{
  "schema": "poker51-wild-census-v1",
  "date": "2026-09-29",
  "categories": [
    "High card",
    "One pair",
    "Two pair",
    "Three of a kind",
    "Straight",
    "Flush",
    "Full house",
    "Four of a kind",
    "Straight flush",
    "Five of a kind"
  ],
  "variants": {
    "standard": {
      "name": "Standard · Ⅰ declared",
      "rule": "Ⅰ = 2♣ is declared and outside the deal; 51 cards are in play.",
      "deckSize": 51,
      "hands": 2349060,
      "withMarker": 0,
      "improvedByMarker": 0,
      "counts": {
        "High card": 1176825,
        "One pair": 992640,
        "Two pair": 111672,
        "Three of a kind": 49632,
        "Straight": 9690,
        "Flush": 4615,
        "Full house": 3384,
        "Four of a kind": 564,
        "Straight flush": 38,
        "Five of a kind": 0
      },
      "standardRankingInversions": [],
      "sameAsFull52": [],
      "percentiles": {
        "pair of jacks": 0.795468,
        "two pair, kings up": 0.957951,
        "three sevens": 0.978836,
        "nine-high straight": 0.99395,
        "king-high flush": 0.997284,
        "kings full": 0.999529
      }
    },
    "wild": {
      "name": "Wild Ⅰ",
      "rule": "Ⅰ is in the deck and stands for any card; with four of a rank it makes five of a kind.",
      "deckSize": 52,
      "hands": 2598960,
      "withMarker": 249900,
      "improvedByMarker": 205244,
      "counts": {
        "High card": 1176825,
        "One pair": 1149069,
        "Two pair": 111672,
        "Three of a kind": 125664,
        "Straight": 19581,
        "Flush": 7098,
        "Full house": 5976,
        "Four of a kind": 2868,
        "Straight flush": 195,
        "Five of a kind": 12
      },
      "standardRankingInversions": [
        [
          "Two pair",
          111672,
          "Three of a kind",
          125664
        ]
      ],
      "sameAsFull52": [],
      "percentiles": {
        "pair of jacks": 0.731925,
        "two pair, kings up": 0.92603,
        "three sevens": 0.956025,
        "nine-high straight": 0.989398,
        "king-high flush": 0.994641,
        "kings full": 0.998346
      },
      "iteration": {
        "consistent": false,
        "cycleFrom": 0,
        "steps": [
          {
            "ranking": [
              "High card",
              "One pair",
              "Two pair",
              "Three of a kind",
              "Straight",
              "Flush",
              "Full house",
              "Four of a kind",
              "Straight flush",
              "Five of a kind"
            ],
            "counts": [
              1176825,
              1149069,
              111672,
              125664,
              19581,
              7098,
              5976,
              2868,
              195,
              12
            ],
            "inversions": [
              [
                "Two pair",
                111672,
                "Three of a kind",
                125664
              ]
            ]
          },
          {
            "ranking": [
              "High card",
              "One pair",
              "Three of a kind",
              "Two pair",
              "Straight",
              "Flush",
              "Full house",
              "Four of a kind",
              "Straight flush",
              "Five of a kind"
            ],
            "counts": [
              1176825,
              1149069,
              49632,
              187704,
              19581,
              7098,
              5976,
              2868,
              195,
              12
            ],
            "inversions": [
              [
                "Three of a kind",
                49632,
                "Two pair",
                187704
              ]
            ]
          },
          {
            "ranking": [
              "High card",
              "One pair",
              "Two pair",
              "Three of a kind",
              "Straight",
              "Flush",
              "Full house",
              "Four of a kind",
              "Straight flush",
              "Five of a kind"
            ],
            "counts": [
              1176825,
              1149069,
              111672,
              125664,
              19581,
              7098,
              5976,
              2868,
              195,
              12
            ],
            "inversions": [
              [
