"""sim-4firms-ev.py の検証用。numba を使わず、口座のルールを素直に書き直した別実装で同じ条件を回し、 (1) 1年間の期待値が誤差の範囲で一致するか (2) ルール違反（1日2.5%超の損失・1回3%超のリスク・失格ラインを割った口座の生存）が起きていないか (3) 1トレードの期待値が式 (2p − 1.05)R と一致するか を確かめる。乱数は numba 版と別。 使い方: python scripts/verify-4firms-ev.py [回数=3000] [numba版の結果JSON] """ import json import math import random import sys DAYS, TRADES_PER_DAY, CYCLE_DAYS = 250, 3, 10 DAILY_STOP = 0.025 COST = 0.05 # 各社のルール（sim-4firms-ev.py と同じ値を、名前つきで書き直したもの） PLANS = { "FTMO 2-Step": dict(price=619, targets=[0.10, 0.05], max_loss=0.10, daily=0.05, daily_from_initial=True, min_days=("trading", 4), payout_share=0.8, refund_after_payouts=1, full_payout=False), "FTMO 1-Step": dict(price=572, targets=[0.10], max_loss=0.10, daily=0.03, daily_from_initial=True, trailing_eod=True, reset_on_payout=True, best_day=0.5, payout_share=0.9, full_payout=True), "The5ers Classic": dict(price=455, targets=[0.08, 0.05], max_loss=0.08, daily=0.04, min_days=("profit", 3), payout_share=0.8, credits=[0.1, 0.2], funded_cash=0.7, payout_cap=0.04, payout_min=0.005, payout_profit_days=3), "The5ers New": dict(price=405, targets=[0.10, 0.05], max_loss=0.08, daily=0.04, min_days=("profit", 3), payout_share=0.8, credits=[0.1, 0.2], funded_cash=0.7, payout_cap=0.04, payout_min=0.005, payout_profit_days=3), "Fintokei": dict(price=549, targets=[0.08, 0.06], max_loss=0.10, daily=0.05, min_days=("trading", 3), payout_share=0.8, refund_after_payouts=2, refund_min_funded_days=20), "Hantec Enhanced": dict(price=599, targets=[0.10, 0.05], max_loss=0.10, daily=0.05, min_days=("profit", 3), payout_share=0.8, lock_on_payout=True, payout_profit_days=3), "Hantec Endurance": dict(price=299, targets=[0.06, 0.06, 0.06], max_loss=0.08, daily=0.04, min_days=("trading", 3), payout_share=0.8), } class Violation(Exception): pass def one_year(plan, p, r, keep, rng, stats): """1年ぶんを回して (報酬の合計, 払った参加費の合計) を返す（口座比）。""" price = plan["price"] / 100000 paid = 0.0 spent = price credit = 0.0 def new_account(): return dict(stage=0, bal=1.0, line=1.0 - plan["max_loss"], eod_high=1.0, days=0, profit_days=0, best=0.0, pos_sum=0.0, funded=False, since=0, payouts=0, funded_days=0, refunded=False, locked=False) acc = new_account() for _ in range(DAYS): start = acc["bal"] firm_floor = start - plan["daily"] if plan.get("daily_from_initial") else start * (1 - plan["daily"]) my_floor = max(firm_floor, start - DAILY_STOP) failed = False reached = False for _ in range(TRADES_PER_DAY): if reached: break # その日のトレードで目標に届いたら、その日はやめる（最低日数の待ちの日も1回は建てる） if acc["bal"] - r * (1 + COST) < my_floor - 1e-12: break # 次に負けたら自分の上限（2.5%）か会社の日次を超えるならやめる if r > 0.03: raise Violation("1回のリスクが3%超") win = rng.random() < p pnl = r * (1 - COST) if win else -r * (1 + COST) stats["trades"] += 1 stats["pnl_R"] += pnl / r acc["bal"] += pnl if acc["bal"] < acc["line"] - 1e-12 or acc["bal"] < firm_floor - 1e-12: failed = True break if not acc["funded"] and acc["bal"] >= 1 + plan["targets"][acc["stage"]] - 1e-12: reached = True day_loss = start - acc["bal"] if not failed and day_loss > DAILY_STOP + 1e-9: raise Violation(f"1日の損失が2.5%超: {day_loss:.4f}") stats["max_day_loss"] = max(stats["max_day_loss"], day_loss) if failed: stats["fails"] += 1 use = min(credit, price) spent += price - use credit -= use acc = new_account() continue dp = acc["bal"] - start acc["days"] += 1 if dp >= 0.005 - 1e-12: acc["profit_days"] += 1 acc["best"] = max(acc["best"], dp) if dp > 0: acc["pos_sum"] += dp if