{ "slug": "how-many-spins-until-everyone-gets-a-turn", "generatedAt": "2026-10-03T20:26:59.018Z", "node": "v24.21.0", "randomJsSha256": "946e82a3c426d698779d3246c37c732f771db3873c93239ef3952aea39be1e2d", "totalSpins": 55137787, "rawDraws": 55137787, "checksTotal": 79, "checksPassed": 79, "runtimeSeconds": 94.4, "params": { "classSizes": [ 10, 15, 20, 25, 30, 35 ], "exactClassSizeRange": [ 5, 40 ], "cdfClassSizes": [ 15, 25, 35 ], "cdfStep": 5, "runsPerClassSize": 80000, "lesson": { "classSize": 25, "calls": 10, "simulatedLessons": 300000 }, "week": { "classSize": 25, "lessons": 5, "callsPerLesson": 10, "calls": 50, "simulatedWeeks": 200000 }, "withoutReplacement": { "classSize": 25, "simulatedWeeks": 20000, "calls": 50, "simulatedRoundsPerClassSize": 2000 }, "histogramClassSize": 25, "histogramBucketWidth": 10, "histogramOpenEndedFrom": 190 }, "results": { "coverage": { "10": { "runs": 80000, "meanSpins": 29.263, "sdSpins": 11.175, "medianSpins": 27, "p90Spins": 44, "p99Spins": 66, "fastestRun": 10, "slowestRun": 138, "meanSpinsPerStudent": 2.9263, "meanSpinsForFirstHalf": 6.463, "meanMostPicksWhenEveryoneDone": 5.7158, "afterNSpins": { "meanNeverPicked": 3.4897, "shareNeverPicked": 0.34897, "meanPickedTwiceOrMore": 2.6366, "shareRunsWithSomeone3Plus": 0.6078, "meanMaxPicks": 2.7544, "neverPickedDistribution": { "0": 0.00042, "1": 0.016, "2": 0.13685, "3": 0.35139, "4": 0.34925, "5": 0.12846, "6": 0.0169, "7": 0.00072 } } }, "15": { "runs": 80000, "meanSpins": 49.711, "sdSpins": 17.501, "medianSpins": 46, "p90Spins": 72, "p99Spins": 107, "fastestRun": 16, "slowestRun": 203, "meanSpinsPerStudent": 3.3141, "meanSpinsForFirstHalf": 10.879, "meanMostPicksWhenEveryoneDone": 6.7324, "afterNSpins": { "meanNeverPicked": 5.3247, "shareNeverPicked": 0.35498, "meanPickedTwiceOrMore": 3.9585, "shareRunsWithSomeone3Plus": 0.78074, "meanMaxPicks": 3.0338, "neverPickedDistribution": { "1": 0.00046, "2": 0.0068, "3": 0.05284, "4": 0.18504, "5": 0.31589, "6": 0.27823, "7": 0.1267, "8": 0.03034, "9": 0.00352, "10": 0.00017, "11": 0.00001 } } }, "20": { "runs": 80000, "meanSpins": 71.939, "sdSpins": 23.697, "medianSpins": 68, "p90Spins": 103, "p99Spins": 148, "fastestRun": 22, "slowestRun": 276, "meanSpinsPerStudent": 3.597, "meanSpinsForFirstHalf": 13.381, "meanMostPicksWhenEveryoneDone": 7.473, "afterNSpins": { "meanNeverPicked": 7.1704, "shareNeverPicked": 0.35852, "meanPickedTwiceOrMore": 5.2819, "shareRunsWithSomeone3Plus": 0.87854, "meanMaxPicks": 3.2319, "neverPickedDistribution": { "2": 0.0003, "3": 0.00284, "4": 0.0215, "5": 0.0871, "6": 0.20363, "7": 0.28075, "8": 0.23603, "9": 0.12227, "10": 0.03804, "11": 0.00688, "12": 0.00064, "13": 0.00004 } } }, "25": { "runs": 80000, "meanSpins": 95.509, "sdSpins": 30.142, "medianSpins": 90, "p90Spins": 135, "p99Spins": 191, "fastestRun": 31, "slowestRun": 357, "meanSpinsPerStudent": 3.8204, "meanSpinsForFirstHalf": 17.823, "meanMostPicksWhenEveryoneDone": 8.0557, "afterNSpins": { "meanNeverPicked": 9.0091, "shareNeverPicked": 0.36036, "meanPickedTwiceOrMore": 6.5963, "shareRunsWithSomeone3Plus": 0.9341, "meanMaxPicks": 3.3816, "neverPickedDistribution": { "2": 0.00001, "3": 0.00013, "4": 0.00114, "5": 0.00983, "6": 0.03986, "7": 0.11254, "8": 0.20829, "9": 0.25327, "10": 0.20804, "11": 0.11414, "12": 0.04144, "13": 0.00954, "14": 0.00164, "15": 0.00014, "16": 0.00001 } }, "histogram": [ { "label": "30-39", "from": 30, "to": 39, "simulatedShare": 0.00047, "exactShare": 0.00046 }, { "label": "40-49", "from": 40, "to": 49, "simulatedShare": 0.01202, "exactShare": 0.01128 }, { "label": "50-59", "from": 50, "to": 59, "simulatedShare": 0.05448, "exactShare": 0.0548 }, { "label": "60-69", "from": 60, "to": 69, "simulatedShare": 0.11492, "exactShare": 0.11588 }, { "label": "70-79", "from": 70, "to": 79, "simulatedShare": 0.15334, "exactShare": 0.1545 }, { "label": "80-89", "from": 80, "to": 89, "simulatedShare": 0.15749, "exactShare": 0.15768 }, { "label": "90-99", "from": 90, "to": 99, "simulatedShare": 0.137, "exactShare": 0.13713 }, { "label": "100-109", "from": 100, "to": 109, "simulatedShare": 0.10701, "exactShare": 0.1081 }, { "label": "110-119", "from": 110, "to": 119, "simulatedShare": 0.08151, "exactShare": 0.08015 }, { "label": "120-129", "from": 120, "to": 129, "simulatedShare": 0.05755, "exactShare": 0.05716 }, { "label": "130-139", "from": 130, "to": 139, "simulatedShare": 0.04052, "exactShare": 0.03977 }, { "label": "140-149", "from": 140, "to": 149, "simulatedShare": 0.02709, "exactShare": 0.02723 }, { "label": "150-159", "from": 150, "to": 159, "simulatedShare": 0.01903, "exactShare": 0.01845 }, { "label": "160-169", "from": 160, "to": 169, "simulatedShare": 0.01261, "exactShare": 0.01242 }, { "label": "170-179", "from": 170, "to": 179, "simulatedShare": 0.00882, "exactShare": 0.00833 }, { "label": "180-189", "from": 180, "to": 189, "simulatedShare": 0.00551, "exactShare": 0.00556 }, { "label": "190+", "from": 190, "to": null, "simulatedShare": 0.01061, "exactShare": 0.01111 } ], "histogramNotes": { "belowFirstBucket": { "label": "under 30", "simulatedShare": 0, "exactShare": 2.8e-7 }, "exactSharesSumTo": 1.00001, "note": "Shares are rounded to 5 decimals, so the exact column sums to about 1, not exactly 1. The last bucket is open-ended." } }, "30": { "runs": 80000, "meanSpins": 119.889, "sdSpins": 36.659, "medianSpins": 113, "p90Spins": 168, "p99Spins": 239, "fastestRun": 42, "slowestRun": 492, "meanSpinsPerStudent": 3.9963, "meanSpinsForFirstHalf": 20.318, "meanMostPicksWhenEveryoneDone": 8.5215, "afterNSpins": { "meanNeverPicked": 10.8473, "shareNeverPicked": 0.36158, "meanPickedTwiceOrMore": 7.9164, "shareRunsWithSomeone3Plus": 0.96384, "meanMaxPicks": 