{
  "model": "One uniformly random unordered hand from 52 distinct standard cards; no known cards, action filters, board or opponent condition.",
  "method": "Enumerate labeled suit-count vectors and weight each by product of C(13,count). Exact integer counts; percentages rounded to six decimals.",
  "seed": null,
  "random_samples": 0,
  "rows": [
    {
      "cards": 4,
      "shape": "1-1-1-1",
      "same_suit_pairs": 0,
      "flush_capable_suits": 0,
      "hands": 28561,
      "total_hands": 270725,
      "percent": "10.549820"
    },
    {
      "cards": 4,
      "shape": "2-1-1",
      "same_suit_pairs": 1,
      "flush_capable_suits": 1,
      "hands": 158184,
      "total_hands": 270725,
      "percent": "58.429772"
    },
    {
      "cards": 4,
      "shape": "2-2",
      "same_suit_pairs": 2,
      "flush_capable_suits": 2,
      "hands": 36504,
      "total_hands": 270725,
      "percent": "13.483794"
    },
    {
      "cards": 4,
      "shape": "3-1",
      "same_suit_pairs": 3,
      "flush_capable_suits": 1,
      "hands": 44616,
      "total_hands": 270725,
      "percent": "16.480192"
    },
    {
      "cards": 4,
      "shape": "4",
      "same_suit_pairs": 6,
      "flush_capable_suits": 1,
      "hands": 2860,
      "total_hands": 270725,
      "percent": "1.056423"
    },
    {
      "cards": 5,
      "shape": "2-1-1-1",
      "same_suit_pairs": 1,
      "flush_capable_suits": 1,
      "hands": 685464,
      "total_hands": 2598960,
      "percent": "26.374550"
    },
    {
      "cards": 5,
      "shape": "2-2-1",
      "same_suit_pairs": 2,
      "flush_capable_suits": 2,
      "hands": 949104,
      "total_hands": 2598960,
      "percent": "36.518607"
    },
    {
      "cards": 5,
      "shape": "3-1-1",
      "same_suit_pairs": 3,
      "flush_capable_suits": 1,
      "hands": 580008,
      "total_hands": 2598960,
      "percent": "22.316927"
    },
    {
      "cards": 5,
      "shape": "3-2",
      "same_suit_pairs": 4,
      "flush_capable_suits": 2,
      "hands": 267696,
      "total_hands": 2598960,
      "percent": "10.300120"
    },
    {
      "cards": 5,
      "shape": "4-1",
      "same_suit_pairs": 6,
      "flush_capable_suits": 1,
      "hands": 111540,
      "total_hands": 2598960,
      "percent": "4.291717"
    },
    {
      "cards": 5,
      "shape": "5",
      "same_suit_pairs": 10,
      "flush_capable_suits": 1,
      "hands": 5148,
      "total_hands": 2598960,
      "percent": "0.198079"
    },
    {
      "cards": 6,
      "shape": "2-2-1-1",
      "same_suit_pairs": 2,
      "flush_capable_suits": 2,
      "hands": 6169176,
      "total_hands": 20358520,
      "percent": "30.302674"
    },
    {
      "cards": 6,
      "shape": "2-2-2",
      "same_suit_pairs": 3,
      "flush_capable_suits": 3,
      "hands": 1898208,
      "total_hands": 20358520,
      "percent": "9.323900"
    },
    {
      "cards": 6,
      "shape": "3-1-1-1",
      "same_suit_pairs": 3,
      "flush_capable_suits": 1,
      "hands": 2513368,
      "total_hands": 20358520,
      "percent": "12.345534"
    },
    {
      "cards": 6,
      "shape": "3-2-1",
      "same_suit_pairs": 4,
      "flush_capable_suits": 2,
      "hands": 6960096,
      "total_hands": 20358520,
      "percent": "34.187632"
    },
    {
      "cards": 6,
      "shape": "3-3",
      "same_suit_pairs": 6,
      "flush_capable_suits": 2,
      "hands": 490776,
      "total_hands": 20358520,
      "percent": "2.410666"
    },
    {
      "cards": 6,
      "shape": "4-1-1",
      "same_suit_pairs": 6,
      "flush_capable_suits": 1,
      "hands": 1450020,
      "total_hands": 20358520,
      "percent": "7.122423"
    },
    {
      "cards": 6,
      "shape": "4-2",
      "same_suit_pairs": 7,
      "flush_capable_suits": 2,
      "hands": 669240,
      "total_hands": 20358520,
      "percent": "3.287272"
    },
    {
      "cards": 6,
      "shape": "5-1",
      "same_suit_pairs": 10,
      "flush_capable_suits": 1,
      "hands": 200772,
      "total_hands": 20358520,
      "percent": "0.986182"
    },
    {
