreThan3": 0.108333, "mostPressesSeen": 14 } }, "30": { "size": { "experiments": 15000, "meanPresses": 1.6985, "pDoneFirstPress": 0.589533, "pMoreThan3": 0.069467, "mostPressesSeen": 13 } } } }, "regenerateAllWeeks": { "note": "simulationOnly except the checks listed. pressesSimulated = presses actually simulated through random.js (detail classes: weeks 2..pressUpTo; fast classes: weeks 2..fastPressUpTo). expectedPresses = 1/p computed exactly for each simulated class's own history, summarized over the classes counted that week (detail classes from week 2, all classes from week fastPressUpTo + 1): median, mean, 10th and 90th percentile. deadEnd = classes for which NO repeat-free pairing exists that week (pressing could never succeed); share is simulated over all classes, with its standard error. Dead ends were looked for in every week where one is possible (from week n/2 + 1); deadEnd.byWeek gives the weeks in which the simulated dead ends happened and deadEnd.allInWeekNMinus2 says whether all of them came in week n-2. That is an observation of this run, not a theorem: earlier dead ends are possible but rare. reachedWeek = share of classes that got an all-new pairing in that week.", "bySize": { "16": { "simulationOnly": true, "classes": 6000, "detailClasses": 300, "pressUpTo": 9, "fastPressUpTo": 5, "pressFallbacks": 0, "completedAllWeeks": 3925, "pCompletedAllWeeks": 0.654167, "deadEnd": { "classes": 2075, "outOf": 6000, "share": 0.345833, "se": 0.00614, "allInWeekNMinus2": true, "earliestWeek": 14, "medianWeek": 14, "latestWeek": 14, "byWeek": [ { "week": 14, "share": 0.345833 } ], "display": { "share": "34.6%", "shareWhole": "35%", "range95": "33% to 36%", "classes": "6,000" } }, "firstWeekMedianPressesOver": { "10": 5, "100": 8, "1000": 11, "10000": 12, "100000": 13, "1000000": 14 }, "rows": [ { "week": 1, "classesStarted": 6000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 6000, "mean": 1, "median": 1, "p90": 1, "most": 1 } }, { "week": 2, "classesStarted": 6000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 6000, "mean": 1.705, "median": 1, "p90": 3, "most": 11 }, "expectedPresses": { "classes": 300, "median": 1.7, "mean": 1.7, "p10": 1.7, "p90": 1.7, "display": "1.7" } }, { "week": 3, "classesStarted": 6000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 6000, "mean": 3.027, "median": 2, "p90": 6, "most": 28 }, "expectedPresses": { "classes": 300, "median": 3.01, "mean": 3.01, "p10": 3.01, "p90": 3.01, "display": "3.0" } }, { "week": 4, "classesStarted": 6000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 6000, "mean": 5.588, "median": 4, "p90": 12, "most": 43 }, "expectedPresses": { "classes": 300, "median": 5.56, "mean": 5.56, "p10": 5.55, "p90": 5.56, "display": "5.6" } }, { "week": 5, "classesStarted": 6000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 6000, "mean": 10.789, "median": 8, "p90": 24, "most": 104 }, "expectedPresses": { "classes": 300, "median": 10.8, "mean": 10.8, "p10": 10.77, "p90": 10.82, "display": "11" } }, { "week": 6, "classesStarted": 6000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 300, "mean": 22.757, "median": 16, "p90": 48, "most": 101 }, "expectedPresses": { "classes": 6000, "median": 22.27, "mean": 22.26, "p10": 22.18, "p90": 22.34, "display": "22" } }, { "week": 7, "classesStarted": 6000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 300, "mean": 50.74, "median": 34, "p90": 114, "most": 252 }, "expectedPresses": { "classes": 6000, "median": 49.32, "mean": 49.31, "p10": 48.99, "p90": 49.61, "display": "49" } }, { "week": 8, "classesStarted": 6000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 