3.4977, "neverPickedDistribution": { "4": 0.00005, "5": 0.00052, "6": 0.0042, "7": 0.01809, "8": 0.06005, "9": 0.13146, "10": 0.20453, "11": 0.23219, "12": 0.1836, "13": 0.10695, "14": 0.04296, "15": 0.01235, "16": 0.0025, "17": 0.00044, "18": 0.00011 } } }, "35": { "runs": 80000, "meanSpins": 145.186, "sdSpins": 42.856, "medianSpins": 137, "p90Spins": 201, "p99Spins": 279, "fastestRun": 54, "slowestRun": 556, "meanSpinsPerStudent": 4.1482, "meanSpinsForFirstHalf": 24.751, "meanMostPicksWhenEveryoneDone": 8.9216, "afterNSpins": { "meanNeverPicked": 12.6835, "shareNeverPicked": 0.36239, "meanPickedTwiceOrMore": 9.2432, "shareRunsWithSomeone3Plus": 0.97976, "meanMaxPicks": 3.5869, "neverPickedDistribution": { "5": 0.00001, "6": 0.00025, "7": 0.00149, "8": 0.00775, "9": 0.03022, "10": 0.07684, "11": 0.14319, "12": 0.20359, "13": 0.21056, "14": 0.16592, "15": 0.09675, "16": 0.04415, "17": 0.01482, "18": 0.00358, "19": 0.00075, "20": 0.00011, "21": 0.00001 } } } }, "lesson": { "lessons": 300000, "shareOfStudentsNeverCalled": 0.66479, "meanStudentsNeverCalled": 16.61972, "meanStudentsCalled": 8.38028, "meanStudentsCalledTwiceOrMore": 1.45354, "shareLessonsWithARepeat": 0.87552, "shareLessonsWithSomeone3Plus": 0.15077, "shareLessonsFirstStudentNeverCalled": 0.66353 }, "week": { "weeks": 200000, "meanStudentsNeverCalled": 3.24736, "shareOfStudentsNeverCalled": 0.12989, "shareWeeksWithSomeoneNeverCalled": 0.98506, "meanStudentsCalledAtMostOnce": 10.00826, "meanStudentsCalled4PlusTimes": 3.47768, "meanMostCallsForOneStudent": 5.20897, "mostCallsDistribution": { "3": 0.00326, "4": 0.21835, "5": 0.45583, "6": 0.2346, "7": 0.06881, "8": 0.01565, "9": 0.00294, "10": 0.00049, "11": 0.00007, "12": 0.00001 } }, "withoutReplacement": { "weeks": 20000, "weeksWhereCallsWereNotExactlyEqual": 0, "callsPerStudentEveryWeek": 2, "spinsPerWeek": 48, "longestGapBetweenTurnsSeen": 49, "meanLongestGapInAWeek": 44.288, "roundsChecked": 12000, "roundsWhereSomeoneWasMissedOrRepeated": 0, "roundsWithOtherThanNMinus1Spins": 0, "lastNameLeftShareRangeClassOf25": [ 0.031, 0.0505 ] }, "notes": [ "fastestRun and slowestRun come from this one simulation run (80,000 simulated classes per size); they change on every run. Quote them as 'in our simulated classes', never as fixed values.", "All spins are simulated with Wheel Cue's random.js; none come from people using the site." ] }, "theory": { "notes": [ "meanSpins = n * H_n (H_n the n-th harmonic number); sdSpins from Var = n^2 * sum(1/i^2) - n * H_n.", "Percentiles are the smallest t with P(T <= t) >= p, from the exact Markov chain on the number of distinct students picked.", "expectedNeverPicked after n spins = n * (1 - 1/n)^n.", "Probabilities about how often one student is picked use m!/n^m * [x^m] (sum_{j<=c} x^j/j!)^n.", "Most picks when everyone is done (meanMostPicksWhenEveryoneDone) is computed numerically, not in closed form: the integral of n e^-v [P(1 <= Poisson(v) <= c)]^(n-1) dv by Simpson's rule (step 0.001). Call it 'computed', not 'exact'.", "With replacement every call is a spin. With winners removed, a round is n calls but n - 1 spins: Wheel Cue will not spin fewer than two entries, so the last name left goes last without a spin.", "meanSpinsForFirstHalf uses ceil(n/2) students (firstHalfStudents), so it zigzags between odd and even n; quote it for one class size only. For a chart against class size use meanSpinsForFloorHalf (floor(n/2) students).", "week.pNextTurnMoreThan2nCallsAway = (1 - 1/n)^(2n): after any one turn, the chance that the same student's next turn is more than 2n calls later. It is per wait, not the chance of such a wait at least once. With winners removed the gap is never more than 2n - 1 calls.", "Site behavior: on /tools/random-student-picker/ the option 'Take each student off the wheel once picked' is ON by default; the with-replacement results apply when it is turned off, or on tools where removal is off by default (e.g. the name picker). A round in progress lives in the open tab: Reset restores the list as it was before the round, but after a reload it restores the page's example list, so carrying rounds across lessons means saving the list (Save) and loading the full class list for the next round." ], "coverage": { "10": { "meanSpins": 29.29, "sdSpins": 11.211, "medianSpins": 27, "p90Spins": 44, "p99Spins": 66, "meanSpinsPerStudent": 2.929, "firstHalfStudents": 5, "meanSpinsForFirstHalf": 6.456, "meanSpinsForLastStudent": 10, "repeatCallsBeforeEveryone": 19.29, "meanMostPicksWhenEveryoneDone": 5.7179, "pEveryonePickedWithin2nSpins": 0.21474, "pEveryonePickedWithin3nSpins": 0.62914, "afterNSpins": { "expectedNeverPicked": 3.4868, "shareNeverPicked": 0.34868, "expectedPickedTwiceOrMore": 2.639, "pSomeonePicked3Plus": 0.60419, "expectedMaxPicks": 2.7487 } }, "15": { "meanSpins": 49.773, "sdSpins": 17.488, "medianSpins": 46, "p90Spins": 73, "p99Spins": 106, "meanSpinsPerStudent": 3.3182, "firstHalfStudents": 8, "meanSpinsForFirstHalf": 10.881, "meanSpinsForLastStudent": 15, "repeatCallsBeforeEveryone": 34.773, "meanMostPicksWhenEveryoneDone": 6.7381, "pEveryonePickedWithin2nSpins": 0.08784, "pEveryonePickedWithin3nSpins": 0.47645, "afterNSpins": { "expectedNeverPicked": 5.329, "shareNeverPicked": 0.35526, "expectedPickedTwiceOrMore": 3.9614, "pSomeonePicked3Plus": 0.78069, "expectedMaxPicks": 3.0331 } }, "20": { "meanSpins": 71.955, "sdSpins": 23.801, "medianSpins": 67, "p90Spins": 103, "p99Spins": 149, "meanSpinsPerStudent": 3.5977, "firstHalfStudents": 10, "meanSpinsForFirstHalf": 13.375, "meanSpinsForLastStudent": 20, "repeatCallsBeforeEveryone": 51.955, "meanMostPicksWhenEveryoneDone": 7.4716, "pEveryonePickedWithin2nSpins": 0.03589, "pEveryonePickedWithin3nSpins": 