{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "76663bd6",
   "metadata": {},
   "source": [
    "# The Bold Play That Passes the Funded Challenge\n",
    "\n",
    "A funded-account evaluation is a simple game with strict rules. At one large futures prop firm, the \\$50,000 evaluation asks for \\$3,000 of profit before the account falls \\$2,000 below its best close, and it watches every tick. Pass, and the firm gives you a funded account; fail, and you pay for another try. The question traders argue about most is how big to trade, and it has an answer even for a trader with no edge at all.\n",
    "\n",
    "Probability has an old answer. Lester Dubins and Leonard Savage proved in 1965 that a gambler facing a game tilted against him, who needs to reach a goal before going broke, does best by playing *boldly*: few, large bets rather than many small ones. Costs tilt every retail trade against the trader, so the evaluation is exactly their game. This notebook works out what the mathematics allows, then replays the firm's own rules, tick limit and all, on three years of one-minute Nasdaq-100 futures bars, for a trader who trades all day and for one who places a single bold bracket a day.\n",
    "\n",
    "**The answer.** For a trader with no edge, trading all day passes at best 10.4% of 500 attempts, at five micros, and *less* at any larger size. One bracket a day at the full size, 16 points wide, passes 25.8%, two and a half times as often and close to a fair coin under the same rules (28.8%). The sizes that pass best are set by the rules' arithmetic, not by skill, so a pass says little about an edge."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "891bf8e6",
   "metadata": {},
   "source": [
    "## The Rules\n",
    "\n",
    "The rules are those of Topstep's \\$50K Trading Combine as its help centre stated them on 3 October 2026:\n",
    "\n",
    "- **Profit target:** \\$3,000.\n",
    "- **Maximum Loss Limit:** \\$2,000 below the highest end-of-day balance. It rises with each new high close, never falls, and stops rising once it reaches the \\$50,000 starting balance. It is checked in real time on open profit and loss: a touch ends the attempt.\n",
    "- **Consistency:** the best single day must be at most 55% of the total profit; if it is more, the target rises until it is not. One great day cannot pass on its own.\n",
    "- **Size:** at most 5 E-mini Nasdaq-100 contracts or 50 micros.\n",
    "- **Costs:** \\$3.78 a round turn for an E-mini and \\$1.22 for a micro (exchange, regulatory and commission together).\n",
    "\n",
    "An E-mini is worth \\$20 a point and a micro \\$2, both moving in ticks of a quarter point (CME). Sizes below are counted in micros, so 50 means five E-minis; any ten micros are traded as one E-mini, which is cheaper. The bars are the regular session, 9:30 AM to 4:00 PM Eastern, from a public-domain Kaggle dataset of one-minute Nasdaq-100 futures bars; the 729 complete sessions from 27 December 2022 to 11 December 2025 are saved in the notebook's data folder, with the shortened holiday sessions left out. The dataset itself stops partway through the evening of 11 December 2025, at a spreadsheet's limit of 1,048,576 rows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f3b8ac09",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-04T00:21:09.020526Z",
     "iopub.status.busy": "2026-10-04T00:21:09.020443Z",
     "iopub.status.idle": "2026-10-04T00:21:09.247802Z",
     "shell.execute_reply": "2026-10-04T00:21:09.247211Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "729 sessions, 2022-12-27 to 2025-12-11, 390 one-minute bars each\n",
      "typical one-minute range 9.50 points, typical session range 222.25 points\n",
      "one micro: $2 a point; the $2,000 limit is 20 points at the full 50 micros\n"
     ]
    }
   ],
   "source": [
    "#| label: The Rules and Three Years of Bars\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "# Topstep $50K Trading Combine, as its help centre stated it on 3 October 2026\n",
    "START, TARGET, MLL, CONSISTENCY = 50_000, 3_000, 2_000, 0.55\n",
    "MAX_MICROS = 50                    # 5 E-minis or 50 micros\n",
    "POINT, TICK = 2.0, 0.25            # dollars a point for one micro (an E-mini: $20)\n",
    "FEE_MINI, FEE_MICRO = 3.78, 1.22   # round turn\n",
    "\n",
    "def fees(k):\n",
    "    # k micros' worth, as E-minis where possible: ten micros = one cheaper E-mini\n",