300, "mean": 115.127, "median": 86, "p90": 248, "most": 837 }, "expectedPresses": { "classes": 6000, "median": 119.21, "mean": 119.13, "p10": 117.85, "p90": 120.31, "display": "119" } }, { "week": 9, "classesStarted": 6000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 300, "mean": 316.747, "median": 222, "p90": 661, "most": 3140 }, "expectedPresses": { "classes": 6000, "median": 321.04, "mean": 320.6, "p10": 315, "p90": 325.89, "display": "321" } }, { "week": 10, "classesStarted": 6000, "reachedWeek": 1, "deadEndThisWeek": 0, "expectedPresses": { "classes": 6000, "median": 991.7, "mean": 990.1, "p10": 960.68, "p90": 1016.56, "display": "992" } }, { "week": 11, "classesStarted": 6000, "reachedWeek": 1, "deadEndThisWeek": 0, "expectedPresses": { "classes": 6000, "median": 3672.15, "mean": 3662.82, "p10": 3465, "p90": 3846.35, "display": "3,672" } }, { "week": 12, "classesStarted": 6000, "reachedWeek": 1, "deadEndThisWeek": 0, "expectedPresses": { "classes": 6000, "median": 17474.35, "mean": 17357.36, "p10": 15356.25, "p90": 19122.88, "display": "17,474" } }, { "week": 13, "classesStarted": 6000, "reachedWeek": 1, "deadEndThisWeek": 0, "expectedPresses": { "classes": 6000, "median": 119236.76, "mean": 118982.51, "p10": 92137.5, "p90": 144787.5, "display": "119,237" } }, { "week": 14, "classesStarted": 6000, "reachedWeek": 0.654167, "deadEndThisWeek": 0.345833, "expectedPresses": { "classes": 3925, "median": 1013512.5, "mean": 872363.13, "p10": 506756.25, "p90": 1013512.5, "display": "1,013,513" } }, { "week": 15, "classesStarted": 6000, "reachedWeek": 0.654167, "deadEndThisWeek": 0, "expectedPresses": { "classes": 3925, "median": 2027025, "mean": 2027025, "p10": 2027025, "p90": 2027025, "display": "2,027,025" } } ] }, "20": { "simulationOnly": true, "classes": 3000, "detailClasses": 200, "pressUpTo": 10, "fastPressUpTo": 8, "pressFallbacks": 0, "completedAllWeeks": 1825, "pCompletedAllWeeks": 0.608333, "deadEnd": { "classes": 1175, "outOf": 3000, "share": 0.391667, "se": 0.008912, "allInWeekNMinus2": true, "earliestWeek": 18, "medianWeek": 18, "latestWeek": 18, "byWeek": [ { "week": 18, "share": 0.391667 } ], "display": { "share": "39.2%", "shareWhole": "39%", "range95": "37% to 41%", "classes": "3,000" } }, "firstWeekMedianPressesOver": { "10": 6, "100": 9, "1000": 11, "10000": 13, "100000": 15, "1000000": 16 }, "rows": [ { "week": 1, "classesStarted": 3000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 3000, "mean": 1, "median": 1, "p90": 1, "most": 1 } }, { "week": 2, "classesStarted": 3000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 3000, "mean": 1.674, "median": 1, "p90": 3, "most": 9 }, "expectedPresses": { "classes": 200, "median": 1.69, "mean": 1.69, "p10": 1.69, "p90": 1.69, "display": "1.7" } }, { "week": 3, "classesStarted": 3000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 3000, "mean": 2.997, "median": 2, "p90": 6, "most": 22 }, "expectedPresses": { "classes": 200, "median": 2.95, "mean": 2.95, "p10": 2.95, "p90": 2.95, "display": "2.9" } }, { "week": 4, "classesStarted": 3000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 3000, "mean": 5.142, "median": 4, "p90": 11, "most": 51 }, "expectedPresses": { "classes": 200, "median": 5.3, "mean": 5.3, "p10": 5.3, "p90": 5.3, "display": "5.3" } }, { "week": 5, "classesStarted": 3000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 3000, "mean": 10.084, "median": 7, "p90": 23, "most": 88 }, "expectedPresses": { "classes": 200, "median": 9.88, "mean": 9.88, "p10": 9.88, "p90": 9.89, "display": "9.9" } }, { "week": 6, "classesStarted": 3000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 