0.36061, "afterNSpins": { "expectedNeverPicked": 7.1697, "shareNeverPicked": 0.35849, "expectedPickedTwiceOrMore": 5.2832, "pSomeonePicked3Plus": 0.87865, "expectedMaxPicks": 3.2312 } }, "25": { "meanSpins": 95.399, "sdSpins": 30.136, "medianSpins": 90, "p90Spins": 135, "p99Spins": 192, "meanSpinsPerStudent": 3.816, "firstHalfStudents": 13, "meanSpinsForFirstHalf": 17.819, "meanSpinsForLastStudent": 25, "repeatCallsBeforeEveryone": 70.399, "meanMostPicksWhenEveryoneDone": 8.045, "pEveryonePickedWithin2nSpins": 0.01466, "pEveryonePickedWithin3nSpins": 0.27286, "afterNSpins": { "expectedNeverPicked": 9.0099, "shareNeverPicked": 0.3604, "expectedPickedTwiceOrMore": 6.6048, "pSomeonePicked3Plus": 0.93289, "expectedMaxPicks": 3.3779 } }, "30": { "meanSpins": 119.85, "sdSpins": 36.484, "medianSpins": 113, "p90Spins": 168, "p99Spins": 237, "meanSpinsPerStudent": 3.995, "firstHalfStudents": 15, "meanSpinsForFirstHalf": 20.303, "meanSpinsForLastStudent": 30, "repeatCallsBeforeEveryone": 89.85, "meanMostPicksWhenEveryoneDone": 8.5159, "pEveryonePickedWithin2nSpins": 0.00598, "pEveryonePickedWithin3nSpins": 0.20645, "afterNSpins": { "expectedNeverPicked": 10.8498, "shareNeverPicked": 0.36166, "expectedPickedTwiceOrMore": 7.9262, "pSomeonePicked3Plus": 0.9629, "expectedMaxPicks": 3.493 } }, "35": { "meanSpins": 145.137, "sdSpins": 42.842, "medianSpins": 137, "p90Spins": 201, "p99Spins": 282, "meanSpinsPerStudent": 4.1468, "firstHalfStudents": 18, "meanSpinsForFirstHalf": 24.753, "meanSpinsForLastStudent": 35, "repeatCallsBeforeEveryone": 110.137, "meanMostPicksWhenEveryoneDone": 8.9154, "pEveryonePickedWithin2nSpins": 0.00244, "pEveryonePickedWithin3nSpins": 0.15619, "afterNSpins": { "expectedNeverPicked": 12.6896, "shareNeverPicked": 0.36256, "expectedPickedTwiceOrMore": 9.2475, "pSomeonePicked3Plus": 0.97949, "expectedMaxPicks": 3.5879 } } }, "byClassSize": [ { "classSize": 5, "meanSpins": 11.417, "sdSpins": 5.017, "medianSpins": 10, "p90Spins": 18, "p99Spins": 28, "meanSpinsPerStudent": 2.2833, "callsPerRoundIfWinnersRemoved": 5, "spinsPerRoundIfWinnersRemoved": 4, "extraCallsVsOneRound": 6.417, "firstHalfStudents": 3, "meanSpinsForFirstHalf": 3.917, "floorHalfStudents": 2, "meanSpinsForFloorHalf": 2.25, "meanSpinsForLastStudent": 5, "afterNSpins": { "expectedNeverPicked": 1.6384, "shareNeverPicked": 0.32768, "expectedPickedTwiceOrMore": 1.3136, "pSomeonePicked3Plus": 0.2896, "expectedMaxPicks": 2.2864 } }, { "classSize": 6, "meanSpins": 14.7, "sdSpins": 6.244, "medianSpins": 13, "p90Spins": 23, "p99Spins": 36, "meanSpinsPerStudent": 2.45, "callsPerRoundIfWinnersRemoved": 6, "spinsPerRoundIfWinnersRemoved": 5, "extraCallsVsOneRound": 8.7, "firstHalfStudents": 3, "meanSpinsForFirstHalf": 3.7, "floorHalfStudents": 3, "meanSpinsForFloorHalf": 3.7, "meanSpinsForLastStudent": 6, "afterNSpins": { "expectedNeverPicked": 2.0094, "shareNeverPicked": 0.3349, "expectedPickedTwiceOrMore": 1.5793, "pSomeonePicked3Plus": 0.36728, "expectedMaxPicks": 2.4082 } }, { "classSize": 7, "meanSpins": 18.15, "sdSpins": 7.479, "medianSpins": 17, "p90Spins": 28, "p99Spins": 43, "meanSpinsPerStudent": 2.5929, "callsPerRoundIfWinnersRemoved": 7, "spinsPerRoundIfWinnersRemoved": 6, "extraCallsVsOneRound": 11.15, "firstHalfStudents": 4, "meanSpinsForFirstHalf": 5.317, "floorHalfStudents": 3, "meanSpinsForFloorHalf": 3.567, "meanSpinsForLastStudent": 7, "afterNSpins": { "expectedNeverPicked": 2.3794, "shareNeverPicked": 0.33992, "expectedPickedTwiceOrMore": 1.8446, "pSomeonePicked3Plus": 0.43697, "expectedMaxPicks": 2.5091 } }, { "classSize": 8, "meanSpins": 21.743, "sdSpins": 8.718, "medianSpins": 20, "p90Spins": 33, "p99Spins": 51, "meanSpinsPerStudent": 2.7179, "callsPerRoundIfWinnersRemoved": 8, "spinsPerRoundIfWinnersRemoved": 7, "extraCallsVsOneRound": 13.743, "firstHalfStudents": 4, "meanSpinsForFirstHalf": 5.076, "floorHalfStudents": 4, "meanSpinsForFloorHalf": 5.076, "meanSpinsForLastStudent": 8, "afterNSpins": { "expectedNeverPicked": 2.7489, "shareNeverPicked": 0.34361, "expectedPickedTwiceOrMore": 2.1096, "pSomeonePicked3Plus": 0.49922, "expectedMaxPicks": 2.5972 } }, { "classSize": 9, "meanSpins": 25.461, "sdSpins": 9.963, "medianSpins": 23, "p90Spins": 38, "p99Spins": 58, "meanSpinsPerStudent": 2.829, "callsPerRoundIfWinnersRemoved": 9, "spinsPerRoundIfWinnersRemoved": 8, "extraCallsVsOneRound": 16.461, "firstHalfStudents": 5, "meanSpinsForFirstHalf": 6.711, "floorHalfStudents": 4, "meanSpinsForFloorHalf": 4.911, "meanSpinsForLastStudent": 9, "afterNSpins": { "expectedNeverPicked": 3.118, "shareNeverPicked": 0.34644, "expectedPickedTwiceOrMore": 2.3743, "pSomeonePicked3Plus": 0.55474, "expectedMaxPicks": 2.6765 } }, { "classSize": 10, "meanSpins": 29.29, "sdSpins": 11.211, "medianSpins": 27, "p90Spins": 44, "p99Spins": 66, "meanSpinsPerStudent": 2.929, "callsPerRoundIfWinnersRemoved": 10, "spinsPerRoundIfWinnersRemoved": 9, "extraCallsVsOneRound": 19.29, "firstHalfStudents": 5, "meanSpinsForFirstHalf": 6.456, "floorHalfStudents": 5, "meanSpinsForFloorHalf": 6.456, "meanSpinsForLastStudent": 10, "afterNSpins": { "expectedNeverPicked": 3.4868, "shareNeverPicked": 0.34868, "expectedPickedTwiceOrMore": 2.639, "pSomeonePicked3Plus": 0.60419, "expectedMaxPicks": 2.7487 } }, { "classSize": 11, "meanSpins": 33.219, "sdSpins": 12.462, "medianSpins": 31, "p90Spins": 50, "p99Spins": 74, "meanSpinsPerStudent": 3.0199, "callsPerRoundIfWinnersRemoved": 11, "spinsPerRoundIfWinnersRemoved": 10, "extraCallsVsOneRound": 22.219, "firstHalfStudents": 6, "meanSpinsForFirstHalf": 8.102, "floorHalfStudents": 5, "meanSpinsForFloorHalf": 6.269, "meanSpinsForLastStudent": 11, "afterNSpins": { "expectedNeverPicked": 3.8554, "shareNeverPicked": 