    "    return FEE_MINI * (k // 10) + FEE_MICRO * (k % 10)\n",
    "\n",
    "bars = pd.read_csv(\"data/nq_rth.csv\")\n",
    "DAYS = bars[\"session\"].unique()\n",
    "O, H, L, C = (bars[x].to_numpy(float).reshape(-1, 390)\n",
    "              for x in (\"open\", \"high\", \"low\", \"close\"))\n",
    "ND = len(DAYS)\n",
    "print(f\"{ND} sessions, {DAYS[0]} to {DAYS[-1]}, 390 one-minute bars each\")\n",
    "print(f\"typical one-minute range {np.median(H - L):.2f} points, \"\n",
    "      f\"typical session range {np.median(H.max(1) - L.min(1)):.2f} points\")\n",
    "print(f\"one micro: ${POINT:.0f} a point; the $2,000 limit is \"\n",
    "      f\"{MLL / (POINT * MAX_MICROS):.0f} points at the full 50 micros\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02d57f1a",
   "metadata": {},
   "source": [
    "## The Ceiling for a Trader With No Edge\n",
    "\n",
    "Suppose a trader's account moved like a fair game, with no edge and no costs. Then its expected value never changes, and that holds at the moment the attempt ends too: this is the optional stopping theorem. If the attempt ends with a gain $G$ when it passes and a loss $\\ell$ when it fails, then $p\\,G = (1-p)\\,\\ell$, so the pass rate is\n",
    "\n",
    "$$p = \\frac{\\ell}{G + \\ell}.$$\n",
    "\n",
    "With a floor that never moves, the loss is the full \\$2,000 and the gain the \\$3,000 target, so a trader with no edge passes 40% of the time, whatever size he trades. A floor that trails the running peak does worse, because the account can fail after climbing. For a continuous account with drift $\\mu$ and volatility $\\sigma$ per unit of time, the peak it reaches before its first drawdown of $d$ has an exponential distribution, a result of Howard Taylor (1975) and John Lehoczky (1977). Writing $\\theta = 2\\mu/\\sigma^2$, the chance of reaching a gain $a$ before a drawdown $d$ is\n",
    "\n",
    "$$P_{\\text{trail}} = \\exp\\!\\Big(-\\frac{a\\,\\theta}{e^{\\theta d} - 1}\\Big) \\;\\longrightarrow\\; e^{-a/d} = e^{-1.5} = 22.3\\% \\quad \\text{when } \\theta \\to 0,$$\n",
    "\n",
    "and for the floor that never moves, $P_{\\text{static}} = (1 - e^{\\theta b})/(e^{-\\theta a} - e^{\\theta b}) \\to b/(a+b)$.\n",
    "\n",
    "Size enters through $\\theta$. Trading $k$ times as large multiplies the drift by $k$ and the variance by $k^2$, so $\\theta$ falls by a factor $k$. With an edge ($\\theta > 0$) a larger size wastes it: the pass rate falls towards the no-edge value. With costs ($\\theta < 0$) a larger size dilutes them, and the pass rate *rises* towards the no-edge value. That is bold play, in Dubins and Savage's sense, and these formulas are its continuous form. The cell below checks both formulas against a simulation of small fair-ish steps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b24fd233",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-04T00:21:09.249010Z",
     "iopub.status.busy": "2026-10-04T00:21:09.248905Z",
     "iopub.status.idle": "2026-10-04T00:21:22.947611Z",
     "shell.execute_reply": "2026-10-04T00:21:22.947174Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "drift a step   theta     fixed floor: formula  simulated   trailing: formula  simulated\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      -0.50   -0.00160                0.0079     0.0070              0.0067     0.0066\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      +0.00   +0.00000                0.4000     0.3942              0.2231     0.2215\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      +0.50   +0.00160                0.9596     0.9573              0.8155     0.8220\n"
     ]
    }
   ],
   "source": [
    "#| label: Two Formulas Against a Simulation\n",
    "def static_pass(theta, a=TARGET, b=MLL):\n",
    "    if abs(theta) < 1e-12:\n",
    "        return b / (a + b)\n",
    "    return (1 - np.exp(theta * b)) / (np.exp(-theta * a) - np.exp(theta * b))\n",
    "\n",
    "def trailing_pass(theta, a=TARGET, d=MLL):\n",
    "    rate = 1 / d if abs(theta) < 1e-12 else theta / np.expm1(theta * d)\n",
    "    return np.exp(-a * rate)\n",
    "\n",
    "def simulate(mu, sd, trailing, n=20_000, seed=7):\n",
    "    rng = np.random.default_rng(seed)\n",
    "    x, peak = np.zeros(n), np.zeros(n)\n",
    "    alive, passed = np.ones(n, bool), np.zeros(n, bool)\n",
    "    while alive.any():\n",
