{
  "trials_per_mode": 10000,
  "seed": 20260908,
  "notes": "Fixed 100-roll sequences, fresh state each trial. Droughts include censored start/end runs. Not full games or production RNG.",
  "modes": {
    "iid": {
      "mean_tv": {
        "36": 0.1952,
        "60": 0.1565,
        "100": 0.1213
      },
      "p95_tv60": 0.2222,
      "p95_longest_no6_run_in60": 30,
      "repeat_rate60": 0.1127,
      "mean_optimal_next_sum_guess100": 0.1667,
      "aggregate_sum_frequencies": [
        0.02773,
        0.05548,
        0.08312,
        0.11071,
        0.13888,
        0.16653,
        0.13976,
        0.11145,
        0.08325,
        0.0556,
        0.0275
      ]
    },
    "deck36_draw36": {
      "mean_tv": {
        "36": 0.0,
        "60": 0.0597,
        "100": 0.0319
      },
      "p95_tv60": 0.0833,
      "p95_longest_no6_run_in60": 24,
      "repeat_rate60": 0.0873,
      "mean_optimal_next_sum_guess100": 0.2409,
      "aggregate_sum_frequencies": [
        0.02774,
        0.05549,
        0.08344,
        0.11101,
        0.13891,
        0.16687,
        0.13888,
        0.11112,
        0.0834,
        0.05543,
        0.02772
      ]
    },
    "deck36_draw31": {
      "mean_tv": {
        "36": 0.0847,
        "60": 0.0658,
        "100": 0.053
      },
      "p95_tv60": 0.0889,
      "p95_longest_no6_run_in60": 24,
      "repeat_rate60": 0.0875,
      "mean_optimal_next_sum_guess100": 0.2086,
      "aggregate_sum_frequencies": [
        0.02783,
        0.05578,
        0.0833,
        0.1112,
        0.13867,
        0.16626,
        0.13908,
        0.11122,
        0.08335,
        0.0555,
        0.02783
      ]
    },
    "deck36_draw24": {
      "mean_tv": {
        "36": 0.1275,
        "60": 0.1012,
        "100": 0.0736
      },
      "p95_tv60": 0.1444,
      "p95_longest_no6_run_in60": 25,
      "repeat_rate60": 0.0872,
      "mean_optimal_next_sum_guess100": 0.1913,
      "aggregate_sum_frequencies": [
        0.02782,
        0.05548,
        0.08309,
        0.11118,
        0.13883,
        0.16691,
        0.13906,
        0.11091,
        0.0833,
        0.05572,
        0.02771
      ]
    },
    "deck72_draw36": {
      "mean_tv": {
        "36": 0.1364,
        "60": 0.1199,
        "100": 0.0895
      },
      "p95_tv60": 0.1667,
      "p95_longest_no6_run_in60": 27,
      "repeat_rate60": 0.1007,
      "mean_optimal_next_sum_guess100": 0.1746,
      "aggregate_sum_frequencies": [
        0.02753,
        0.05552,
        0.0834,
        0.11126,
        0.13881,
        0.16652,
        0.13934,
        0.11109,
        0.08311,
        0.05554,
        0.02787
      ]
    },
    "dueness_noise2": {
      "mean_tv": {
        "36": 0.0219,
        "60": 0.0352,
        "100": 0.0212
      },
      "p95_tv60": 0.05,
      "p95_longest_no6_run_in60": 17,
      "repeat_rate60": 0.0374,
      "mean_optimal_next_sum_guess100": 0.2992,
      "aggregate_sum_frequencies": [
        0.02971,
        0.05676,
        0.08326,
        0.11024,
        0.13756,
        0.16497,
        0.13755,
        0.11015,
        0.08329,
        0.05683,
        0.02968
      ]
    }
  }
}