"""Plinko: exact binomial landing distribution per row count, checked against 1M simulated balls."""
import numpy as np
from math import comb
from common import save

SEED = 20261004
rng = np.random.default_rng(SEED)
N = 1_000_000
out = []
rows_csv = []
for rows in range(8, 17):
    exact = [comb(rows, k) / 2 ** rows for k in range(rows + 1)]
    sim = np.bincount(rng.binomial(rows, 0.5, N), minlength=rows + 1) / N
    edge_pct = exact[0] * 2 * 100
    mid = [rows // 2 - 1, rows // 2, rows // 2 + 1] if rows % 2 == 0 else [rows // 2, rows // 2 + 1]
    centre3 = sum(exact[i] for i in mid) * 100
    out.append({"rows": rows, "exact_pct": [round(x * 100, 5) for x in exact],
                "sim_pct": [round(x * 100, 5) for x in sim],
                "either_edge_slot_pct": round(edge_pct, 5),
                "one_in_edge": round(1 / (exact[0] * 2)),
                "centre_slots": len(mid), "centre_pct": round(centre3, 2)})
    for k in range(rows + 1):
        rows_csv.append([rows, k, round(exact[k] * 100, 6), round(sim[k] * 100, 6)])

# streaks: how often 100 balls in a row (16 rows) miss the outer 4 slots on each side
p_outer = sum(comb(16, k) for k in (0, 1, 2, 3)) * 2 / 2 ** 16
streak = {"rows": 16, "p_outer_4_each_side_pct": round(p_outer * 100, 4),
          "chance_none_in_100_balls_pct": round((1 - p_outer) ** 100 * 100, 2),
          "expected_balls_between_outer_hits": round(1 / p_outer, 1)}

save("plinko", {"game": "Plinko", "balls_per_row_setting": N, "seed": SEED,
                "note": "Landing odds only. Payout tables differ by operator, so RTP must be computed from each game's published table.",
                "script": "plinko_sim.py"},
     {"distribution": out, "streak": streak}, rows_csv, ["rows", "slot", "exact_pct", "simulated_pct"])