plan.get("trailing_eod"): acc["eod_high"] = max(acc["eod_high"], acc["bal"]) acc["line"] = max(acc["line"], acc["eod_high"] - plan["max_loss"]) if not acc["funded"]: tgt = plan["targets"][acc["stage"]] if acc["bal"] >= 1 + tgt - 1e-12: kind, n = plan.get("min_days", (None, 0)) ok = not (kind == "trading" and acc["days"] < n) and not (kind == "profit" and acc["profit_days"] < n) if plan.get("best_day") and acc["best"] > plan["best_day"] * acc["pos_sum"] + 1e-12: ok = False if ok: credits = plan.get("credits") if credits and acc["stage"] < len(credits): credit += credits[acc["stage"]] * price stage = acc["stage"] + 1 acc = new_account() acc["stage"] = stage if stage == len(plan["targets"]): acc["funded"] = True acc["bal"] += plan.get("funded_cash", 0.0) * price stats["funded"] += 1 else: acc["since"] += 1 acc["funded_days"] += 1 if acc["since"] >= CYCLE_DAYS: profit = acc["bal"] - 1.0 ok = True if plan.get("payout_profit_days") and acc["profit_days"] < plan["payout_profit_days"]: ok = False if plan.get("best_day") and profit > 0 and acc["best"] > plan["best_day"] * acc["pos_sum"] + 1e-12: ok = False amount = profit if plan.get("full_payout") else acc["bal"] - (1 + keep) amount = min(amount, plan.get("payout_cap", 9.0)) if ok and amount >= plan.get("payout_min", 0.0002): if plan.get("payout_cap") and amount > plan["payout_cap"] + 1e-12: raise Violation("出金上限超") paid += amount * plan["payout_share"] acc["payouts"] += 1 n = plan.get("refund_after_payouts", 0) if (n and not acc["refunded"] and acc["payouts"] >= n and acc["funded_days"] >= plan.get("refund_min_funded_days", 0)): paid += price acc["refunded"] = True acc["bal"] -= amount acc.update(since=0, profit_days=0, best=0.0, pos_sum=0.0) if plan.get("lock_on_payout"): acc["line"] = 1.0 if plan.get("reset_on_payout"): acc.update(bal=1.0, line=1.0 - plan["max_loss"], eod_high=1.0) # 生き残っている口座が失格ラインより下にいないか if acc["bal"] < acc["line"] - 1e-9: raise Violation("失格ラインを割った口座が生きている") return paid, spent def main(): n = int(sys.argv[1]) if len(sys.argv) > 1 else 3000 ref_path = sys.argv[2] if len(sys.argv) > 2 else None ref = json.load(open(ref_path, encoding="utf-8")) if ref_path else [] edges = [("ゼロ", 0.50), ("小", 0.52), ("中", 0.55), ("強", 0.58)] rng = random.Random(20260927) worst_z = 0.0 print(f"{'プラン':16s}{'実力':4s}{'r':>6s}{'B':>5s}{'検証の平均':>12s}{'±誤差':>9s}{'numba版':>11s}{'z':>7s}{'1回の期待値R':>12s}{'式':>8s}") for r in (0.01, 0.015): for name, plan in PLANS.items(): for ename, p in edges: # numba 版で一番よかった「残す利益」を使う（無ければ0） cand = [x for x in ref if x["plan"] == name and x["edge"] == ename and abs(x["r"] - r) < 1e-9] best = max(cand, key=lambda x: x["net"]) if cand else None keep = best["buf"] if best else 0.0 stats = dict(trades=0, pnl_R=0.0, max_day_loss=0.0, fails=0, funded=0) nets = [] for _ in range(n): paid, spent = one_year(plan, p, r, keep, rng, stats) nets.append((paid - spent) * 100000) mean = sum(nets) / n sd = math.sqrt(sum((x - mean) ** 2 for x in nets) / (n - 1)) se = sd / math.sqrt(n) ref_mean = best["net"] if best else float("nan") z = (mean - ref_mean) / se if best and se > 0 else float("nan") if best: worst_z = max(worst_z, abs(z)) per_trade = stats["pnl_R"] / max(stats["trades"], 1) print(f"{name:16s}{ename:4s}{r*100:5.1f}%{keep*100:4.0f}%{mean:+12.0f}{1.96*se:9.0f}{ref_mean:+11.0f}{z:+7.2f}" f"{per_trade:+12.4f}{2*p-1.05:+8.3f} 最大の1日損失 {stats['max_day_loss']*100:.2f}%") print(f"\nルール違反: なし（違反があれば例外で止まる）／ numba 版との差の最大 |z| = {worst_z:.2f}") if __name__ == "__main__": main()