    "        x[alive] += mu + sd * rng.standard_normal(alive.sum())\n",
    "        peak = np.maximum(peak, x)\n",
    "        floor = (peak - MLL) if trailing else -MLL\n",
    "        won, lost = alive & (x >= TARGET), alive & (x <= floor)\n",
    "        passed |= won\n",
    "        alive &= ~(won | lost)\n",
    "    return passed.mean()\n",
    "\n",
    "sd = 25.0                        # dollars a step: small against the $2,000 limit\n",
    "print(\"drift a step   theta     fixed floor: formula  simulated\"\n",
    "      \"   trailing: formula  simulated\")\n",
    "for mu in (-0.5, 0.0, 0.5):\n",
    "    th = 2 * mu / sd**2\n",
    "    print(f\"{mu:+11.2f}   {th:+.5f}   {static_pass(th):19.4f}\"\n",
    "          f\"  {simulate(mu, sd, False):9.4f}   {trailing_pass(th):17.4f}\"\n",
    "          f\"  {simulate(mu, sd, True):9.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2be4cf5a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-04T00:21:22.948642Z",
     "iopub.status.busy": "2026-10-04T00:21:22.948531Z",
     "iopub.status.idle": "2026-10-04T00:21:23.300116Z",
     "shell.execute_reply": "2026-10-04T00:21:23.299490Z"
    }
   },
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 1260x500 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 480,
       "width": 1242
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| echo: false\n",
    "#| fig-cap: The pass rate against size for an account that moves like a Brownian motion, $50 of risk a trade per micro, at three edges per micro and per trade. Left, a loss limit that never moves; right, one that trails the peak. With costs (orange) the pass rate rises with size, with an edge (teal) it falls, and both approach the no-edge value (white, dashed), 40% for the fixed floor and 22.3% for the trailing one. The trailing floor takes close to half of the fixed floor's chance away from every trader.\n",
    "import matplotlib.pyplot as plt\n",
    "TEAL, ORANGE, GREY, ROSE = \"#2a9d8f\", \"#f4a261\", \"#8a94a6\", \"#e76f51\"\n",
    "plt.style.use(\"dark_background\"); plt.rcParams[\"font.size\"] = 12\n",
    "\n",
    "def tidy(ax):\n",
    "    ax.spines[\"top\"].set_visible(False); ax.spines[\"right\"].set_visible(False)\n",
    "\n",
    "k = np.arange(1, MAX_MICROS + 1)\n",
    "risk = 50.0                       # dollars at risk per micro and trade: 25 points\n",
    "panels = ((static_pass, \"a loss limit that never moves\"),\n",
    "          (trailing_pass, \"a loss limit that trails the peak\"))\n",
    "edges = ((-1.5, ORANGE, \"costs: −$1.50 a trade per micro\"),\n",
    "         (0.0, \"white\", \"no edge\"),\n",
    "         (1.5, TEAL, \"an edge: +$1.50 a trade per micro\"))\n",
    "fig, axes = plt.subplots(1, 2, figsize=(12.6, 5.0), sharey=True)\n",
    "for ax, (f, name) in zip(axes, panels):\n",
    "    for edge, col, lab in edges:\n",
    "        th = 2 * edge / (k * risk**2)   # k micros: drift k·edge, variance (k·risk)²\n",
    "        ax.plot(k, [100 * f(t) for t in th], color=col, lw=2.2,\n",
    "                ls=\"--\" if edge == 0 else \"-\", label=lab)\n",
    "    ax.set_title(name, fontsize=12)\n",
    "    ax.set_xlabel(\"size (micros; 10 = one E-mini)\")\n",
    "    ax.set_xlim(1, MAX_MICROS); tidy(ax)\n",
    "axes[0].set_ylabel(\"chance of passing (%)\"); axes[0].set_ylim(0, 100)\n",
    "axes[1].legend(frameon=False, fontsize=10, loc=\"upper right\")\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cfdb429b",
   "metadata": {},
   "source": [
    "## Trading All Day on Three Years of Nasdaq Futures\n",
    "\n",
    "The formulas assume an account that moves smoothly and a floor that trails continuously. The real rules differ in three ways that matter: the floor trails only the end-of-day balance and stops at \\$50,000; the consistency rule forbids passing on one day; and trades come in lumps, which at a large size can be bigger than the whole loss limit.\n",
    "\n",
    "So the rules are replayed on the bars. The trader has no edge by construction: he enters at the open of a bar in a direction chosen by a coin, with a stop and a target 25 points away, and enters again on the next bar after each exit, all session, flat by 3:55 PM. A target fills only when the price trades a tick through it; a stop fills a tick worse than its price; if one bar touches both, the stop is taken first. Every attempt starts on one of the first 500 sessions with its own coin, and at every size the same trades are scored, with the account checked against the floor at each trade's worst open loss."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "520b1477",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-04T00:21:23.301427Z",