3000, "mean": 18.547, "median": 13, "p90": 42, "most": 164 }, "expectedPresses": { "classes": 200, "median": 19.22, "mean": 19.22, "p10": 19.19, "p90": 19.24, "display": "19" } }, { "week": 7, "classesStarted": 3000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 3000, "mean": 38.835, "median": 26, "p90": 90, "most": 336 }, "expectedPresses": { "classes": 200, "median": 39.18, "mean": 39.18, "p10": 39.1, "p90": 39.26, "display": "39" } }, { "week": 8, "classesStarted": 3000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 3000, "mean": 80.88, "median": 55, "p90": 192, "most": 566 }, "expectedPresses": { "classes": 200, "median": 84.3, "mean": 84.33, "p10": 84.05, "p90": 84.63, "display": "84" } }, { "week": 9, "classesStarted": 3000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 200, "mean": 194.285, "median": 152, "p90": 406, "most": 1151 }, "expectedPresses": { "classes": 3000, "median": 193.39, "mean": 193.38, "p10": 192.41, "p90": 194.29, "display": "193" } }, { "week": 10, "classesStarted": 3000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 200, "mean": 477.525, "median": 352, "p90": 1055, "most": 2768 }, "expectedPresses": { "classes": 3000, "median": 477.88, "mean": 477.8, "p10": 474.4, "p90": 481.16, "display": "478" } }, { "week": 11, "classesStarted": 3000, "reachedWeek": 1, "deadEndThisWeek": 0, "expectedPresses": { "classes": 3000, "median": 1291.23, "mean": 1290.95, "p10": 1277.63, "p90": 1304.02, "display": "1,291" } }, { "week": 12, "classesStarted": 3000, "reachedWeek": 1, "deadEndThisWeek": 0, "expectedPresses": { "classes": 3000, "median": 3892.38, "mean": 3888.63, "p10": 3829.23, "p90": 3943.11, "display": "3,892" } }, { "week": 13, "classesStarted": 3000, "reachedWeek": 1, "deadEndThisWeek": 0, "expectedPresses": { "classes": 3000, "median": 13424.28, "mean": 13408.77, "p10": 13100.61, "p90": 13697.83, "display": "13,424" } }, { "week": 14, "classesStarted": 3000, "reachedWeek": 1, "deadEndThisWeek": 0, "expectedPresses": { "classes": 3000, "median": 54926.94, "mean": 54853.82, "p10": 52877.49, "p90": 56715.96, "display": "54,927" } }, { "week": 15, "classesStarted": 3000, "reachedWeek": 1, "deadEndThisWeek": 0, "expectedPresses": { "classes": 3000, "median": 282454.3, "mean": 281443.81, "p10": 264643.93, "p90": 297064.01, "display": "282,454" } }, { "week": 16, "classesStarted": 3000, "reachedWeek": 1, "deadEndThisWeek": 0, "expectedPresses": { "classes": 3000, "median": 1972075.53, "mean": 1966114.27, "p10": 1750612.5, "p90": 2167977.07, "display": "1,972,076" } }, { "week": 17, "classesStarted": 3000, "reachedWeek": 1, "deadEndThisWeek": 0, "expectedPresses": { "classes": 3000, "median": 21120292.74, "mean": 21705277.95, "p10": 16368226.88, "p90": 27280378.13, "display": "21,120,293" } }, { "week": 18, "classesStarted": 3000, "reachedWeek": 0.608333, "deadEndThisWeek": 0.391667, "expectedPresses": { "classes": 1825, "median": 327364537.5, "mean": 273461499.96, "p10": 163682268.75, "p90": 327364537.5, "display": "327,364,538" } }, { "week": 19, "classesStarted": 3000, "reachedWeek": 0.608333, "deadEndThisWeek": 0, "expectedPresses": { "classes": 1825, "median": 654729075, "mean": 654729075, "p10": 654729075, "p90": 654729075, "display": "654,729,075" } } ] }, "24": { "simulationOnly": true, "classes": 1000, "detailClasses": 100, "pressUpTo": 10, "fastPressUpTo": 9, "pressFallbacks": 0, "completedAllWeeks": 606, "pCompletedAllWeeks": 0.606, "deadEnd": { "classes": 394, "outOf": 1000, "share": 0.394, "se": 0.015452, "allInWeekNMinus2": true, "earliestWeek": 22, "medianWeek": 22, "latestWeek": 