0.35049, "expectedPickedTwiceOrMore": 2.9036, "pSomeonePicked3Plus": 0.64821, "expectedMaxPicks": 2.8149 } }, { "classSize": 12, "meanSpins": 37.239, "sdSpins": 13.716, "medianSpins": 35, "p90Spins": 55, "p99Spins": 82, "meanSpinsPerStudent": 3.1032, "callsPerRoundIfWinnersRemoved": 12, "spinsPerRoundIfWinnersRemoved": 11, "extraCallsVsOneRound": 25.239, "firstHalfStudents": 6, "meanSpinsForFirstHalf": 7.839, "floorHalfStudents": 6, "meanSpinsForFloorHalf": 7.839, "meanSpinsForLastStudent": 12, "afterNSpins": { "expectedNeverPicked": 4.2239, "shareNeverPicked": 0.352, "expectedPickedTwiceOrMore": 3.1681, "pSomeonePicked3Plus": 0.68737, "expectedMaxPicks": 2.876 } }, { "classSize": 13, "meanSpins": 41.342, "sdSpins": 14.971, "medianSpins": 38, "p90Spins": 61, "p99Spins": 90, "meanSpinsPerStudent": 3.1801, "callsPerRoundIfWinnersRemoved": 13, "spinsPerRoundIfWinnersRemoved": 12, "extraCallsVsOneRound": 28.342, "firstHalfStudents": 7, "meanSpinsForFirstHalf": 9.492, "floorHalfStudents": 6, "meanSpinsForFloorHalf": 7.635, "meanSpinsForLastStudent": 13, "afterNSpins": { "expectedNeverPicked": 4.5924, "shareNeverPicked": 0.35326, "expectedPickedTwiceOrMore": 3.4326, "pSomeonePicked3Plus": 0.7222, "expectedMaxPicks": 2.9324 } }, { "classSize": 14, "meanSpins": 45.522, "sdSpins": 16.229, "medianSpins": 42, "p90Spins": 67, "p99Spins": 98, "meanSpinsPerStudent": 3.2516, "callsPerRoundIfWinnersRemoved": 14, "spinsPerRoundIfWinnersRemoved": 13, 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"p90Spins": 79, "p99Spins": 115, "meanSpinsPerStudent": 3.3807, "callsPerRoundIfWinnersRemoved": 16, "spinsPerRoundIfWinnersRemoved": 15, "extraCallsVsOneRound": 38.092, "firstHalfStudents": 8, "meanSpinsForFirstHalf": 10.606, "floorHalfStudents": 8, "meanSpinsForFloorHalf": 10.606, "meanSpinsForLastStudent": 16, "afterNSpins": { "expectedNeverPicked": 5.6972, "shareNeverPicked": 0.35607, "expectedPickedTwiceOrMore": 4.2258, "pSomeonePicked3Plus": 0.80516, "expectedMaxPicks": 3.0782 } }, { "classSize": 17, "meanSpins": 58.472, "sdSpins": 20.01, "medianSpins": 55, "p90Spins": 85, "p99Spins": 123, "meanSpinsPerStudent": 3.4396, "callsPerRoundIfWinnersRemoved": 17, "spinsPerRoundIfWinnersRemoved": 16, "extraCallsVsOneRound": 41.472, "firstHalfStudents": 9, "meanSpinsForFirstHalf": 12.269, "floorHalfStudents": 8, "meanSpinsForFloorHalf": 10.38, "meanSpinsForLastStudent": 17, "afterNSpins": { "expectedNeverPicked": 6.0654, "shareNeverPicked": 0.35679, "expectedPickedTwiceOrMore": 4.4902, "pSomeonePicked3Plus": 0.8269, "expectedMaxPicks": 3.1203 } }, { "classSize": 18, "meanSpins": 62.912, "sdSpins": 21.273, "medianSpins": 59, "p90Spins": 91, "p99Spins": 132, "meanSpinsPerStudent": 3.4951, "callsPerRoundIfWinnersRemoved": 18, "spinsPerRoundIfWinnersRemoved": 17, "extraCallsVsOneRound": 44.912, "firstHalfStudents": 9, "meanSpinsForFirstHalf": 11.991, "floorHalfStudents": 9, "meanSpinsForFloorHalf": 11.991, "meanSpinsForLastStudent": 18, "afterNSpins": { "expectedNeverPicked": 6.4335, "shareNeverPicked": 0.35742, "expectedPickedTwiceOrMore": 4.7545, "pSomeonePicked3Plus": 0.84622, "expectedMaxPicks": 3.1597 } }, { "classSize": 19, "meanSpins": 67.407, "sdSpins": 22.537, "medianSpins": 63, "p90Spins": 97, "p99Spins": 140, "meanSpinsPerStudent": 3.5477, "callsPerRoundIfWinnersRemoved": 19, "spinsPerRoundIfWinnersRemoved": 18, "extraCallsVsOneRound": 48.407, "firstHalfStudents": 10, "meanSpinsForFirstHalf": 13.657, "floorHalfStudents": 9, "meanSpinsForFloorHalf": 11.757, "meanSpinsForLastStudent": 19, "afterNSpins": { "expectedNeverPicked": 6.8016, "shareNeverPicked": 0.35798, "expectedPickedTwiceOrMore": 5.0189, "pSomeonePicked3Plus": 0.86339, "expectedMaxPicks": 3.1966 } }, { "classSize": 20, "meanSpins": 71.955, "sdSpins": 23.801, "medianSpins": 67, "p90Spins": 103, "p99Spins": 149, "meanSpinsPerStudent": 3.5977, "callsPerRoundIfWinnersRemoved": 20, "spinsPerRoundIfWinnersRemoved": 19, "extraCallsVsOneRound": 51.955, "firstHalfStudents": 10, "meanSpinsForFirstHalf": 13.375, "floorHalfStudents": 10, "meanSpinsForFloorHalf": 13.375, "meanSpinsForLastStudent": 20, "afterNSpins": { "expectedNeverPicked": 7.1697, "shareNeverPicked": 0.35849, "expectedPickedTwiceOrMore": 5.2832, "pSomeonePicked3Plus": 0.87865, "expectedMaxPicks": 3.2312 } }, { "classSize": 21, "meanSpins": 76.553, "sdSpins": 25.067, "medianSpins": 72, "p90Spins": 109, "p99Spins": 157, "meanSpinsPerStudent": 3.6454, "callsPerRoundIfWinnersRemoved": 21, "spinsPerRoundIfWinnersRemoved": 20, "extraCallsVsOneRound": 55.553, "firstHalfStudents": 11, "meanSpinsForFirstHalf": 15.044, "floorHalfStudents": 10, "meanSpinsForFloorHalf": 13.135, "meanSpinsForLastStudent": 21, "afterNSpins": { "expectedNeverPicked": 7.5378, "shareNeverPicked": 0.35894, "expectedPickedTwiceOrMore": 5.5475, "pSomeonePicked3Plus": 0.8922, "expectedMaxPicks": 3.2639 } }, { "classSize": 22, "meanSpins": 81.198, "sdSpins": 26.333, "medianSpins": 76, "p90Spins": 116, "p99Spins": 166, "meanSpinsPerStudent": 3.6908, "callsPerRoundIfWinnersRemoved": 22, "spinsPerRoundIfWinnersRemoved": 21, "extraCallsVsOneRound": 59.198, "firstHalfStudents": 11, "meanSpinsForFirstHalf": 14.761, "floorHalfStudents": 11, "meanSpinsForFloorHalf": 14.761, "meanSpinsForLastStudent": 22, "afterNSpins": { "expectedNeverPicked": 7.9058, "shareNeverPicked": 0.35936, "expectedPickedTwiceOrMore": 5.8118, "pSomeonePicked3Plus": 0.90425, "expectedMaxPicks": 3.2947 } }, { "classSize": 23, "meanSpins": 85.889, "sdSpins": 27.6, "medianSpins": 81, "p90Spins": 122, "p99Spins": 175, "meanSpinsPerStudent": 3.7343, "callsPerRoundIfWinnersRemoved": 23, "spinsPerRoundIfWinnersRemoved": 22, "extraCallsVsOneRound": 62.889, "firstHalfStudents": 12, "meanSpinsForFirstHalf": 