     "iopub.status.busy": "2026-10-04T00:21:23.301256Z",
     "iopub.status.idle": "2026-10-04T00:21:27.721395Z",
     "shell.execute_reply": "2026-10-04T00:21:27.720944Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "500 attempts, 4,523,644 trades, 39.5 a session\n",
      "a trade averages -0.431 points (sd 24.91); 49.4% are winners\n"
     ]
    }
   ],
   "source": [
    "#| label: Brackets, Attempts and the Rules\n",
    "LAST = 384                         # the 3:55 PM bar: flat at its close\n",
    "\n",
    "def brackets(S):\n",
    "    # an entry at every bar's open, long (+1) and short (-1):\n",
    "    # the exit bar, the P&L in points and the worst open loss in points\n",
    "    out = {}\n",
    "    entry = O[:, :LAST + 1]\n",
    "    for side in (+1, -1):\n",
    "        exit_bar = np.full(entry.shape, LAST)\n",
    "        pnl, worst = np.zeros(entry.shape), np.zeros(entry.shape)\n",
    "        done = np.zeros(entry.shape, bool)\n",
    "        for j in range(LAST + 1):\n",
    "            bar = np.arange(LAST + 1) + j\n",
    "            live = (bar <= LAST) & ~done\n",
    "            b = np.minimum(bar, LAST)\n",
    "            against = (entry - L[:, b]) if side > 0 else (H[:, b] - entry)\n",
    "            towards = (H[:, b] - entry) if side > 0 else (entry - L[:, b])\n",
    "            worst = np.where(live, np.maximum(worst, np.minimum(against, S)),\n",
    "                             worst)\n",
    "            stop = live & (against >= S)\n",
    "            target = live & ~stop & (towards >= S + TICK)\n",
    "            pnl = np.where(stop, -S - TICK, np.where(target, S, pnl))\n",
    "            exit_bar = np.where(stop | target, b, exit_bar)\n",
    "            done |= stop | target\n",
    "        at_close = side * (C[:, LAST][:, None] - entry)   # still open at 3:55\n",
    "        out[side] = (exit_bar, np.where(done, pnl, at_close), worst)\n",
    "    return out\n",
    "\n",
    "def all_day(B, first, seed, horizon=229):\n",
    "    # one attempt: a coin for every entry, again on the bar after each exit\n",
    "    coin = np.random.default_rng(seed)\n",
    "    trades = []\n",
    "    for d in range(first, min(ND, first + horizon)):\n",
    "        i = 0\n",
    "        while i <= LAST:\n",
    "            exit_bar, pnl, worst = B[1 if coin.random() < 0.5 else -1]\n",
    "            trades.append((d - first, pnl[d, i], worst[d, i]))\n",
    "            i = exit_bar[d, i] + 1\n",
    "    return np.array(trades)\n",
    "\n",
    "def one_a_day(B, first, seed, horizon=229):\n",
    "    # one attempt: one bracket a day, at the session's first bar\n",
    "    coin = np.random.default_rng(seed)\n",
    "    trades = []\n",
    "    for d in range(first, min(ND, first + horizon)):\n",
    "        exit_bar, pnl, worst = B[1 if coin.random() < 0.5 else -1]\n",
    "        trades.append((d - first, pnl[d, 0], worst[d, 0]))\n",
    "    return np.array(trades)\n",
    "\n",
    "def attempt(trades, k):\n",
    "    # the rules at k micros: (1, day) passed, (0, day) failed, (-1, None) open\n",
    "    day = trades[:, 0].astype(int)\n",
    "    pl = POINT * k * trades[:, 1] - fees(k)\n",
    "    worst_open = -POINT * k * trades[:, 2] - fees(k)\n",
    "    after = START + np.cumsum(pl)\n",
    "    before = after - pl\n",
    "    n = day.max() + 1\n",
    "    close = np.full(n, -np.inf)\n",
    "    last = np.r_[np.flatnonzero(np.diff(day)), len(day) - 1]\n",
    "    close[day[last]] = after[last]\n",
    "    best_close = np.maximum.accumulate(close)\n",
    "    trail = np.r_[START, best_close[:-1]] - MLL\n",
    "    floor = np.minimum(START, np.maximum(START - MLL, trail))\n",
    "    breach = np.flatnonzero(before + worst_open <= floor[day])\n",
    "    fail_day = day[breach[0]] if breach.size else None\n",
    "    daily = np.bincount(day, weights=pl, minlength=n)\n",
    "    total, best = np.cumsum(daily), np.maximum.accumulate(daily)\n",
    "    ok = np.flatnonzero(total >= np.maximum(TARGET, best / CONSISTENCY))\n",
    "    pass_day = ok[0] if ok.size else None\n",