22, "byWeek": [ { "week": 22, "share": 0.394 } ], "display": { "share": "39.4%", "shareWhole": "39%", "range95": "36% to 42%", "classes": "1,000" } }, "firstWeekMedianPressesOver": { "10": 6, "100": 9, "1000": 12, "10000": 14, "100000": 16, "1000000": 18 }, "rows": [ { "week": 1, "classesStarted": 1000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 1000, "mean": 1, "median": 1, "p90": 1, "most": 1 } }, { "week": 2, "classesStarted": 1000, "reachedWeek": 1, "deadEndThisWeek": 0, "pressesSimulated": { "classes": 1000, "mean": 1.683, "median": 1, "p90": 3, "most": 8 }, "expectedPresses": { "classes": 100, "median": 1.68, "mean": 1.68, "p10": 1.68, "p90": 1.68, "display": 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People per team 2, 12 weeks: pairs who have worked together 3+ times (mean)", "kind": "simulated vs exact", "simulated": 4.26527778, "exact": 4.25887797, "se": 0.013708, "z": 0.47, "tolerance": 0.0548318, "pass": true }, { "name": "class of 20, People per team 2, 18 weeks: student 1's different partners (mean)", "kind": "simulated vs exact", "simulated": 11.83916667, "exact": 11.82050536, "se": 0.0100656, "z": 1.85, "tolerance": 0.0402625, "pass": true }, { "name": "class of 20, People per team 2, 18 weeks: pairs who have worked together 2+ times (mean)", "kind": "simulated vs exact", "simulated": 46.43566667, "exact": 46.41010718, "se": 0.024567, "z": 1.04, "tolerance": 0.0982678, "pass": true }, { "name": "class of 20, People per team 2, 18 weeks: pairs who have worked together 3+ times (mean)", "kind": "simulated vs exact", "simulated": 12.4995, "exact": 12.50693805, "se": 0.0201473, "z": -0.37, "tolerance": 0.0805891, "pass": true }, { "name": "class of 20, People per team 2, week 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13.58392308, "exact": 13.580205, "se": 0.0124246, "z": 0.3, "tolerance": 0.0496984, "pass": true }, { "name": "class of 30, People per team 2, 18 weeks: P(student 1 has repeated a partner)", "kind": "simulated vs exact", "simulated": 0.99892308, "exact": 0.99894751, "se": 0.000284387, "z": -0.09, "tolerance": 0.00113755, "pass": true }, { "name": "class of 30, People per team 2, 18 weeks: pairs who have worked together 2+ times (mean)", "kind": "simulated vs exact", "simulated": 55.06361538, "exact": 55.01219473, "se": 0.038444, "z": 1.34, "tolerance": 0.153776, "pass": true }, { "name": "class of 30, People per team 2, 18 weeks: pairs who have worked together 3+ times (mean)", "kind": "simulated vs exact", "simulated": 9.88061538, "exact": 9.87389178, "se": 0.0241501, "z": 0.28, "tolerance": 0.0966004, "pass": true }, { "name": "class of 30, People per team 2, week 4: pairs who already worked together earlier (mean)", "kind": "simulated vs exact (simulation se)", "simulated": 1.48938462, "exact": 1.49883144, "se": 0.0104038, "z": -0.91, "tolerance": 0.0416154, "pass": true }, { "name": "class of 30, People per team 2, week 8: pairs who already worked together earlier (mean)", "kind": "simulated vs exact (simulation se)", "simulated": 3.26892308, "exact": 3.26693455, "se": 0.0143386, "z": 0.14, "tolerance": 0.0573546, "pass": true }, { "name": "class of 30, People per team 2, week 12: pairs who already worked together earlier (mean)", "kind": "simulated vs exact (simulation se)", "simulated": 4.80792308, "exact": 4.80348818, "se": 0.0159473, "z": 0.28, "tolerance": 0.0637891, "pass": true }, { "name": "class of 30, People per team 2, week 18: pairs who already worked together earlier (mean)", "kind": "simulated vs exact (simulation se)", "simulated": 6.76684615, "exact": 6.73939554, "se": 0.0170995, "z": 1.61, "tolerance": 