{
  "schemaVersion": 1,
  "sourceHashes": {
    "US_births_1994-2003_CDC_NCHS.csv": "2d0d0c2734468e22a7195f30bfee99885da2322ccf538dbad5d2125d4a06c011",
    "US_births_2000-2014_SSA.csv": "67ed396cecc999664a737ee75f287cf3472e24c3257fcca795b672579f0ed910"
  },
  "baseline": {
    "population": "Historical U.S. recorded births",
    "start": "1994-01-01",
    "end": "2014-12-31",
    "totalBirths": 85712738,
    "sources": "CDC/NCHS 1994–1999; SSA 2000–2014, no overlapping years"
  },
  "assumptions": {
    "classic": "Independent draws from 365 equally likely dates; leap day excluded.",
    "historical": "Independent draws from 366 observed birth shares; leap day included.",
    "family": "Non-twin independent-draw benchmark only, not measured family probabilities."
  },
  "pair": {
    "classic": 0.0027397260273972603,
    "historical": 0.002744051480544938,
    "classicOneIn": 365,
    "historicalOneIn": 364.42464986167505
  },
  "triple": {
    "classic": 7.5060987051979735e-06,
    "historical": 7.550016456712396e-06,
    "classicOneIn": 133225,
    "historicalOneIn": 132450.04242486687,
    "classicFiftyThreshold": 88,
    "historicalFiftyThreshold": 87
  },
  "dateExamples": [
    {
      "date": "09-09",
      "label": "September 9",
      "share": 0.003024381276911257,
      "oneMatchOneIn": 330.64614162050395,
      "twoMatchProbability": 9.146882108131365e-06,
      "twoMatchOneIn": 109326.87096852635,
      "atLeastOneOf22": 0.06446545495387906
    },
    {
      "date": "07-04",
      "label": "July 4",
      "share": 0.0021620473727020596,
      "oneMatchOneIn": 462.5245554866039,
      "twoMatchProbability": 4.674448841807879e-06,
      "twoMatchOneIn": 213928.96442808054,
      "atLeastOneOf22": 0.04650064974221558
    },
    {
      "date": "12-25",
      "label": "December 25",
      "share": 0.0016173558707225056,
      "oneMatchOneIn": 618.2931153879448,
      "twoMatchProbability": 2.6158400125605544e-06,
      "twoMatchOneIn": 382286.3765361303,
      "atLeastOneOf22": 0.034984035695412155
    },
    {
      "date": "02-29",
      "label": "February 29",
      "share": 0.0006132227394252649,
      "oneMatchOneIn": 1630.7288293601719,
      "twoMatchProbability": 3.7604212814822633e-07,
      "twoMatchOneIn": 2659276.5149063966,
      "atLeastOneOf22": 0.01340438862391527
    }
  ],
  "groupMatches": [
    {
      "people": 3,
      "classicAnyPair": 0.008204165884783898,
      "historicalAnyPair": 0.008217054408721558,
      "classicAnyTriple": 7.506098708476294e-06,
      "historicalAnyTriple": 7.55001645635911e-06
    },
    {
      "people": 10,
      "classicAnyPair": 0.11694817771107757,
      "historicalAnyPair": 0.1171186956039264,
      "classicAnyTriple": 0.0008877449130194615,
      "historicalAnyTriple": 0.0008928558878563697
    },
    {
      "people": 23,
      "classicAnyPair": 0.5072972343239849,
      "historicalAnyPair": 0.5078220129591833,
      "classicAnyTriple": 0.01270542106874728,
      "historicalAnyTriple": 0.01277610991014222
    },
    {
      "people": 30,
      "classicAnyPair": 0.7063162427192684,
      "historicalAnyPair": 0.7068480569716223,
      "classicAnyTriple": 0.028530503744329527,
      "historicalAnyTriple": 0.028685644076290928
    },
    {
      "people": 50,
      "classicAnyPair": 0.9703735795779884,
      "historicalAnyPair": 0.9705192874184908,