    "    if pass_day is not None and (fail_day is None or pass_day < fail_day):\n",
    "        return 1, int(pass_day)\n",
    "    return (0, int(fail_day)) if fail_day is not None else (-1, None)\n",
    "\n",
    "B25 = brackets(25.0)\n",
    "FIRST = range(500)\n",
    "attempts = [all_day(B25, s, seed=s) for s in FIRST]\n",
    "pts = np.concatenate([a[:, 1] for a in attempts])\n",
    "per_session = np.mean([len(a) / (a[-1, 0] + 1) for a in attempts])\n",
    "print(f\"{len(FIRST)} attempts, {sum(len(a) for a in attempts):,} trades, \"\n",
    "      f\"{per_session:.1f} a session\")\n",
    "print(f\"a trade averages {pts.mean():+.3f} points (sd {pts.std():.2f}); \"\n",
    "      f\"{np.mean(pts > 0):.1%} are winners\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6ef5ba4a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-04T00:21:27.722580Z",
     "iopub.status.busy": "2026-10-04T00:21:27.722475Z",
     "iopub.status.idle": "2026-10-04T00:21:28.318065Z",
     "shell.execute_reply": "2026-10-04T00:21:28.317568Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "micros   passed   failed   median sessions to pass\n",
      "     1     0.6%    99.4%           60\n",
      "     2     5.6%    94.4%           18\n",
      "     3     8.8%    91.2%            9\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     5    10.4%    89.6%            6\n",
      "     8     8.4%    91.6%            5\n",
      "    10     8.2%    91.8%            4\n",
      "    15     5.4%    94.6%            4\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    20     5.4%    94.6%            4\n",
      "    30     3.4%    96.6%            4\n",
      "    40     2.8%    97.2%            4\n",
      "    50     2.4%    97.6%            4\n"
     ]
    }
   ],
   "source": [
    "#| label: All Day, at Every Size\n",
    "SIZES = [1, 2, 3, 5, 8, 10, 15, 20, 30, 40, 50]\n",
    "allday = {}\n",
    "print(\"micros   passed   failed   median sessions to pass\")\n",
    "for k in SIZES:\n",
    "    r = [attempt(a, k) for a in attempts]\n",
    "    res = np.array([x[0] for x in r])\n",
    "    days = [x[1] + 1 for x in r if x[0] == 1]\n",
    "    allday[k] = res\n",
    "    med = np.median(days) if days else float(\"nan\")\n",
    "    print(f\"{k:6d}   {np.mean(res == 1):6.1%}   {np.mean(res == 0):6.1%}   \"\n",
    "          f\"{med:10.0f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "96c40854",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-04T00:21:28.318989Z",
     "iopub.status.busy": "2026-10-04T00:21:28.318910Z",
     "iopub.status.idle": "2026-10-04T00:21:28.430822Z",
     "shell.execute_reply": "2026-10-04T00:21:28.430400Z"
    }
   },
   "outputs": [
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",
      "text/plain": [
       "<Figure size 1080x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 480,
       "width": 1062
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| echo: false\n",
    "#| fig-cap: Trading all day, replayed on the bars: the share of 500 attempts that pass at each size, with 95% intervals, against the two formulas fed the trades' own average and spread. The formulas, for an account that moves smoothly, promise a pass rate that keeps rising with size; the replay peaks near five micros and then falls, because past that size a single 25-point trade is a large part of the loss limit and the consistency rule makes the account keep trading after a good day. Up to five micros the replay follows the trailing-floor formula; the formulas step up at 10, 20 and 30 micros, where ten micros become one cheaper E-mini.\n",
    "m, s = pts.mean(), pts.std()\n",
    "rate = np.array([np.mean(allday[k] == 1) for k in SIZES])\n",
    "half = 1.96 * np.sqrt(rate * (1 - rate) / len(FIRST))\n",
    "fig, ax = plt.subplots(figsize=(10.8, 5.0))\n",
    "ax.errorbar(SIZES, 100 * rate, yerr=100 * half, color=ORANGE, lw=2.2,\n",
    "            marker=\"o\", capsize=3, label=\"replayed on the bars\")\n",
    "kk = np.arange(1, MAX_MICROS + 1)\n",
    "theta = [2 * (POINT * k * m - fees(k)) / (POINT * k * s) ** 2 for k in kk]\n",
    "ax.plot(kk, [100 * trailing_pass(t) for t in theta], color=TEAL, lw=1.8,\n",
    "        label=\"formula, trailing floor\")\n",
    "ax.plot(kk, [100 * static_pass(t) for t in theta], color=GREY, lw=1.8, ls=\":\",\n",
    "        label=\"formula, fixed floor\")\n",
    "ax.set_xlabel(\"size (micros; 10 = one E-mini)\")\n",