0.0683979, "pass": true }, { "name": "class of 30, People per team 2: P(first repeat already in week 2)", "kind": "simulated vs exact", "simulated": 0.39623077, "exact": 0.40364561, "se": 0.00430309, "z": -1.72, "tolerance": 0.0172124, "pass": true }, { "name": "class of 30, People per team 2: P(a repeat has appeared by week 3)", "kind": "simulated vs exact", "simulated": 0.78607692, "exact": 0.79178744, "se": 0.00356112, "z": -1.6, "tolerance": 0.0142445, "pass": true }, { "name": "class of 30, Number of teams 15, 12 weeks: student 1's different partners (mean)", "kind": "simulated vs exact", "simulated": 9.95, "exact": 9.96651127, "se": 0.0174992, "z": -0.94, "tolerance": 0.069997, "pass": true }, { "name": "class of 30, Number of teams 15, 12 weeks: P(student 1 has repeated a partner)", "kind": "simulated vs exact", "simulated": 0.92725, "exact": 0.92974223, "se": 0.00404109, "z": -0.62, "tolerance": 0.0161644, "pass": true }, { "name": "class of 30, Number of teams 15, 12 weeks: pairs who have worked together 2+ times (mean)", "kind": "simulated vs exact", "simulated": 27.19075, "exact": 27.13952728, "se": 0.058141, "z": 0.88, "tolerance": 0.232564, "pass": true }, { "name": "class of 30, Number of teams 15, 12 weeks: pairs who have worked together 3+ times (mean)", "kind": "simulated vs exact", "simulated": 3.1225, "exact": 3.10489228, "se": 0.0264186, "z": 0.67, "tolerance": 0.105675, "pass": true }, { "name": "class of 30, Number of teams 15, week 12: pairs who already worked together earlier (mean)", "kind": "simulated vs exact (simulation se)", "simulated": 4.82325, "exact": 4.80348818, "se": 0.0289137, "z": 0.68, "tolerance": 0.115655, "pass": true }, { "name": "class of 30, Number of teams 15: P(first repeat already in week 2)", "kind": "simulated vs exact", "simulated": 0.41325, "exact": 0.40364561, "se": 0.00775751, "z": 1.24, "tolerance": 0.03103, "pass": true }, { "name": "class of 30, Number of teams 15: P(a repeat has appeared by week 3)", "kind": "simulated vs exact", "simulated": 0.804, "exact": 0.79178744, "se": 0.00641989, "z": 1.9, "tolerance": 0.0256796, "pass": true }, { "name": "class of 25, People per team 2, 4 weeks: student 1's different partners (mean)", "kind": "simulated vs exact", "simulated": 3.622, "exact": 3.61568256, "se": 0.00559316, "z": 1.13, "tolerance": 0.0223726, "pass": true }, { "name": "class of 25, People per team 2, 4 weeks: P(student 1 has repeated a partner)", "kind": "simulated vs exact", "simulated": 0.2125, "exact": 0.21405696, "se": 0.00410167, "z": -0.38, "tolerance": 0.0164067, "pass": true }, { "name": "class of 25, People per team 2, 8 weeks: student 1's different partners (mean)", "kind": "simulated vs exact", "simulated": 6.7002, "exact": 6.6866501, "se": 0.00926328, "z": 1.46, "tolerance": 0.0370531, "pass": true }, { "name": "class of 25, People per team 2, 8 weeks: P(student 1 has repeated a partner)", "kind": "simulated vs exact", "simulated": 0.6902, "exact": 0.69442704, "se": 0.0046065, "z": -0.92, "tolerance": 0.018426, "pass": true }, { "name": "class of 25, People per team 2, 12 weeks: student 1's different partners (mean)", "kind": "simulated vs exact", "simulated": 9.3151, "exact": 9.29496582, "se": 0.0119115, "z": 1.69, "tolerance": 0.0476462, "pass": true }, { "name": "class of 25, People per team 2, 12 weeks: P(student 1 has repeated a partner)", "kind": "simulated vs exact", "simulated": 0.9475, "exact": 0.94830585, "se": 0.00221409, "z": -0.36, "tolerance": 0.00885635, "pass": true }, { "name": "class of 25, People per team 2, 12 weeks: P(student 1 left single at least once)", "kind": "simulated