{
  "calculatedOn": "2026-10-09",
  "method": "Exact enumeration, not random sampling or app testing",
  "assumptions": {
    "deck": 52,
    "ranks": 13,
    "suits": 4,
    "cardsPerHand": 3,
    "unordered": true,
    "replacement": false,
    "wildCards": false,
    "validRuns": [
      "A23",
      "234",
      "345",
      "456",
      "567",
      "678",
      "789",
      "8910",
      "910J",
      "10JQ",
      "JQK",
      "QKA"
    ],
    "excluded": "KA2",
    "categoryPrecedence": "Trail > Pure Sequence > Sequence > Colour > Pair > High Card"
  },
  "totalHands": 22100,
  "rows": [
    {
      "category": "Trail / Trio",
      "categoryHi": "Trail / तिकड़ी",
      "formula": "13 × C(4,3)",
      "count": 52,
      "probabilityPercent": 0.23529411764705882
    },
    {
      "category": "Pure Sequence",
      "categoryHi": "Pure Sequence / एक सूट का क्रम",
      "formula": "12 × 4",
      "count": 48,
      "probabilityPercent": 0.2171945701357466
    },
    {
      "category": "Sequence",
      "categoryHi": "Sequence / मिले-जुले सूट का क्रम",
      "formula": "12 × (4³ − 4)",
      "count": 720,
      "probabilityPercent": 3.257918552036199
    },
    {
      "category": "Colour",
      "categoryHi": "Colour / एक सूट",
      "formula": "4 × (C(13,3) − 12)",
      "count": 1096,
      "probabilityPercent": 4.959276018099548
    },
    {
      "category": "Pair",
      "categoryHi": "Pair / जोड़ी",
      "formula": "13 × C(4,2) × 12 × 4",
      "count": 3744,
      "probabilityPercent": 16.941176470588236
    },
    {
      "category": "High Card",
      "categoryHi": "High Card / सबसे ऊँचा पत्ता",
      "formula": "(C(13,3) − 12) × (4³ − 4)",
      "count": 16440,
      "probabilityPercent": 74.38914027149322
    }
  ],
  "checks": {
    "categoryCountsSumToTotal": true,
    "aceOrderChangePreservesCategoryCounts": true,
    "withoutA23Counts": {
      "trail": 52,
      "pureSequence": 44,
      "sequence": 660,
      "colour": 1100,
      "pair": 3744,
      "highCard": 16500
    }
  },
  "pseudocode": [
    "make the 52 distinct rank/suit cards",
    "for i from 0 to 49",
    "  for j from i+1 to 50",
    "    for k from j+1 to 51",
    "      classify cards i,j,k into the first matching category",
    "      increment that category once",
    "compare all six counts with the independent formulas"
  ],
  "limitations": [
    "Not the probability of winning a round",
    "No conclusions about any app random-number generator",
    "Wild-card games require a different model"
  ]
}