    "ax.set_ylabel(\"chance of passing (%)\")\n",
    "ax.set_xlim(0, MAX_MICROS + 1); ax.set_ylim(0, 45)\n",
    "ax.legend(frameon=False, fontsize=10); tidy(ax)\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1b9f391",
   "metadata": {},
   "source": [
    "## One Bold Bracket a Day\n",
    "\n",
    "Bold play means few bets, so the second trader places one bracket a day, at the session's first bar, at the full 50 micros, and lets it run to its stop, its target or 3:55 PM. The only choice left is the width of the bracket, which sets the stake: at five E-minis every point is \\$100.\n",
    "\n",
    "The rules do the rest of the arithmetic. Two winning days are the fewest that can pass, since each must then be half of the total, under the 55% limit. They pass only if two wins clear \\$3,000 after costs, which takes a bracket of at least 16 points: two 15-point wins come to \\$2,977, and a third win is needed. A bracket of 20 points would risk the whole \\$2,000 limit on the first trade. For each width the replay is set beside a fair coin, an account that moves like a Brownian motion with no edge inside the same bracket, under the same rules and costs, and beside the optional stopping ceiling for that width. The coin must move continuously: a winning trade can first go against the account, and once a losing day has brought the floor within a few points, that dip is enough to end the attempt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a4beb82c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-04T00:21:28.431940Z",
     "iopub.status.busy": "2026-10-04T00:21:28.431761Z",
     "iopub.status.idle": "2026-10-04T00:21:45.189698Z",
     "shell.execute_reply": "2026-10-04T00:21:45.189256Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bracket   stake    win     2 wins    passed   fair coin   ceiling\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    8 pt  $  800  $ 781.10  $ 1562.20     3.6%     20.3%     39.0%\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    9 pt  $  900  $ 881.10  $ 1762.20     7.4%     21.6%     36.2%\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   10 pt  $ 1000  $ 981.10  $ 1962.20     8.8%     19.8%     33.8%\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   11 pt  $ 1100  $1081.10  $ 2162.20    17.2%     25.3%     38.1%\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   12 pt  $ 1200  $1181.10  $ 2362.20    16.4%     24.2%     36.1%\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   13 pt  $ 1300  $1281.10  $ 2562.20    16.4%     22.9%     34.2%\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   14 pt  $ 1400  $1381.10  $ 2762.20    15.8%     21.6%     32.6%\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   15 pt  $ 1500  $1481.10  $ 2962.20    16.2%     20.2%     31.0%\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   16 pt  $ 1600  $1581.10  $ 3162.20    25.8%     28.8%     38.7%\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   17 pt  $ 1700  $1681.10  $ 3362.20    24.4%     28.7%     37.3%\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   18 pt  $ 1800  $1781.10  $ 3562.20    24.4%     27.1%     36.0%\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   19 pt  $ 1900  $1881.10  $ 3762.20    22.4%     24.9%     34.7%\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   20 pt  $ 2000  $1981.10  $ 3962.20    22.4%     24.4%     33.5%\n",
      "\n",
      "the first minute reaches both sides of a bracket 8 points wide on 26.5% of sessions\n",
      "the first minute reaches both sides of a bracket 12 points wide on 9.7% of sessions\n",
      "the first minute reaches both sides of a bracket 16 points wide on 3.4% of sessions\n"
     ]
    }
   ],
   "source": [
    "#| label: One a Day, at Every Bracket\n",
    "def fair_coin(S, k, rng, horizon=229):\n",
    "    # the same bracket and rules for an account that moves like a Brownian motion\n",
    "    # with no edge: inside a trade it reaches the target (a tick beyond S) before\n",
    "    # the stop or the loss limit, whichever is nearer, at the gambler's-ruin odds\n",
    "    balance, best_close, best_day, total = START, START, 0.0, 0.0\n",
    "    for _ in range(horizon):\n",
    "        floor = min(START, max(START - MLL, best_close - MLL))\n",
    "        room = (balance - fees(k) - floor) / (POINT * k)   # points it may fall\n",
    "        down = min(S, room)\n",