vs exact", "simulated": 0.387, "exact": 0.38729024, "se": 0.00487131, "z": -0.06, "tolerance": 0.0194852, "pass": true }, { "name": "class of 25, People per team 2, 18 weeks: student 1's different partners (mean)", "kind": "simulated vs exact", "simulated": 12.5135, "exact": 12.48951995, "se": 0.0144229, "z": 1.66, "tolerance": 0.0576915, "pass": true }, { "name": "class of 25, People per team 2, 18 weeks: P(student 1 has repeated a partner)", "kind": "simulated vs exact", "simulated": 0.9989, "exact": 0.99948384, "se": 0.000227133, "z": -2.57, "tolerance": 0.000908532, "pass": true }, { "name": "class of 25, People per team 2, week 4: pairs who already worked together earlier (mean)", "kind": "simulated vs exact (simulation se)", "simulated": 1.3915, "exact": 1.383168, "se": 0.0111903, "z": 0.74, "tolerance": 0.0447612, "pass": true }, { "name": "class of 25, People per team 2, week 8: pairs who already worked together earlier (mean)", "kind": "simulated vs exact (simulation se)", "simulated": 2.9577, "exact": 2.98263026, "se": 0.0151628, "z": -1.64, "tolerance": 0.0606513, "pass": true }, { "name": "class of 25, People per team 2, week 12: pairs who already worked together earlier (mean)", "kind": "simulated vs exact (simulation se)", "simulated": 4.3375, "exact": 4.34112803, "se": 0.0166385, "z": -0.22, "tolerance": 0.066554, "pass": true }, { "name": "class of 25, People per team 2, week 18: pairs who already worked together earlier (mean)", "kind": "simulated vs exact (simulation se)", "simulated": 5.9767, "exact": 6.00495831, "se": 0.0176679, "z": -1.6, "tolerance": 0.0706717, "pass": true }, { "name": "class of 25, People per team 2: P(first repeat already in week 2)", "kind": "simulated vs exact", "simulated": 0.3779, "exact": 0.38146754, "se": 0.00485747, "z": -0.73, "tolerance": 0.0194299, "pass": true }, { "name": "class of 25, Number of teams 12, 12 weeks: student 1's different partners (mean)", "kind": "simulated vs exact", "simulated": 10.4623, "exact": 10.47464781, "se": 0.0138229, "z": -0.89, "tolerance": 0.0552917, "pass": true }, { "name": "class of 25, Number of teams 12, 12 weeks: P(student 1 has repeated a partner)", "kind": "simulated vs exact", "simulated": 0.9813, "exact": 0.98295444, "se": 0.00129441, "z": -1.28, "tolerance": 0.00517764, "pass": true }, { "name": "class of 25, Number of teams 12, 12 weeks: P(student 1 in the trio at least once)", "kind": "simulated vs exact", "simulated": 0.786, "exact": 0.78432884, "se": 0.00411287, "z": 0.41, "tolerance": 0.0164515, "pass": true }, { "name": "class of 25, Number of teams 12, week 12: pairs who already worked together earlier (mean)", "kind": "simulated vs exact (simulation se)", "simulated": 5.7279, "exact": 5.72399779, "se": 0.0187031, "z": 0.21, "tolerance": 0.0748124, "pass": true }, { "name": "class of 25, Number of teams 12: P(first repeat already in week 2)", "kind": "simulated vs exact", "simulated": 0.4852, "exact": 0.48438451, "se": 0.00499756, "z": 0.16, "tolerance": 0.0199902, "pass": true }, { "name": "class of 16: presses until no pair from last week repeats (mean)", "kind": "simulated vs exact", "simulated": 1.69606667, "exact": 1.70242099, "se": 0.00892867, "z": -0.71, "tolerance": 0.0357147, "pass": true }, { "name": "class of 16: P(more than 3 presses needed)", "kind": "simulated vs exact", "simulated": 0.071, "exact": 0.07024114, "se": 0.00208658, "z": 0.36, "tolerance": 0.00834633, "pass": true }, { "name": "class of 20: presses until no pair from last week repeats (mean)", "kind": "simulated vs exact", "simulated": 1.6786, "exact": 1.69136963, "se": 