      "classicAnyTriple": 0.12637518418618043,
      "historicalAnyTriple": 0.1270001885343508
    },
    {
      "people": 87,
      "classicAnyPair": 0.9999859253976947,
      "historicalAnyPair": 0.9999861191931546,
      "classicAnyTriple": 0.49945485063140005,
      "historicalAnyTriple": 0.5011601156648748
    },
    {
      "people": 88,
      "classicAnyPair": 0.9999892801659155,
      "historicalAnyPair": 0.9999894307803807,
      "classicAnyTriple": 0.5110651106247299,
      "historicalAnyTriple": 0.5127839667876739
    },
    {
      "people": 100,
      "classicAnyPair": 0.9999996927510721,
      "historicalAnyPair": 0.999999698137179,
      "classicAnyTriple": 0.6458645065451718,
      "historicalAnyTriple": 0.6476291788995072
    }
  ],
  "siblings": [
    {
      "children": 2,
      "classicAnyPair": 0.0027397260274001356,
      "historicalAnyPair": 0.0027440514805446847
    },
    {
      "children": 3,
      "classicAnyPair": 0.008204165884783898,
      "historicalAnyPair": 0.008217054408721558
    },
    {
      "children": 4,
      "classicAnyPair": 0.016355912466552547,
      "historicalAnyPair": 0.016381444203693807
    },
    {
      "children": 5,
      "classicAnyPair": 0.02713557369979569,
      "historicalAnyPair": 0.027177604709078595
    }
  ],
  "workedSteps": [
    {
      "people": 1,
      "nextAvailableDates": 365,
      "noMatchProbability": 1.0,
      "matchProbability": 0.0,
      "possiblePairs": 0,
      "expectedMatchingPairs": 0.0
    },
    {
      "people": 2,
      "nextAvailableDates": 364,
      "noMatchProbability": 0.9972602739726028,
      "matchProbability": 0.002739726027397249,
      "possiblePairs": 1,
      "expectedMatchingPairs": 0.0027397260273972603
    },
    {
      "people": 3,
      "nextAvailableDates": 363,
      "noMatchProbability": 0.9917958341152187,
      "matchProbability": 0.008204165884781345,
      "possiblePairs": 3,
      "expectedMatchingPairs": 0.00821917808219178
    },
    {
      "people": 10,
      "nextAvailableDates": 356,
      "noMatchProbability": 0.8830518222889223,
      "matchProbability": 0.11694817771107768,
      "possiblePairs": 45,
      "expectedMatchingPairs": 0.1232876712328767
    },
    {
      "people": 20,
      "nextAvailableDates": 346,
      "noMatchProbability": 0.5885616164194197,
      "matchProbability": 0.41143838358058027,
      "possiblePairs": 190,
      "expectedMatchingPairs": 0.5205479452054794
    },
    {
      "people": 22,
      "nextAvailableDates": 344,
      "noMatchProbability": 0.5243046923374497,
      "matchProbability": 0.4756953076625503,
      "possiblePairs": 231,
      "expectedMatchingPairs": 0.6328767123287671
    },
    {
      "people": 23,
      "nextAvailableDates": 343,
      "noMatchProbability": 0.4927027656760144,
      "matchProbability": 0.5072972343239857,
      "possiblePairs": 253,
      "expectedMatchingPairs": 0.6931506849315069
    },
    {
      "people": 50,
      "nextAvailableDates": 316,
      "noMatchProbability": 0.029626420422011596,
      "matchProbability": 0.9703735795779884,
      "possiblePairs": 1225,
      "expectedMatchingPairs": 3.356164383561644
    }
  ],
  "expectedPairs23": 0.6931506849315069,
  "calculation": "No triple = n! coefficient of x^n in product(1+p_i*x+p_i^2*x^2/2). Descending scaled coefficient recurrence; group event includes three or more, not exactly three."
}