16.432, "floorHalfStudents": 11, "meanSpinsForFloorHalf": 14.515, "meanSpinsForLastStudent": 23, "afterNSpins": { "expectedNeverPicked": 8.2739, "shareNeverPicked": 0.35973, "expectedPickedTwiceOrMore": 6.0762, "pSomeonePicked3Plus": 0.91494, "expectedMaxPicks": 3.3239 } }, { "classSize": 24, "meanSpins": 90.623, "sdSpins": 28.868, "medianSpins": 85, "p90Spins": 128, "p99Spins": 183, "meanSpinsPerStudent": 3.776, "callsPerRoundIfWinnersRemoved": 24, "spinsPerRoundIfWinnersRemoved": 23, "extraCallsVsOneRound": 66.623, "firstHalfStudents": 12, "meanSpinsForFirstHalf": 16.146, "floorHalfStudents": 12, "meanSpinsForFloorHalf": 16.146, "meanSpinsForLastStudent": 24, "afterNSpins": { "expectedNeverPicked": 8.6419, "shareNeverPicked": 0.36008, "expectedPickedTwiceOrMore": 6.3405, "pSomeonePicked3Plus": 0.92445, "expectedMaxPicks": 3.3516 } }, { "classSize": 25, "meanSpins": 95.399, "sdSpins": 30.136, "medianSpins": 90, "p90Spins": 135, "p99Spins": 192, "meanSpinsPerStudent": 3.816, "callsPerRoundIfWinnersRemoved": 25, "spinsPerRoundIfWinnersRemoved": 24, "extraCallsVsOneRound": 70.399, "firstHalfStudents": 13, "meanSpinsForFirstHalf": 17.819, "floorHalfStudents": 12, "meanSpinsForFloorHalf": 15.896, "meanSpinsForLastStudent": 25, "afterNSpins": { "expectedNeverPicked": 9.0099, "shareNeverPicked": 0.3604, "expectedPickedTwiceOrMore": 6.6048, "pSomeonePicked3Plus": 0.93289, "expectedMaxPicks": 3.3779 } }, { "classSize": 26, "meanSpins": 100.215, "sdSpins": 31.405, "medianSpins": 94, "p90Spins": 141, "p99Spins": 201, "meanSpinsPerStudent": 3.8544, "callsPerRoundIfWinnersRemoved": 26, "spinsPerRoundIfWinnersRemoved": 25, "extraCallsVsOneRound": 74.215, "firstHalfStudents": 13, "meanSpinsForFirstHalf": 17.531, "floorHalfStudents": 13, "meanSpinsForFloorHalf": 17.531, "meanSpinsForLastStudent": 26, "afterNSpins": { "expectedNeverPicked": 9.3779, "shareNeverPicked": 0.36069, "expectedPickedTwiceOrMore": 6.869, "pSomeonePicked3Plus": 0.94039, "expectedMaxPicks": 3.403 } }, { "classSize": 27, "meanSpins": 105.069, "sdSpins": 32.674, "medianSpins": 99, "p90Spins": 148, "p99Spins": 210, "meanSpinsPerStudent": 3.8915, "callsPerRoundIfWinnersRemoved": 27, "spinsPerRoundIfWinnersRemoved": 26, "extraCallsVsOneRound": 78.069, "firstHalfStudents": 14, "meanSpinsForFirstHalf": 19.206, "floorHalfStudents": 13, "meanSpinsForFloorHalf": 17.277, "meanSpinsForLastStudent": 27, "afterNSpins": { "expectedNeverPicked": 9.7459, "shareNeverPicked": 0.36096, "expectedPickedTwiceOrMore": 7.1333, "pSomeonePicked3Plus": 0.94705, "expectedMaxPicks": 3.4269 } }, { "classSize": 28, "meanSpins": 109.961, "sdSpins": 33.944, "medianSpins": 104, "p90Spins": 154, "p99Spins": 219, "meanSpinsPerStudent": 3.9272, "callsPerRoundIfWinnersRemoved": 28, "spinsPerRoundIfWinnersRemoved": 27, "extraCallsVsOneRound": 81.961, "firstHalfStudents": 14, "meanSpinsForFirstHalf": 18.917, "floorHalfStudents": 14, "meanSpinsForFloorHalf": 18.917, "meanSpinsForLastStudent": 28, "afterNSpins": { "expectedNeverPicked": 10.1139, "shareNeverPicked": 0.36121, "expectedPickedTwiceOrMore": 7.3976, "pSomeonePicked3Plus": 0.95297, "expectedMaxPicks": 3.4499 } }, { "classSize": 29, "meanSpins": 114.888, "sdSpins": 35.214, "medianSpins": 108, "p90Spins": 161, "p99Spins": 228, "meanSpinsPerStudent": 3.9617, "callsPerRoundIfWinnersRemoved": 29, "spinsPerRoundIfWinnersRemoved": 28, "extraCallsVsOneRound": 85.888, "firstHalfStudents": 15, "meanSpinsForFirstHalf": 20.593, "floorHalfStudents": 14, "meanSpinsForFloorHalf": 18.659, "meanSpinsForLastStudent": 29, "afterNSpins": { "expectedNeverPicked": 10.4819, "shareNeverPicked": 0.36144, "expectedPickedTwiceOrMore": 7.6619, "pSomeonePicked3Plus": 0.95823, "expectedMaxPicks": 3.4719 } }, { "classSize": 30, "meanSpins": 119.85, "sdSpins": 36.484, "medianSpins": 113, "p90Spins": 168, "p99Spins": 237, "meanSpinsPerStudent": 3.995, "callsPerRoundIfWinnersRemoved": 30, "spinsPerRoundIfWinnersRemoved": 29, "extraCallsVsOneRound": 89.85, "firstHalfStudents": 15, "meanSpinsForFirstHalf": 20.303, "floorHalfStudents": 15, "meanSpinsForFloorHalf": 20.303, "meanSpinsForLastStudent": 30, "afterNSpins": { "expectedNeverPicked": 10.8498, "shareNeverPicked": 0.36166, "expectedPickedTwiceOrMore": 7.9262, "pSomeonePicked3Plus": 0.9629, "expectedMaxPicks": 3.493 } }, { "classSize": 31, "meanSpins": 124.845, "sdSpins": 37.755, "medianSpins": 118, "p90Spins": 174, "p99Spins": 246, "meanSpinsPerStudent": 4.0272, "callsPerRoundIfWinnersRemoved": 31, "spinsPerRoundIfWinnersRemoved": 30, "extraCallsVsOneRound": 93.845, "firstHalfStudents": 16, "meanSpinsForFirstHalf": 21.98, "floorHalfStudents": 15, "meanSpinsForFloorHalf": 20.042, "meanSpinsForLastStudent": 31, "afterNSpins": { "expectedNeverPicked": 11.2178, "shareNeverPicked": 0.36186, "expectedPickedTwiceOrMore": 8.1905, "pSomeonePicked3Plus": 0.96704, "expectedMaxPicks": 3.5133 } }, { "classSize": 32, "meanSpins": 129.872, "sdSpins": 39.026, "medianSpins": 123, "p90Spins": 181, "p99Spins": 255, "meanSpinsPerStudent": 4.0585, "callsPerRoundIfWinnersRemoved": 32, "spinsPerRoundIfWinnersRemoved": 31, "extraCallsVsOneRound": 97.872, "firstHalfStudents": 16, "meanSpinsForFirstHalf": 21.689, "floorHalfStudents": 16, "meanSpinsForFloorHalf": 21.689, "meanSpinsForLastStudent": 32, "afterNSpins": { "expectedNeverPicked": 11.5858, "shareNeverPicked": 0.36206, "expectedPickedTwiceOrMore": 8.4547, "pSomeonePicked3Plus": 0.97073, "expectedMaxPicks": 3.5329 } }, { "classSize": 33, "meanSpins": 134.93, "sdSpins": 40.298, "medianSpins": 128, "p90Spins": 188, "p99Spins": 264, "meanSpinsPerStudent": 4.0888, "callsPerRoundIfWinnersRemoved": 33, "spinsPerRoundIfWinnersRemoved": 32, "extraCallsVsOneRound": 101.93, "firstHalfStudents": 