      "cards": 6,
      "shape": "6",
      "same_suit_pairs": 15,
      "flush_capable_suits": 1,
      "hands": 6864,
      "total_hands": 20358520,
      "percent": "0.033716"
    }
  ],
  "examples": [
    {
      "id": "three-paired-suits",
      "cards": [
        "As",
        "Ks",
        "Ah",
        "Kh",
        "Ad",
        "Kd"
      ],
      "shape": "2-2-2",
      "same_suit_pairs": 3,
      "flush_capable_suits": [
        "s",
        "h",
        "d"
      ],
      "pair_witnesses": [
        [
          "As",
          "Ks"
        ],
        [
          "Ah",
          "Kh"
        ],
        [
          "Ad",
          "Kd"
        ]
      ]
    },
    {
      "id": "two-three-card-suits",
      "cards": [
        "As",
        "Ks",
        "Qs",
        "Ah",
        "Kh",
        "Qh"
      ],
      "shape": "3-3",
      "same_suit_pairs": 6,
      "flush_capable_suits": [
        "s",
        "h"
      ],
      "pair_witnesses": [
        [
          "As",
          "Ks"
        ],
        [
          "As",
          "Qs"
        ],
        [
          "Ks",
          "Qs"
        ],
        [
          "Ah",
          "Kh"
        ],
        [
          "Ah",
          "Qh"
        ],
        [
          "Kh",
          "Qh"
        ]
      ]
    },
    {
      "id": "one-six-card-suit",
      "cards": [
        "As",
        "Ks",
        "Qs",
        "Js",
        "Ts",
        "9s"
      ],
      "shape": "6",
      "same_suit_pairs": 15,
      "flush_capable_suits": [
        "s"
      ],
      "pair_witnesses": [
        [
          "As",
          "Ks"
        ],
        [
          "As",
          "Qs"
        ],
        [
          "As",
          "Js"
        ],
        [
          "As",
          "Ts"
        ],
        [
          "As",
          "9s"
        ],
        [
          "Ks",
          "Qs"
        ],
        [
          "Ks",
          "Js"
        ],
        [
          "Ks",
          "Ts"
        ],
        [
          "Ks",
          "9s"
        ],
        [
          "Qs",
          "Js"
        ],
        [
          "Qs",
          "Ts"
        ],
        [
          "Qs",
          "9s"
        ],
        [
          "Js",
          "Ts"
        ],
        [
          "Js",
          "9s"
        ],
        [
          "Ts",
          "9s"
        ]
      ]
    },
    {
      "id": "five-card-221",
      "cards": [
        "As",
        "Ks",
        "Ah",
        "Kh",
        "Qd"
      ],
      "shape": "2-2-1",
      "same_suit_pairs": 2,
      "flush_capable_suits": [
        "s",
        "h"
      ],
      "pair_witnesses": [
        [
          "As",
          "Ks"
        ],
        [
          "Ah",
          "Kh"
        ]
      ]
    },
    {
      "id": "five-card-32",
      "cards": [
        "As",
        "Ks",
        "Qs",
        "Ah",
        "Kh"
      ],
      "shape": "3-2",
      "same_suit_pairs": 4,
      "flush_capable_suits": [
        "s",
        "h"
      ],
      "pair_witnesses": [
        [
          "As",
          "Ks"
        ],
        [
          "As",
          "Qs"
        ],
        [
          "Ks",
          "Qs"
        ],
        [
          "Ah",
          "Kh"
        ]
      ]
    },
    {
      "id": "same-shape-ace-paired",
      "cards": [
        "As",
        "Ks",
        "Qh",
        "Jh",
        "Td",
        "9c"
      ],
      "shape": "2-2-1-1",
      "same_suit_pairs": 2,
      "flush_capable_suits": [
        "s",
        "h"
      ],
      "pair_witnesses": [
        [
          "As",
          "Ks"
        ],
        [
          "Qh",
          "Jh"
        ]
      ]
    },
    {
      "id": "same-shape-ace-alone",
      "cards": [
        "As",
        "Kh",
        "Qh",
        "Jd",
        "Td",
        "9c"
      ],
      "shape": "2-2-1-1",
      "same_suit_pairs": 2,
      "flush_capable_suits": [
        "h",
        "d"
      ],
      "pair_witnesses": [
        [
          "Kh",
          "Qh"
        ],
        [
          "Jd",
          "Td"
        ]
      ]
    }
  ]
}