{
  "schema": "second-best-gate-evidence-v1",
  "method": "exact enumeration of the two leading scout ranks",
  "assumptions": [
    "distinct ranks",
    "uniformly random arrival order",
    "eight sampled candidates remain recallable",
    "best-so-far is selected at the first later candidate above the second-best scout",
    "best scout is selected if no candidate crosses the gate"
  ],
  "rows": [
    {"pool_size": 9, "scout_count": 8, "expected_absolute_rank": 1.0, "expected_rank_percentile": 1.0, "probability_literal_best": 1.0, "expected_candidates_seen": 9.0},
    {"pool_size": 10, "scout_count": 8, "expected_absolute_rank": 1.0222222222222221, "expected_rank_percentile": 0.9975308641975309, "probability_literal_best": 0.9777777777777777, "expected_candidates_seen": 9.777777777777779},
    {"pool_size": 12, "scout_count": 8, "expected_absolute_rank": 1.1043771043771045, "expected_rank_percentile": 0.9905111723293542, "probability_literal_best": 0.9090909090909091, "expected_candidates_seen": 10.909090909090908},
    {"pool_size": 16, "scout_count": 8, "expected_absolute_rank": 1.337037037037037, "expected_rank_percentile": 0.9775308641975309, "probability_literal_best": 0.7666666666666667, "expected_candidates_seen": 12.266666666666667},
    {"pool_size": 18, "scout_count": 8, "expected_absolute_rank": 1.4684095860566448, "expected_rank_percentile": 0.9724464949378444, "probability_literal_best": 0.7058823529411765, "expected_candidates_seen": 12.705882352941176},
    {"pool_size": 20, "scout_count": 8, "expected_absolute_rank": 1.6046783625730994, "expected_rank_percentile": 0.9681748230224685, "probability_literal_best": 0.6526315789473685, "expected_candidates_seen": 13.052631578947368},
    {"pool_size": 24, "scout_count": 8, "expected_absolute_rank": 1.8856682769726247, "expected_rank_percentile": 0.9614926836098858, "probability_literal_best": 0.5652173913043478, "expected_candidates_seen": 13.565217391304348},
    {"pool_size": 32, "scout_count": 8, "expected_absolute_rank": 2.4632616487455197, "expected_rank_percentile": 0.9527980113307897, "probability_literal_best": 0.4435483870967742, "expected_candidates_seen": 14.193548387096774},
    {"pool_size": 50, "scout_count": 8, "expected_absolute_rank": 3.7853968253968255, "expected_rank_percentile": 0.9431551668286362, "probability_literal_best": 0.29714285714285715, "expected_candidates_seen": 14.857142857142858},
    {"pool_size": 100, "scout_count": 8, "expected_absolute_rank": 7.483367003367003, "expected_rank_percentile": 0.9345114444104343, "probability_literal_best": 0.15434343434343434, "expected_candidates_seen": 15.434343434343434},
    {"pool_size": 250, "scout_count": 8, "expected_absolute_rank": 18.592892458723785, "expected_rank_percentile": 0.92934581341878, "probability_literal_best": 0.0631004016064257, "expected_candidates_seen": 15.775100401606426},
    {"pool_size": 1000, "scout_count": 8, "expected_absolute_rank": 74.14816683350017, "expected_rank_percentile": 0.9267786117782781, "probability_literal_best": 0.015943943943943942, "expected_candidates_seen": 15.943943943943944}
  ]
}