{
  "description": "Exact first-hit races; fair marginal streams, altered same-round coupling",
  "disjoint_shared_blocks_control": {
    "A_win": "1/2",
    "expected_blocks_until_either_finishes": "4",
    "expected_tosses_until_either_finishes": "12",
    "each_pattern_expected_tosses_alone": "24",
    "warning": "Unlike the coupling comparison, disjoint blocks change each marginal waiting-time law."
  },
  "coupled_races": [
    {
      "A": "HHT",
      "B": "HTT",
      "r": "-1",
      "A_strict": "1/4",
      "B_strict": "3/4",
      "tie": "0",
      "A_with_half_ties": "1/4",
      "expected_rounds_until_either_finishes": "13/2",
      "reachable_transient_states": 5
    },
    {
      "A": "HHT",
      "B": "HTT",
      "r": "-1/2",
      "A_strict": "8227597/21362445",
      "B_strict": "12421901/21362445",
      "tie": "237649/7120815",
      "A_with_half_ties": "17168141/42724890",
      "expected_rounds_until_either_finishes": "121676288/21362445",
      "reachable_transient_states": 9
    },
    {
      "A": "HHT",
      "B": "HTT",
      "r": "0",
      "A_strict": "377/825",
      "B_strict": "377/825",
      "tie": "71/825",
      "A_with_half_ties": "1/2",
      "expected_rounds_until_either_finishes": "4544/825",
      "reachable_transient_states": 9
    },
    {
      "A": "HHT",
      "B": "HTT",
      "r": "1/2",
      "A_strict": "12909487/23928751",
      "B_strict": "8715183/23928751",
      "tie": "2304081/23928751",
      "A_with_half_ties": "28123055/47857502",
      "expected_rounds_until_either_finishes": "131076608/23928751",
      "reachable_transient_states": 9
    },
    {
      "A": "HHT",
      "B": "HTT",
      "r": "1",
      "A_strict": "2/3",
      "B_strict": "1/3",
      "tie": "0",
      "A_with_half_ties": "2/3",
      "expected_rounds_until_either_finishes": "16/3",
      "reachable_transient_states": 4
    }
  ],
  "single_pattern_mean_waits": {
    "HHT": "8",
    "HTT": "8",
    "TTH": "8",
    "THH": "8"
  },
  "shared_stream_cycle": [
    {
      "A": "HHT",
      "B": "HTT",
      "r": "1",
      "A_strict": "2/3",
      "B_strict": "1/3",
      "tie": "0",
      "A_with_half_ties": "2/3",
      "expected_rounds_until_either_finishes": "16/3",
      "reachable_transient_states": 4
    },
    {
      "A": "HTT",
      "B": "TTH",
      "r": "1",
      "A_strict": "3/4",
      "B_strict": "1/4",
      "tie": "0",
      "A_with_half_ties": "3/4",
      "expected_rounds_until_either_finishes": "13/2",
      "reachable_transient_states": 5
    },
    {
      "A": "TTH",
      "B": "THH",
      "r": "1",
      "A_strict": "2/3",
      "B_strict": "1/3",
      "tie": "0",
      "A_with_half_ties": "2/3",
      "expected_rounds_until_either_finishes": "16/3",
      "reachable_transient_states": 4
    },
    {
      "A": "THH",
      "B": "HHT",
      "r": "1",
      "A_strict": "3/4",
      "B_strict": "1/4",
      "tie": "0",
      "A_with_half_ties": "3/4",
      "expected_rounds_until_either_finishes": "13/2",
      "reachable_transient_states": 5
    }
  ],
  "equal_survival_counts": [
    {
      "length": 0,
      "each_avoiding_count": 1
    },
    {
      "length": 1,
      "each_avoiding_count": 2
    },
    {
      "length": 2,
      "each_avoiding_count": 4
    },
    {
      "length": 3,
      "each_avoiding_count": 7
    },
    {
      "length": 4,
      "each_avoiding_count": 12
    },
    {
      "length": 5,
      "each_avoiding_count": 20
    },
    {
      "length": 6,
      "each_avoiding_count": 33
    },
    {
      "length": 7,
      "each_avoiding_count": 54
    },
    {
      "length": 8,
      "each_avoiding_count": 88
    },
    {
      "length": 9,
      "each_avoiding_count": 143
    },
    {
      "length": 10,
      "each_avoiding_count": 232
    },
    {
      "length": 11,
      "each_avoiding_count": 376
    },
    {
      "length": 12,
      "each_avoiding_count": 609
    },
    {
      "length": 13,
      "each_avoiding_count": 986
    },
    {
      "length": 14,
      "each_avoiding_count": 1596
    }
  ],
  "checks": {
    "arithmetic": "fractions.Fraction throughout; linear-system residuals exactly zero",
    "raw_history_crosscheck": "all five couplings, all pair histories of six rounds",
    "single_stream_bijection": "all binary words of lengths 0 through 14",
    "sampling": "none"
  }
}