    "        if rng.random() < down / (down + S + TICK):\n",
    "            day = POINT * k * S - fees(k)\n",
    "        elif room <= S:\n",
    "            return False                   # the loss limit, touched in real time\n",
    "        else:\n",
    "            day = -POINT * k * (S + TICK) - fees(k)\n",
    "        balance += day\n",
    "        total += day\n",
    "        best_close, best_day = max(best_close, balance), max(best_day, day)\n",
    "        if total >= max(TARGET, best_day / CONSISTENCY):\n",
    "            return True\n",
    "    return False\n",
    "\n",
    "WIDTHS = list(range(8, 21))\n",
    "daily, coin_rate, ceiling = {}, {}, {}\n",
    "print(\"bracket   stake    win     2 wins    passed   fair coin   ceiling\")\n",
    "for S in WIDTHS:\n",
    "    B = brackets(float(S))\n",
    "    res = np.array([attempt(one_a_day(B, f, seed=10_000 + f), MAX_MICROS)[0]\n",
    "                    for f in FIRST])\n",
    "    daily[S] = res\n",
    "    win = POINT * MAX_MICROS * S - fees(MAX_MICROS)\n",
    "    rng = np.random.default_rng(S)\n",
    "    coin_rate[S] = np.mean([fair_coin(S, MAX_MICROS, rng)\n",
    "                            for _ in range(20_000)])\n",
    "    n_wins = max(2, int(np.ceil(TARGET / win)))   # consistency: two days at least\n",
    "    ceiling[S] = MLL / (n_wins * win + MLL)\n",
    "    stake = POINT * MAX_MICROS * S\n",
    "    print(f\"{S:5d} pt  ${stake:5.0f}  ${win:7.2f}  ${2 * win:8.2f}\"\n",
    "          f\"   {np.mean(res == 1):6.1%}    {coin_rate[S]:6.1%}\"\n",
    "          f\"    {ceiling[S]:6.1%}\")\n",
    "print()\n",
    "for S in (8, 12, 16):              # the first minute, where these trades start\n",
    "    both = np.mean((H[:, 0] - O[:, 0] >= S + TICK) & (O[:, 0] - L[:, 0] >= S))\n",
    "    print(f\"the first minute reaches both sides of a bracket {S} points wide \"\n",
    "          f\"on {both:.1%} of sessions\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "141ad2fe",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-04T00:21:45.190808Z",
     "iopub.status.busy": "2026-10-04T00:21:45.190720Z",
     "iopub.status.idle": "2026-10-04T00:21:45.293516Z",
     "shell.execute_reply": "2026-10-04T00:21:45.293017Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1080x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 480,
       "width": 1062
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| echo: false\n",
    "#| fig-cap: One bracket a day at 50 micros, replayed on the bars (orange, 500 attempts, 95% intervals), against a fair coin under the same rules (teal) and the optional stopping ceiling for a trader with no edge (white, dashed). The jump between 15 and 16 points is the target's arithmetic: from 16 points two winning days pass. The grey band is the best that trading all day reached at any size.\n",
    "rate = np.array([np.mean(daily[S] == 1) for S in WIDTHS])\n",
    "half = 1.96 * np.sqrt(rate * (1 - rate) / len(FIRST))\n",
    "best_all = max(np.mean(allday[k] == 1) for k in SIZES)\n",
    "fig, ax = plt.subplots(figsize=(10.8, 5.0))\n",
    "ax.axhspan(0, 100 * best_all, color=GREY, alpha=0.18, lw=0)\n",
    "ax.text(8.2, 100 * best_all + 1, f\"trading all day, best size: {best_all:.1%}\",\n",
    "        color=GREY, fontsize=10)\n",
    "ax.errorbar(WIDTHS, 100 * rate, yerr=100 * half, color=ORANGE, lw=2.2,\n",
    "            marker=\"o\", capsize=3, label=\"replayed on the bars\")\n",
    "ax.plot(WIDTHS, [100 * coin_rate[S] for S in WIDTHS], color=TEAL, lw=1.8,\n",
    "        marker=\"s\", ms=4, label=\"a fair coin, same rules\")\n",
    "ax.plot(WIDTHS, [100 * ceiling[S] for S in WIDTHS], color=\"white\", lw=1.4,\n",
    "        ls=\"--\", label=\"optional stopping ceiling\")\n",
    "ax.set_xlabel(\"bracket (points; at 50 micros a point is $100)\")\n",
    "ax.set_ylabel(\"chance of passing (%)\")\n",
    "ax.set_xticks(WIDTHS); ax.set_ylim(0, 50)\n",
    "ax.legend(frameon=False, fontsize=10, loc=\"upper center\", ncol=3); tidy(ax)\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0b21a1a",
   "metadata": {},
   "source": [
    "## What the Evaluation Rewards"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4a9fd311",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-04T00:21:45.294448Z",
     "iopub.status.busy": "2026-10-04T00:21:45.294337Z",
     "iopub.status.idle": "2026-10-04T00:21:45.297995Z",
