"""Crash/Limbo: reach probabilities and auto-cashout outcomes, using the published 1%-edge formula."""
import numpy as np
from common import save

SEED = 20261004
EDGE = 0.01
rng = np.random.default_rng(SEED)
N = 10_000_000
# crashpoint = max(1, (2^32 / (int + 1)) * (1 - edge)), int uniform in [0, 2^32)
ints = rng.integers(0, 2 ** 32, N, dtype=np.uint64).astype(np.float64)
cp = np.maximum(1.0, np.floor((2 ** 32 / (ints + 1)) * (1 - EDGE) * 100) / 100)

targets = [1.01, 1.1, 1.25, 1.5, 2, 3, 5, 10, 20, 50, 100, 1000]
reach = []
for t in targets:
    reach.append({"target": t, "theoretical_pct": round((1 - EDGE) / t * 100, 4),
                  "simulated_pct": round((cp >= t).mean() * 100, 4)})

instant = round((cp == 1.0).mean() * 100, 3)

# 100 bets of 1 USDT at fixed auto-cashout, 50,000 sessions
SESS = 50_000
auto = []
for t in (1.1, 1.5, 2, 3, 10, 100):
    p = (1 - EDGE) / t
    wins = rng.binomial(100, p, SESS)
    net = wins * (t - 1) - (100 - wins)
    auto.append({"cashout": t, "win_chance_pct": round(p * 100, 3), "expected_net_usdt": round(100 * (p * t - 1), 2),
                 "median_net_usdt": round(float(np.median(net)), 2), "chance_up_after_100_pct": round((net > 0).mean() * 100, 2),
                 "worst_5pct_usdt": round(float(np.percentile(net, 5)), 2), "best_5pct_usdt": round(float(np.percentile(net, 95)), 2)})

save("crash", {"game": "Crash / Limbo", "house_edge": EDGE, "rounds": N, "sessions": SESS, "seed": SEED,
               "formula": "crash point = max(1, 2^32/(int+1) x 0.99), truncated to 2 decimals", "script": "crash_sim.py"},
     {"reach": reach, "instant_bust_pct": instant, "auto_cashout": auto},
     [[r["target"], r["theoretical_pct"], r["simulated_pct"]] for r in reach], ["target_multiplier", "theoretical_reach_pct", "simulated_reach_pct"])