17, "meanSpinsForFirstHalf": 23.366, "floorHalfStudents": 16, "meanSpinsForFloorHalf": 21.425, "meanSpinsForLastStudent": 33, "afterNSpins": { "expectedNeverPicked": 11.9537, "shareNeverPicked": 0.36223, "expectedPickedTwiceOrMore": 8.719, "pSomeonePicked3Plus": 0.974, "expectedMaxPicks": 3.5519 } }, { "classSize": 34, "meanSpins": 140.019, "sdSpins": 41.569, "medianSpins": 133, "p90Spins": 194, "p99Spins": 273, "meanSpinsPerStudent": 4.1182, "callsPerRoundIfWinnersRemoved": 34, "spinsPerRoundIfWinnersRemoved": 33, "extraCallsVsOneRound": 106.019, "firstHalfStudents": 17, "meanSpinsForFirstHalf": 23.074, "floorHalfStudents": 17, "meanSpinsForFloorHalf": 23.074, "meanSpinsForLastStudent": 34, "afterNSpins": { "expectedNeverPicked": 12.3217, "shareNeverPicked": 0.3624, "expectedPickedTwiceOrMore": 8.9833, "pSomeonePicked3Plus": 0.97691, "expectedMaxPicks": 3.5702 } }, { "classSize": 35, "meanSpins": 145.137, "sdSpins": 42.842, "medianSpins": 137, "p90Spins": 201, "p99Spins": 282, "meanSpinsPerStudent": 4.1468, "callsPerRoundIfWinnersRemoved": 35, "spinsPerRoundIfWinnersRemoved": 34, "extraCallsVsOneRound": 110.137, "firstHalfStudents": 18, "meanSpinsForFirstHalf": 24.753, "floorHalfStudents": 17, "meanSpinsForFloorHalf": 22.809, "meanSpinsForLastStudent": 35, "afterNSpins": { "expectedNeverPicked": 12.6896, "shareNeverPicked": 0.36256, "expectedPickedTwiceOrMore": 9.2475, "pSomeonePicked3Plus": 0.97949, "expectedMaxPicks": 3.5879 } }, { "classSize": 36, "meanSpins": 150.284, "sdSpins": 44.114, "medianSpins": 142, "p90Spins": 208, "p99Spins": 291, "meanSpinsPerStudent": 4.1746, "callsPerRoundIfWinnersRemoved": 36, "spinsPerRoundIfWinnersRemoved": 35, "extraCallsVsOneRound": 114.284, "firstHalfStudents": 18, "meanSpinsForFirstHalf": 24.46, "floorHalfStudents": 18, "meanSpinsForFloorHalf": 24.46, "meanSpinsForLastStudent": 36, "afterNSpins": { "expectedNeverPicked": 13.0576, "shareNeverPicked": 0.36271, "expectedPickedTwiceOrMore": 9.5118, "pSomeonePicked3Plus": 0.98178, "expectedMaxPicks": 3.6052 } }, { "classSize": 37, "meanSpins": 155.459, "sdSpins": 45.387, "medianSpins": 147, "p90Spins": 215, "p99Spins": 300, "meanSpinsPerStudent": 4.2016, "callsPerRoundIfWinnersRemoved": 37, "spinsPerRoundIfWinnersRemoved": 36, "extraCallsVsOneRound": 118.459, "firstHalfStudents": 19, "meanSpinsForFirstHalf": 26.14, "floorHalfStudents": 18, "meanSpinsForFloorHalf": 24.192, "meanSpinsForLastStudent": 37, "afterNSpins": { "expectedNeverPicked": 13.4255, "shareNeverPicked": 0.36285, "expectedPickedTwiceOrMore": 9.7761, "pSomeonePicked3Plus": 0.98382, "expectedMaxPicks": 3.6219 } }, { "classSize": 38, "meanSpins": 160.66, "sdSpins": 46.66, "medianSpins": 152, "p90Spins": 222, "p99Spins": 309, "meanSpinsPerStudent": 4.2279, "callsPerRoundIfWinnersRemoved": 38, "spinsPerRoundIfWinnersRemoved": 37, "extraCallsVsOneRound": 122.66, "firstHalfStudents": 19, "meanSpinsForFirstHalf": 25.846, "floorHalfStudents": 19, "meanSpinsForFloorHalf": 25.846, "meanSpinsForLastStudent": 38, "afterNSpins": { "expectedNeverPicked": 13.7934, "shareNeverPicked": 0.36299, "expectedPickedTwiceOrMore": 10.0403, "pSomeonePicked3Plus": 0.98563, "expectedMaxPicks": 3.6381 } }, { "classSize": 39, "meanSpins": 165.888, "sdSpins": 47.933, "medianSpins": 157, "p90Spins": 229, "p99Spins": 319, "meanSpinsPerStudent": 4.2535, "callsPerRoundIfWinnersRemoved": 39, "spinsPerRoundIfWinnersRemoved": 38, "extraCallsVsOneRound": 126.888, "firstHalfStudents": 20, "meanSpinsForFirstHalf": 27.526, "floorHalfStudents": 19, "meanSpinsForFloorHalf": 25.576, "meanSpinsForLastStudent": 39, "afterNSpins": { "expectedNeverPicked": 14.1614, "shareNeverPicked": 0.36311, "expectedPickedTwiceOrMore": 10.3046, "pSomeonePicked3Plus": 0.98723, "expectedMaxPicks": 3.6539 } }, { "classSize": 40, "meanSpins": 171.142, "sdSpins": 49.206, "medianSpins": 162, "p90Spins": 235, "p99Spins": 328, "meanSpinsPerStudent": 4.2785, "callsPerRoundIfWinnersRemoved": 40, "spinsPerRoundIfWinnersRemoved": 39, "extraCallsVsOneRound": 131.142, "firstHalfStudents": 20, "meanSpinsForFirstHalf": 27.232, "floorHalfStudents": 20, "meanSpinsForFloorHalf": 27.232, "meanSpinsForLastStudent": 40, "afterNSpins": { "expectedNeverPicked": 14.5293, "shareNeverPicked": 0.36323, "expectedPickedTwiceOrMore": 10.5689, "pSomeonePicked3Plus": 0.98866, "expectedMaxPicks": 3.6693 } } ], "cdf": { "spins": [ 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, 255, 260, 265, 270, 275, 280, 285, 290, 295, 300, 305, 310, 315, 320, 325, 330, 335, 340, 345, 350, 355, 360, 365 ], "probabilityEveryonePickedBySpin": { "15": [ 0, 0, 0, 0, 0.0018, 0.0223, 0.0878, 0.2004, 0.3382, 0.4764, 0.5994, 0.7006, 0.78, 0.8401, 0.8848, 0.9174, 0.941, 0.958, 0.9701, 0.9788, 0.9849, 0.9893, 0.9924, 0.9946, 0.9962, 0.9973, 0.9981, 0.9986, 0.999, 0.9993, 0.9995, 0.9997, 0.9998, 0.9998, 0.9999, 0.9999, 0.9999, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], "25": [ 0, 0, 0, 0, 0, 0, 0, 0.0001, 0.0007, 0.0041, 0.0147, 0.0373, 0.0755, 0.1295, 0.1967, 0.2729, 0.3531, 0.433, 0.5095, 0.5802, 0.6439, 0.7001, 0.749, 0.791, 0.8266, 0.8567, 0.8818, 0.9027, 0.9201, 0.9345, 0.9463, 0.9561, 0.9641, 0.9706, 0.976, 0.9804, 0.984, 0.9869, 0.9893, 0.9913, 0.9929, 0.9942, 0.9953, 0.9961, 0.9969, 0.9974, 0.9979, 0.9983, 0.9986, 0.9989, 0.9991, 0.9992, 0.9994, 0.9995, 0.9996, 0.9997, 0.9997, 0.9998, 0.9998, 0.9999, 0.9999, 0.9999, 0.9999, 0.9999, 0.9999, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], "35": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0002, 0.0007, 0.0024, 0.0066, 0.0146, 0.0284, 0.049, 0.0774, 0.1133, 0.1562, 0.2048, 0.2575, 0.3128, 0.3691, 0.425, 0.4794, 0.5314, 0.5803, 0.6259, 0.6679, 0.7061, 0.7408, 0.7719, 0.7998, 