0.00882935, "z": -1.45, "tolerance": 0.0353174, "pass": true }, { "name": "class of 20: P(more than 3 presses needed)", "kind": "simulated vs exact", "simulated": 0.066, "exact": 0.06829915, "se": 0.00205968, "z": -1.12, "tolerance": 0.00823873, "pass": true }, { "name": "class of 24: presses until no pair from last week repeats (mean)", "kind": "simulated vs exact", "simulated": 1.685775, "exact": 1.68407872, "se": 0.00536666, "z": 0.32, "tolerance": 0.0214666, "pass": true }, { "name": "class of 24: P(more than 3 presses needed)", "kind": "simulated vs exact", "simulated": 0.0677, "exact": 0.06702411, "se": 0.00125032, "z": 0.54, "tolerance": 0.00500128, "pass": true }, { "name": "class of 25, People per team 2: presses until no pair from last week repeats (mean)", "kind": "simulated vs exact", "simulated": 1.61158333, "exact": 1.61673003, "se": 0.0091154, "z": -0.56, "tolerance": 0.0364616, "pass": true }, { "name": "class of 25, People per team 2: P(more than 3 presses needed)", "kind": "simulated vs exact", "simulated": 0.05375, "exact": 0.0555102, "se": 0.00209023, "z": -0.84, "tolerance": 0.00836093, "pass": true }, { "name": "class of 25, Number of teams 12: presses until no pair from last week repeats (mean)", "kind": "simulated vs exact", "simulated": 1.92283333, "exact": 1.9394297, "se": 0.0123219, "z": -1.35, "tolerance": 0.0492877, "pass": true }, { "name": "class of 25, Number of teams 12: P(more than 3 presses needed)", "kind": "simulated vs exact", "simulated": 0.10833333, "exact": 0.11365034, "se": 0.00289733, "z": -1.84, "tolerance": 0.0115893, "pass": true }, { "name": "class of 30: presses until no pair from last week repeats (mean)", "kind": "simulated vs exact", "simulated": 1.69853333, "exact": 1.67685527, "se": 0.00869861, "z": 2.49, "tolerance": 0.0347945, "pass": true }, { "name": "class of 30: P(more than 3 presses needed)", "kind": "simulated vs exact", "simulated": 0.06946667, "exact": 0.06576589, "se": 0.00202387, "z": 1.83, "tolerance": 0.00809548, "pass": true }, { "name": "class of 16, week 4, press until all-new: presses vs exact 1/p for each class's history (mean)", "kind": "simulated vs exact (given each history)", "simulated": 5.58333333, "exact": 5.55771649, "se": 0.290577, "z": 0.09, "tolerance": 1.16231, "pass": true }, { "name": "class of 16, week 9, press until all-new: presses vs exact 1/p for each class's history (mean)", "kind": "simulated vs exact (given each history)", "simulated": 316.74666667, "exact": 320.71888804, "se": 18.4899, "z": -0.21, "tolerance": 73.9597, "pass": true }, { "name": "class of 16, weeks 2-9 pooled (300 detail classes), press until all-new: presses vs exact 1/p for each class's history (mean)", "kind": "simulated vs exact (given each history)", "simulated": 65.7875, "exact": 66.56587996, "se": 2.49622, "z": -0.31, "tolerance": 9.98487, "pass": true }, { "name": "class of 16, week 2, press until all-new: presses (mean) = 1/P(no repeat)", "kind": "simulated vs exact", "simulated": 1.705, "exact": 1.70242099, "se": 0.0141175, "z": 0.18, "tolerance": 0.0564698, "pass": true }, { "name": "class of 20, week 4, press until all-new: presses vs exact 1/p for each class's history (mean)", "kind": "simulated vs exact (given each history)", "simulated": 5.075, "exact": 5.29784944, "se": 0.337412, "z": -0.66, "tolerance": 1.34965, "pass": true }, { "name": "class of 20, week 10, press until all-new: presses vs exact 1/p for each class's history (mean)", "kind": "simulated vs exact (given each history)", "simulated": 477.525, "exact": 477.96364338, "se": 33.7623, "z": -0.01, "tolerance": 135.049, "pass": true }, { "name": "class