                "Two pair",
                111672,
                "Three of a kind",
                125664
              ]
            ]
          }
        ]
      }
    },
    "bug": {
      "name": "The bug",
      "rule": "Ⅰ is in the deck and stands for an ace, or for any card that completes a straight, flush or straight flush; with four aces it makes five aces.",
      "deckSize": 52,
      "hands": 2598960,
      "withMarker": 249900,
      "improvedByMarker": 69277,
      "counts": {
        "High card": 1283106,
        "One pair": 1100868,
        "Two pair": 125730,
        "Three of a kind": 57640,
        "Straight": 19581,
        "Flush": 7098,
        "Full house": 3978,
        "Four of a kind": 763,
        "Straight flush": 195,
        "Five of a kind": 1
      },
      "standardRankingInversions": [],
      "sameAsFull52": [],
      "percentiles": {
        "pair of jacks": 0.776404,
        "two pair, kings up": 0.94909,
        "three sevens": 0.972945,
        "nine-high straight": 0.990981,
        "king-high flush": 0.996224,
        "kings full": 0.999272
      }
    },
    "suit": {
      "name": "Ⅰ any suit",
      "rule": "Ⅰ is in the deck and is a two of any suit you choose.",
      "deckSize": 52,
      "hands": 2598960,
      "withMarker": 249900,
      "improvedByMarker": 1485,
      "counts": {
        "High card": 1301061,
        "One pair": 1098240,
        "Two pair": 123552,
        "Three of a kind": 54912,
        "Straight": 10194,
        "Flush": 6587,
        "Full house": 3744,
        "Four of a kind": 624,
        "Straight flush": 46,
        "Five of a kind": 0
      },
      "standardRankingInversions": [],
      "sameAsFull52": [
        "One pair",
        "Two pair",
        "Three of a kind",
        "Full house",
        "Four of a kind"
      ],
      "percentiles": {
        "pair of jacks": 0.800027,
        "two pair, kings up": 0.958278,
        "three sevens": 0.979249,
        "nine-high straight": 0.993609,
        "king-high flush": 0.99706,
        "kings full": 0.999544
      }
    },
    "rank": {
      "name": "Ⅰ any rank",
      "rule": "Ⅰ is in the deck and is a club of any rank you choose.",
      "deckSize": 52,
      "hands": 2598960,
      "withMarker": 249900,
      "improvedByMarker": 196757,
      "counts": {
        "High card": 1176825,
        "One pair": 1153071,
        "Two pair": 146718,
        "Three of a kind": 89628,
        "Straight": 19704,
        "Flush": 5076,
        "Full house": 6678,
        "Four of a kind": 1188,
        "Straight flush": 72,
        "Five of a kind": 0
      },
      "standardRankingInversions": [
        [
          "Flush",
          5076,
          "Full house",
          6678
        ]
      ],
      "sameAsFull52": [],
      "percentiles": {
        "pair of jacks": 0.740091,
        "two pair, kings up": 0.936249,
        "three sevens": 0.96615,
        "nine-high straight": 0.990577,
        "king-high flush": 0.995847,
        "kings full": 0.999105
      },
      "iteration": {
        "consistent": true,
        "steps": [
          {
            "ranking": [
              "High card",
              "One pair",
              "Two pair",
              "Three of a kind",
              "Straight",
              "Flush",
              "Full house",
              "Four of a kind",
              "Straight flush"
            ],
            "counts": [
              1176825,
              1153071,
              146718,
              89628,
              19704,
              5076,
              6678,
              1188,
              72
            ],
            "inversions": [
              [
                "Flush",
                5076,
                "Full house",
                6678
              ]
            ]
          },
          {
            "ranking": [
              "High card",
              "One pair",
              "Two pair",
              "Three of a kind",
              "Straight",
              "Full house",
              "Flush",
              "Four of a kind",
              "Straight flush"
            ],
            "counts": [
              1176825,
              1153071,
              146718,
              89628,
              19704,
              6678,
              5076,
              1188,
              72
            ],
            "inversions": []
          }
        ]
      }
    }
  },
  "seconds": 183
}