     "shell.execute_reply": "2026-10-04T00:21:45.297630Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the case                                      passes   from\n",
      "no edge, a floor that never moves              40.0%   optional stopping\n",
      "no edge, a floor that trails every tick        22.3%   Taylor and Lehoczky\n",
      "all day, best size (5 micros)                  10.4%   500 attempts on the bars\n",
      "all day, full size (50 micros)                  2.4%   500 attempts on the bars\n",
      "one bracket a day, 16 points at 50 micros      25.8%   500 attempts on the bars\n",
      "a fair coin, same bracket and rules            28.8%   20,000 simulated attempts\n"
     ]
    }
   ],
   "source": [
    "#| echo: false\n",
    "#| label: The Findings\n",
    "best_k = max(SIZES, key=lambda k: np.mean(allday[k] == 1))\n",
    "best_S = max(WIDTHS, key=lambda S: np.mean(daily[S] == 1))\n",
    "rows = [\n",
    "    (\"no edge, a floor that never moves\", static_pass(0.0),\n",
    "     \"optional stopping\"),\n",
    "    (\"no edge, a floor that trails every tick\", trailing_pass(0.0),\n",
    "     \"Taylor and Lehoczky\"),\n",
    "    (f\"all day, best size ({best_k} micros)\", np.mean(allday[best_k] == 1),\n",
    "     \"500 attempts on the bars\"),\n",
    "    (f\"all day, full size ({MAX_MICROS} micros)\",\n",
    "     np.mean(allday[MAX_MICROS] == 1), \"500 attempts on the bars\"),\n",
    "    (f\"one bracket a day, {best_S} points at {MAX_MICROS} micros\",\n",
    "     np.mean(daily[best_S] == 1), \"500 attempts on the bars\"),\n",
    "    (\"a fair coin, same bracket and rules\", coin_rate[best_S],\n",
    "     \"20,000 simulated attempts\"),\n",
    "]\n",
    "print(f\"{'the case':44s}{'passes':>8s}   from\")\n",
    "for name, p, src in rows:\n",
    "    print(f\"{name:44s}{p:8.1%}   {src}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21f02852",
   "metadata": {},
   "source": [
    "1. **Bold beats busy.** One bracket a day passes two and a half times as often as trading all day at its best size, because costs and bad luck grow with the number of bets. That is Dubins and Savage's bold play.\n",
    "2. **Trading all day, bigger is worse.** Up to five micros the pass rate rises, as the formulas say. Beyond that each 25-point trade is a large lump of the \\$2,000 limit and the consistency rule keeps the account trading after its best days, so 50 micros passes only 2.4%.\n",
    "3. **The rules' arithmetic picks the winning sizes.** From 11 points three winning days clear the target after costs, and from 16 points two, so the pass rate jumps at both widths. Narrower brackets fail at the open: the first minute alone reaches both sides of an 8-point bracket on 26.5% of sessions.\n",
    "4. **The firm's floor is gentler than the formula's.** It trails only the day's close and stops at \\$50,000, which is why a bold daily bracket can beat the 22.3% of a floor that trails every tick; its own ceiling, from optional stopping, is 38.7%.\n",
    "5. **A pass is weak evidence of skill.** A fair coin passes 28.8% of the time at the right size. A trader who does have an edge should do the opposite of the bold player and trade small and often, where the formulas show an edge doing the most for the pass rate.\n",
    "\n",
    "## Sources\n",
    "\n",
    "1. L. E. Dubins and L. J. Savage, *How to Gamble If You Must: Inequalities for Stochastic Processes*, McGraw-Hill, New York, 1965.\n",
    "2. H. M. Taylor, \"A stopped Brownian motion formula\", *The Annals of Probability* 3 (1975) 234–246.\n",
    "3. J. P. Lehoczky, \"Formulas for stopped diffusion processes with stopping times based on the maximum\", *The Annals of Probability* 5 (1977) 601–607.\n",
    "4. D. Williams, *Probability with Martingales*, Cambridge University Press, Cambridge, 1991 (the optional stopping theorem).\n",
    "5. Topstep help centre, read 3 October 2026: \"What is the Maximum Loss Limit?\", \"Consistency at Topstep\", \"Trading Combine® Parameters\" and \"TopstepX™ — Commissions and Fees\" (help.topstep.com).\n",
    "6. CME Group, contract specifications of the E-mini and Micro E-mini Nasdaq-100 futures (cmegroup.com).\n",
    "7. TGT Analytics, \"NQ Futures - 1min Bar 2022 2025\", Kaggle dataset tgtanalytics/nq-futures-1min-bar-2022-2025, CC0: Public Domain."
   ]
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