of 20, weeks 2-10 pooled (200 detail classes), press until all-new: presses vs exact 1/p for each class's history (mean)", "kind": "simulated vs exact (given each history)", "simulated": 91.83166667, "exact": 92.65051816, "se": 4.11381, "z": -0.2, "tolerance": 16.4552, "pass": true }, { "name": "class of 20, week 2, press until all-new: presses (mean) = 1/P(no repeat)", "kind": "simulated vs exact", "simulated": 1.674, "exact": 1.69136963, "se": 0.019743, "z": -0.88, "tolerance": 0.0789721, "pass": true }, { "name": "class of 24, week 4, press until all-new: presses vs exact 1/p for each class's history (mean)", "kind": "simulated vs exact (given each history)", "simulated": 5.61, "exact": 5.13871472, "se": 0.461169, "z": 1.02, "tolerance": 1.84468, "pass": true }, { "name": "class of 24, week 10, press until all-new: presses vs exact 1/p for each class's history (mean)", "kind": "simulated vs exact (given each history)", "simulated": 300.35, "exact": 324.84556805, "se": 32.4346, "z": -0.76, "tolerance": 129.738, "pass": true }, { "name": "class of 24, weeks 2-10 pooled (100 detail classes), press until all-new: presses vs exact 1/p for each class's history (mean)", "kind": "simulated vs exact (given each history)", "simulated": 66.99, "exact": 67.90122719, "se": 4.04733, "z": -0.23, "tolerance": 16.1893, "pass": true }, { "name": "class of 24, week 2, press until all-new: presses (mean) = 1/P(no repeat)", "kind": "simulated vs exact", "simulated": 1.683, "exact": 1.68407872, "se": 0.0339418, "z": -0.03, "tolerance": 0.135767, "pass": true }, { "name": "circle schedule from a random start, class of 16: P(students 1 and 2 partners in week 1) = 1/15", "kind": "simulated vs exact", "simulated": 0.0663, "exact": 0.06666667, "se": 0.00124722, "z": -0.29, "tolerance": 0.00498888, "pass": true }, { "name": "circle schedule from a random start, class of 16: P(students 1 and 2 partners within 12 weeks) = 12/15", "kind": "simulated vs exact", "simulated": 0.8006, "exact": 0.8, "se": 0.002, "z": 0.3, "tolerance": 0.008, "pass": true }, { "name": "circle schedule from a random start, class of 16: week in which students 1 and 2 are partners (mean 8)", "kind": "simulated vs exact", "simulated": 8.001325, "exact": 8, "se": 0.0216025, "z": 0.06, "tolerance": 0.0864099, "pass": true }, { "name": "circle schedule from a random start, class of 16: repeated partners in 2,000 full 15-week schedules", "kind": "sanity", "simulated": 0, "exact": 0, "se": 0, "z": 0, "tolerance": 0, "pass": true }, { "name": "circle schedule from a random start, class of 24: P(students 1 and 2 partners in week 1) = 1/23", "kind": "simulated vs exact", "simulated": 0.04313, "exact": 0.04347826, "se": 0.000644887, "z": -0.54, "tolerance": 0.00257955, "pass": true }, { "name": "circle schedule from a random start, class of 24: P(students 1 and 2 partners within 12 weeks) = 12/23", "kind": "simulated vs exact", "simulated": 0.5227, "exact": 0.52173913, "se": 0.00157964, "z": 0.61, "tolerance": 0.00631857, "pass": true }, { "name": "circle schedule from a random start, class of 24: week in which students 1 and 2 are partners (mean 12)", "kind": "simulated vs exact", "simulated": 11.9636, "exact": 12, "se": 0.0209762, "z": -1.74, "tolerance": 0.0839047, "pass": true }, { "name": "circle schedule from a random start, class of 24: repeated partners in 2,000 full 23-week schedules", "kind": "sanity", "simulated": 0, "exact": 0, "se": 0, "z": 0, "tolerance": 0, "pass": true }, { "name": "raw draws cover every counted draw", "kind": "sanity", "simulated": 0, "exact": 0, "se": 0, "z": 0, "tolerance": 0, "pass": true } ] }