0.8246, 0.8467, 0.8661, 0.8832, 0.8983, 0.9115, 0.923, 0.9331, 0.9419, 0.9496, 0.9563, 0.9621, 0.9671, 0.9715, 0.9753, 0.9786, 0.9815, 0.984, 0.9861, 0.988, 0.9896, 0.991, 0.9922, 0.9933, 0.9942, 0.9949, 0.9956, 0.9962, 0.9967, 0.9972, 0.9975, 0.9979, 0.9982, 0.9984, 0.9986, 0.9988, 0.999, 0.9991 ] } }, "lesson": { "pGivenStudentNeverCalled": 0.66483, "expectedStudentsNeverCalled": 16.62082, "expectedStudentsCalled": 8.37918, "expectedStudentsCalledTwiceOrMore": 1.45384, "pSomeoneCalledTwiceOrMore": 0.87562, "pSomeoneCalled3Plus": 0.15132, "pGivenStudentCalledTwiceOrMore": 0.05815 }, "week": { "pGivenStudentNeverCalled": 0.12989, "expectedStudentsNeverCalled": 3.24714, "pAtLeastOneStudentNeverCalled": 0.98534, "pGivenStudentCalledAtMostOnce": 0.40048, "expectedStudentsCalledAtMostOnce": 10.01203, "expectedStudentsCalled4PlusTimes": 3.47827, "expectedMostCallsForOneStudent": 5.20967, "callsPerStudentIfShared": 2, "pNextTurnMoreThan2nCallsAway": 0.12989 }, "withoutReplacement": { "callsUntilEveryonePicked": "n (exactly one call per student per round)", "spinsPerRound": "n - 1 (the last name left is called without a spin)", "spinsPerRoundClassOf25": 24, "callsPerStudentPerWeek": 2, "longestPossibleGapBetweenTurns": 49, "limitShareNeverPickedAfterNSpins": 0.36788 } }, "checks": [ { "name": "n=10: mean spins until everyone is picked", "simulated": 29.26251, "exact": 29.28968, "tolerance": 0.15855, "pass": true }, { "name": "n=10: median spins", "simulated": 27, "exact": 27, "tolerance": 1.17396, "pass": true }, { "name": "n=10: 90th percentile spins", "simulated": 44, "exact": 44, "tolerance": 1.41715, "pass": true }, { "name": "n=10: 99th percentile spins", "simulated": 66, "exact": 66, "tolerance": 2.33175, "pass": true }, { "name": "n=10: mean spins until half the class is picked", "simulated": 6.46267, "exact": 6.45635, "tolerance": 0.02086, "pass": true }, { "name": "n=10: students never picked after n spins", "simulated": 3.48965, "exact": 3.48678, "tolerance": 0.01408, "pass": true }, { "name": "n=10: students picked 2+ times after n spins", "simulated": 2.63659, "exact": 2.63901, "tolerance": 0.01087, "pass": true }, { "name": "n=10: P(someone picked 3+ times in n spins)", "simulated": 0.6078, "exact": 0.60419, "tolerance": 0.00692, "pass": true }, { "name": "n=10: most picks of one student after n spins", "simulated": 2.7544, "exact": 2.74869, "tolerance": 0.01021, "pass": true }, { "name": "n=10: most picks of one student when everyone is done", "simulated": 5.71582, "exact": 5.71792, "tolerance": 0.03043, "pass": true }, { "name": "n=15: mean spins until everyone is picked", "simulated": 49.7109, "exact": 49.77343, "tolerance": 0.24732, "pass": true }, { "name": "n=15: median spins", "simulated": 46, "exact": 46, "tolerance": 1.27053, "pass": true }, { "name": "n=15: 90th percentile spins", "simulated": 72, "exact": 73, "tolerance": 1.65263, "pass": true }, { "name": "n=15: 99th percentile spins", "simulated": 107, "exact": 106, "tolerance": 2.98159, "pass": true }, { "name": "n=15: mean spins until half the class is picked", "simulated": 10.87909, "exact": 10.88058, "tolerance": 0.03017, "pass": true }, { "name": "n=15: students never picked after n spins", "simulated": 5.32472, "exact": 5.32897, "tolerance": 0.0172, "pass": true }, { "name": "n=15: students picked 2+ times after n spins", "simulated": 3.95849, "exact": 3.96143, "tolerance": 0.01329, "pass": true }, { "name": "n=15: P(someone picked 3+ times in n spins)", "simulated": 0.78074, "exact": 0.78069, "tolerance": 0.00585, "pass": true }, { "name": "n=15: most picks of one student after n spins", "simulated": 3.03383, "exact": 3.03312, "tolerance": 0.01055, "pass": true }, { "name": "n=15: most picks of one student when everyone is done", "simulated": 6.73238, "exact": 6.7381, "tolerance": 0.03139, "pass": true }, { "name": "n=20: mean spins until everyone is picked", "simulated": 71.93948, "exact": 71.95479, "tolerance": 0.3366, "pass": true }, { "name": "n=20: median spins", "simulated": 68, "exact": 67, "tolerance": 1.37006, "pass": true }, { "name": "n=20: 90th percentile spins", "simulated": 103, "exact": 103, "tolerance": 1.85793, "pass": true }, { "name": "n=20: 99th percentile spins", "simulated": 148, "exact": 149, "tolerance": 3.80547, "pass": true }, { "name": "n=20: mean spins until half the class is picked", "simulated": 13.38146, "exact": 13.37543, "tolerance": 0.03226, "pass": true }, { "name": "n=20: students never picked after n spins", "simulated": 7.17042, "exact": 7.16972, "tolerance": 0.01982, "pass": true }, { "name": "n=20: students picked 2+ times after n spins", "simulated": 5.28193, "exact": 5.28321, "tolerance": 0.0154, "pass": true }, { "name": "n=20: P(someone picked 3+ times in n spins)", "simulated": 0.87854, "exact": 0.87865, "tolerance": 0.00462, "pass": true }, { "name": "n=20: most picks of one student after n spins", "simulated": 3.2319, "exact": 3.23124, "tolerance": 0.01051, "pass": true }, { "name": "n=20: most picks of one student when everyone is done", "simulated": 7.47305, "exact": 7.47164, "tolerance": 0.03178, "pass": true }, { "name": "n=25: mean spins until everyone is picked", "simulated": 95.50944, "exact": 95.39895, "tolerance": 0.42619, "pass": true }, { "name": "n=25: median spins", "simulated": 90, "exact": 90, "tolerance": 1.4751, "pass": true }, { "name": "n=25: 90th percentile spins", "simulated": 135, "exact": 135, "tolerance": 2.09251, "pass": true }, { "name": "n=25: 99th percentile spins", "simulated": 191, "exact": 192, "tolerance": 4.4483, "pass": true }, { "name": "n=25: mean spins until half the class is picked", "simulated": 17.82331, "exact": 17.81869, "tolerance": 0.0389, "pass": true }, { "name": "n=25: students never picked after n spins", "simulated": 9.0091, "exact": 9.00992, "tolerance": 0.02211, "pass": true }, { "name": "n=25: students picked 2+ times after n spins", "simulated": 6.59631, "exact": 6.60475, "tolerance": 0.01717, "pass": true }, { "name": "n=25: P(someone picked 3+ times in n spins)", "simulated": 0.9341, "exact": 0.93289, "tolerance": 0.00354, "pass": true }, { "name": "n=25: most picks of one student after n spins", "simulated": 3.38159, "exact": 3.37789, "tolerance": 0.01051, "pass": true }, { "name": "n=25: most picks of one student when everyone is done", "simulated": 8.05571, "exact": 8.045, "tolerance": 0.03243, "pass": true }, { "name": "n=25: histogram, largest bucket gap (standard errors)", "simulated": 2.00701, "exact": 0, "tolerance": 4.5, "pass": true }, { "name": "n=25: histogram, exact share below the first bucket is negligible", "simulated": 0, "exact": 0, "tolerance": 0.0001, "pass": true }, { "name": "n=30: mean spins until everyone is picked", "simulated": 119.88909, "exact": 119.84961, "tolerance": 0.51596, "pass": true }, { "name": "n=30: median spins", "simulated": 113, "exact": 113, "tolerance": 1.57325, "pass": true }, { "name": "n=30: 90th percentile spins", "simulated": 168, "exact": 168, "tolerance": 2.32633, "pass": true }, { "name": "n=30: 99th percentile spins", "simulated": 239, "exact": 237, "tolerance": 5.22876, "pass": true }, { "name": "n=30: mean spins until half the class is picked", "simulated": 20.31796, "exact": 20.30274, "tolerance": 0.04083, "pass": true }, { "name": "n=30: students never picked after n spins", "simulated": 10.84725, "exact": 10.84985, "tolerance": 0.02426, "pass": true }, { "name": "n=30: students picked 2+ times after n spins", "simulated": 7.91638, "exact": 7.92618, "tolerance": 0.01884, "pass": true }, { "name": "n=30: P(someone picked 3+ times in n spins)", "simulated": 0.96384, "exact": 0.9629, "tolerance": 0.00267, "pass": true }, { "name": "n=30: most picks of one student after n spins", "simulated": 3.49766, "exact": 3.49299, "tolerance": 0.01053, "pass": true }, { "name": "n=30: most picks of one student when everyone is done", "simulated": 8.52155, "exact": 8.51585, "tolerance": 0.03268, "pass": true }, { "name": "n=35: mean spins until everyone is picked", "simulated": 145.18592, "exact": 145.13735, "tolerance": 0.60587, "pass": true }, { "name": "n=35: median spins", "simulated": 137, "exact": 137, "tolerance": 1.67278, "pass": true }, { "name": "n=35: 90th percentile spins", "simulated": 201, "exact": 201, "tolerance": 2.52572, "pass": true }, { "name": "n=35: 99th percentile spins", "simulated": 279, "exact": 282, "tolerance": 5.88921, "pass": true }, { "name": "n=35: mean spins until half the class is picked", "simulated": 24.75116, "exact": 24.75301, "tolerance": 0.04641, "pass": true }, { "name": "n=35: students never picked after n spins", "simulated": 12.68354, "exact": 12.68962, "tolerance": 0.02616, "pass": true }, { "name": "n=35: students picked 2+ times after n spins", "simulated": 9.24316, "exact": 9.24754, "tolerance": 0.02032, "pass": true }, { "name": "n=35: P(someone picked 3+ times in n spins)", "simulated": 0.97976, "exact": 0.97949, "tolerance": 0.002, "pass": true }, { "name": "n=35: most picks of one student after n spins", "simulated": 3.58689, "exact": 3.58794, "tolerance": 0.0106, "pass": true }, { "name": "n=35: most picks of one student when everyone is done", "simulated": 8.92163, "exact": 8.9154, "tolerance": 0.03267, "pass": true }, { "name": "lesson: share of students never called", "simulated": 0.66479, "exact": 0.66483, "tolerance": 0.00029, "pass": true }, { "name": "lesson: one named student never called", "simulated": 0.66353, "exact": 0.66483, "tolerance": 0.00345, "pass": true }, { "name": "lesson: students called twice or more", "simulated": 1.45354, "exact": 1.45384, "tolerance": 0.00627, "pass": true }, { "name": "lesson: P(someone called twice or more)", "simulated": 0.87552, "exact": 0.87562, "tolerance": 0.00241, "pass": true }, { "name": "lesson: P(someone called 3+ times)", "simulated": 0.15077, "exact": 0.15132, "tolerance": 0.00262, "pass": true }, { "name": "week: students never called", "simulated": 3.24736, "exact": 3.24714, "tolerance": 0.01263, "pass": true }, { "name": "week: P(at least one student never called)", "simulated": 0.98506, "exact": 0.98534, "tolerance": 0.00107, "pass": true }, { "name": "week: students called at most once", "simulated": 10.00826, "exact": 10.01203, "tolerance": 0.0138, "pass": true }, { "name": "week: students called 4+ times", "simulated": 3.47768, "exact": 3.47827, "tolerance": 0.01078, "pass": true }, { "name": "week: most calls for one student", "simulated": 5.20897, "exact": 5.20967, "tolerance": 0.00849, "pass": true }, { "name": "without replacement: weeks with unequal calls", "simulated": 0, "exact": 0, "tolerance": 0, "pass": true }, { "name": "without replacement: rounds that missed or repeated someone", "simulated": 0, "exact": 0, "tolerance": 0, "pass": true }, { "name": "without replacement: every round took n-1 spins", "simulated": 0, "exact": 0, "tolerance": 0, "pass": true }, { "name": "without replacement: spins per week (2 rounds of 25 = 48)", "simulated": 48, "exact": 48, "tolerance": 0, "pass": true }, { "name": "without replacement: longest gap between turns <= 2n-1", "simulated": 0, "exact": 0, "tolerance": 0, "pass": true }, { "name": "without replacement: last name left is uniform (largest gap, standard errors)", "simulated": 2.39629, "exact": 0, "tolerance": 4.5, "pass": true }, { "name": "raw draws cover every spin", "simulated": 0, "exact": 0, "tolerance": 0, "pass": true } ] }