{
  "approach": "Measurement lane: return the base strategy byte-for-byte unchanged. It uses tick probes, a sub-tick probability belief, quotes inside the competitor with marginal sizing, and cheap YES inventory for near-zero retail demand. No tuning or new mechanism is introduced. Reproduce the original 600-run score, evaluate the required two 600-run ranges, and measure an independent 4000-run reference with standard errors and settlement-side, competitor-spread and starting-probability splits, reported in tried.",
  "blocked": null,
  "python_version": "3.12.3",
  "base_mean_edge": 102.33197908899267,
  "score": {
    "simulations": 600,
    "failures": 0,
    "mean_edge": 107.2442092237515,
    "retail_edge": 135.80165652288784,
    "arb_edge": -28.557447299150834,
    "seed_start": 1000
  },
  "holdout": {
    "mean_edge": 96.0405203261775,
    "simulations": 600,
    "failures": 0,
    "seed_start": 30000
  },
  "code": "\"\"\"Stale-quote defence with tick probes, a sub-tick belief and cheap YES stock.\n\nEvery step the arbitrageur removes any order on the wrong side of p, so tiny\ntwo-sided probes around the estimate locate p to a tick; a grid filter narrows\nthat further.  Quotes sit one tick inside the competitor and are sized by the\nmarginal rule: one more share is worth quoting while the chance a retail order\nreaches it, times its edge, exceeds the expected arbitrage loss.  Near p=0 a\nretail buy pays almost its whole notional as edge, so YES is held to cover low\nasks.  That YES is bought when it is cheap: a large bid rests at tick 1 while p\nis above it, so the arbitrageur fills it on the crossing for about 0.1 tick a\nshare instead of nearly a full tick once p is near zero, and smaller bids sit on\nwhichever tick p is within 0.15 of.  Below tick 1 the estimate of p decays with\nthe time spent there, since no probe can see it.\n\"\"\"\nimport math\nfrom orderbook_pm_challenge.strategy import BaseStrategy\nfrom orderbook_pm_challenge.types import CancelOrder, PlaceOrder, Side\n\nP = dict(lam_r=0.25, m=5.0, sig_n=1.2, lam_j=0.0019, sig_j=0.35, sig=0.02,\n         qmax=3000.0, rmin=2, kA=0.7, kL=0.15, pL=0.05,\n         ammo=1.0, ydem=0.4, W=200.0, fy=0.6, ammo_q=60.0, ammo_pmax=0.05, ammo_maxpay=0.02,\n         fb=0.9, fu=0.7, xu=0.1, sticky=1.0, min_ahead=2.0, keep_hi=1.5, keep_lo=0.7, Hu=300.0, bins=8.0, filt=1.0, uni=0.01, jumpinfo=1.0, dmin=0.0, kLb=0.08, kLf=0.08, pinf=1.0, pre=0.0, H1=100.0,\n         ydf=0.6, Wf=2000.0, g_hi=0.15, g_lo=0.15, qf=400.0, pmaxf=0.05, pre_gap=1.0,\n         ydf1=0.6, g1=5.0, f1=0.6, a1=100.0, nb1=0.0, gs=1.0, p1t=1.0, m1=1.0, zd=1.0, pfl=0.0005)\nSQ2 = math.sqrt(2.0)\nSQ2PI = math.sqrt(2.0 * math.pi)\ndef cdf(x): return 0.5 * (1.0 + math.erf(x / SQ2))\ndef pdf(x): return math.exp(-0.5 * x * x) / SQ2PI\ndef inv(p):\n    p = min(max(p, 1e-9), 1 - 1e-9)\n    t = math.sqrt(-2.0 * math.log(min(p, 1 - p)))\n    x = t - (2.515517 + 0.802853 * t + 0.010328 * t * t) / (1 + 1.432788 * t + 0.189269 * t * t + 0.001308 * t ** 3)\n    x = -x if p < 0.5 else x\n    for _ in range(2):\n        d = pdf(x)\n        if d < 1e-12:\n            break\n        x -= (cdf(x) - p) / d\n    return x\ndef lpm(k):\n    return pdf(k) + k * cdf(k)\ndef fl(q):\n    return math.floor(q * 100 + 1e-9) / 100\n\nNODES = [(-2.2, .06), (-1.3, .17), (-0.6, .27), (0.6, .27), (1.3, .17), (2.2, .06)]\nPROBE = 0.01\n\n\nclass Strategy(BaseStrategy):\n    def __init__(self):\n        self.n = 0\n        self.ahead = set()     # main orders placed strictly ahead of any competitor order at their tick\n        self.res = {}          # order id -> uncovered quantity at placement\n        self.bc = None         # belief: sub-tick grid centres (ticks)\n        self.bw = None         # belief: weights\n        self.st = 0.5          # last one-step sd in ticks\n        self.pcb = self.pca = None\n        self.pb = set()\n        self.pa = set()\n        self.tb = 0\n        self.s = None          # competitor spread parameter\n\n    def _oid(self, tag):\n        self.n += 1\n        return tag + str(self.n)\n\n    def on_step(self, state):\n        H = max(1, state.steps_remaining)\n        cb = state.competitor_best_bid_ticks or 0\n        ca = state.competitor_best_ask_ticks or 100\n        if self.s is None:\n            self.s = max(1, (ca - cb + 1) // 2)\n        lo, hi = cb, ca\n        for o in state.own_orders:\n            if o.side is Side.BUY:\n                lo = max(lo, o.price_ticks)\n            else:\n                hi = min(hi, o.price_ticks)\n        if P['pinf'] > 0:\n            sb = {o.price_ticks for o in state.own_orders if o.side is Side.BUY and o.remaining_quantity <= PROBE + 1e-9}\n            sa = {o.price_ticks for o in state.own_orders if o.side is Side.SELL and o.remaining_quantity <= PROBE + 1e-9}\n            ea = self.pa - sa\n            eb = self.pb - sb\n            if sa and ea:\n                lo = max(lo, min(max(ea), hi))\n            if eb and (sb or min(eb) <= P['p1t']):\n                hi = min(hi, max(min(eb), lo))\n        if P['jumpinfo'] > 0 and self.pcb is not None:\n            if ca > self.pca + 1:\n                lo = max(lo, ca - 1)\n            if cb < self.pcb - 1:\n                hi = min(hi, cb + 1)\n        self.pcb, self.pca = cb, ca\n        if lo > hi:\n            lo, hi = hi, lo\n        # sub-tick belief over p_(t-1): predict with one-step noise, truncate to [lo, hi]\n        wid = max(hi - lo, 1e-6)\n        nb = max(2, min(48, int(round(wid * P['bins']))))\n        cs = [lo + (i + 0.5) * wid / nb for i in range(nb)]\n        if self.bc is None or P['filt'] <= 0:\n            ws = [1.0 / nb] * nb\n        else:\n            sg = max(self.st, 0.6 * wid / nb)\n            k = -0.5 / (sg * sg)\n            ws = []\n            uni = P['uni'] * sg\n            for c in cs:\n                t = uni\n                for ci, wi in zip(self.bc, self.bw):\n                    d = c - ci\n                    d2 = d * d * k\n                    if d2 > -12.5:\n                        t += wi * math.exp(d2)\n                ws.append(t)\n            tot = sum(ws)\n            ws = [w / tot for w in ws]\n        self.bc, self.bw = cs, ws\n        mean_t = sum(c * w for c, w in zip(cs, ws))\n        var_t = max(sum(c * c * w for c, w in zip(cs, ws)) - mean_t * mean_t, 0.0)\n        phat = min(max(mean_t / 100.0, 0.002), 0.998)\n        var = P['sig'] ** 2 + P['lam_j'] * P['sig_j'] ** 2\n        sd = math.sqrt(H * var)\n        self.tb = self.tb + 1 if hi <= 1 else 0\n        if self.tb > 0 and P['zd'] > 0:\n            # below the last tick there is no probe: the score keeps walking away from it\n            phat = min(phat, max(P['pfl'], cdf(inv(0.01) - P['zd'] * 0.02 * math.sqrt(self.tb) / sd)))\n        z = inv(phat)\n        Z = z * sd\n        sp = pdf(z) / sd * P['sig']\n        self.st = sp * 100.0\n        s = math.sqrt(sp * sp + var_t / 1e4 + 1e-8)\n        sd1 = math.sqrt(max(1.0, H - 1.0) * var)\n        jp = [(cdf((Z + n * P['sig_j']) / sd1), w) for n, w in NODES]\n        lj = P['lam_j']\n\n        def AB(x):\n            k = (x - phat) / s\n            a = s * lpm(k)\n            b = a - (x - phat)\n            ja = sum(w * max(0.0, x - p) for p, w in jp)\n            jb = sum(w * max(0.0, p - x) for p, w in jp)\n            return (1 - lj) * a + lj * ja, (1 - lj) * b + lj * jb\n\n        if H == 1:\n            def AB(x):\n                return (1 - phat) * x, phat * (1 - x)\n        rho = P['lam_r'] * 0.5\n        mu = math.log(P['m']) - 0.5 * P['sig_n'] ** 2\n        kA = P['kL'] if phat < P['pL'] else P['kA']\n\n        def qsize(loss, gain, px):\n            loss *= kA\n            if gain <= 0:\n                return 0.0\n            tail = loss / (rho * gain)\n            if tail >= 1.0:\n                return 0.0\n            return min(P['qmax'], math.exp(mu + P['sig_n'] * inv(1 - max(tail, 1e-6))) / px)\n\n        ptk = phat * 100\n        def qbid(t):\n            if not 1 <= t <= 99:\n                return 0.0\n            a, b = AB(t / 100.0)\n            if phat * 100 - t < P['dmin']:\n                return 0.0\n            if P['nb1'] > 0 and self.s == 1 and t == 1 and ptk < 1.0:\n                return 0.0\n            if phat < P['pL']:\n                ytg = P['ydem'] * min(H, P['W']) / max(ca - 1, ptk + 1) * 100.0\n                a *= (P['kLb'] if state.yes_inventory < ytg else P['kLf']) / P['kL']\n            return qsize(a, b, max(phat, 0.05))\n\n        def qask(t):\n            if not 1 <= t <= 99:\n                return 0.0\n            a, b = AB(t / 100.0)\n            if t - phat * 100 < P['dmin']:\n                return 0.0\n            return qsize(b, a, t / 100.0)\n\n        bids = [o for o in state.own_orders if o.side is Side.BUY and o.remaining_quantity > PROBE + 1e-9]\n        asks = [o for o in state.own_orders if o.side is Side.SELL and o.remaining_quantity > PROBE + 1e-9]\n        sticky = P['sticky'] > 0\n        def top(orders, comp, step):\n            if sticky and sum(o.remaining_quantity for o in orders if o.price_ticks == comp and o.order_id in self.ahead) >= P['min_ahead']:\n                return comp\n            return comp + step\n        bid_t = top(bids, cb, 1)\n        ask_t = top(asks, ca, -1)\n        qb = qbid(bid_t)\n        qa = qask(ask_t)\n\n        Y = state.yes_inventory\n        if ask_t == 1 and H > P['H1'] and P['pre'] > 0:\n            qa = qa if Y >= P['a1'] > 0 else 0.0          # let the competitor's 2-tick ask erode instead of fronting it for nothing\n        # ammunition: hold YES so that low asks are covered\n        ptick = phat * 100\n        amt = 0\n        qam = 0.0\n        if P['ammo'] > 0 and ask_t >= 2 and phat < max(P['ammo_pmax'], P['pmaxf']):\n            wealth = state.cash + Y * phat\n            x = max(ask_t, ptick + 1) / 100.0\n            capw = P['fy'] * wealth / max(phat, 0.005)\n            target = min(P['ydem'] * min(H, P['W']) / x, capw)\n            full = min(P['ydf'] * min(H, P['Wf']) / x, capw) if phat < P['pmaxf'] else 0.0\n            t = max(1, min(99, int(math.ceil(ptick + 1e-9))))\n            g = t - ptick\n            if Y < full and g <= P['g_hi'] and bid_t <= t < ask_t:\n                amt, qam = t, min(P['qf'], full - Y)     # a tick p has just crossed: nearly free\n            elif Y < target and phat < P['ammo_pmax'] and bid_t <= t < ask_t and t / 100.0 - phat < P['ammo_maxpay']:\n                amt, qam = t, min(P['ammo_q'], target - Y)\n            elif Y < full and t >= 2 and 1.0 - g <= P['g_lo']:\n                amt, qam = t - 1, min(P['qf'], full - Y)  # rest just under p: filled only on the crossing, or by retail\n\n        if P['pre'] > 0 and ca == 2 and phat < 0.01 and H > P['H1'] and Y < P['pre'] and not qam and 1.0 - ptick < P['pre_gap']:\n            amt, qam = 1, min(P['ammo_q'], P['pre'] - Y)\n        q1 = 0.0\n        if P['ydf1'] > 0 and P['m1'] < ptick < P['g1'] + 1.0 and amt != 1:\n            q1 = max(0.0, P['ydf1'] * min(H, P['Wf']) / (self.s / 100.0) - Y)\n        # order management\n        actions = []\n        free = state.free_cash - 2.0\n        keep_ask = 0.0\n        new_b = []\n        new_a = []\n        def cancel(o):\n            nonlocal free\n            actions.append(CancelOrder(o.order_id))\n            x = o.price_ticks / 100.0\n            if o.side is Side.BUY:\n                free += x * o.remaining_quantity\n            else:\n                free += (1 - x) * min(self.res.get(o.order_id, 0.0), o.remaining_quantity)\n            self.ahead.discard(o.order_id)\n            self.res.pop(o.order_id, None)\n        for o in state.own_orders:\n            if o.remaining_quantity <= PROBE + 1e-9:\n                cancel(o)\n        kept_ids = set()\n        def manage(orders, t, q, comp):\n            kept = 0.0\n            for o in orders:\n                if o.price_ticks == t and q > 0 and kept + o.remaining_quantity <= max(q * P['keep_hi'], 1.0):\n                    kept += o.remaining_quantity\n                    kept_ids.add(o.order_id)\n                else:\n                    cancel(o)\n            return kept\n        kb = manage(bids, bid_t, qb, cb)\n        ka = manage(asks, ask_t, qa, ca)\n        add_b = (qb - kb) if (kb < qb * P['keep_lo'] and bid_t != cb) else 0.0\n        add_a = (qa - ka) if (ka < qa * P['keep_lo'] and ask_t != ca) else 0.0\n\n        budget = P['fb'] * max(free, 0.0)\n        cost = add_b * bid_t / 100.0 + qam * amt / 100.0\n        if cost > budget:\n            f = budget / cost\n            add_b *= f\n            qam *= f\n            cost = budget\n        out = []\n        q1 = min(q1, P['f1'] * max(budget - cost, 0.0) * 100.0)\n        if q1 >= 0.01:\n            out.append(PlaceOrder(side=Side.BUY, price_ticks=1, quantity=fl(q1)))\n            free -= fl(q1) / 100.0 + 1e-6\n        if amt and qam >= 0.01:\n            q = fl(qam)\n            out.append(PlaceOrder(side=Side.BUY, price_ticks=amt, quantity=q))\n            free -= q * amt / 100.0 + 1e-6\n        if bid_t >= 1 and add_b >= 0.01:\n            q = fl(add_b)\n            oid = self._oid('b')\n            out.append(PlaceOrder(side=Side.BUY, price_ticks=bid_t, quantity=q, client_order_id=oid))\n            free -= q * bid_t / 100.0 + 1e-6\n            if bid_t > cb:\n                self.ahead.add(oid)\n        if ask_t <= 99 and add_a >= 0.01:\n            x = ask_t / 100.0\n            covk = sum(o.remaining_quantity - min(self.res.get(o.order_id, 0.0), o.remaining_quantity)\n                       for o in asks if o.order_id in kept_ids)\n            cov = max(0.0, Y - covk - 0.1)\n            unc = max(0.0, add_a - cov)\n            if unc > 0:\n                ub = max(0.0, free - (1 - P['fu']) * max(state.cash, 0.0)) if x >= P['xu'] else 0.0\n                if H < P['Hu'] and phat < 0.05:\n                    ub = max(0.0, free * (1 - H / P['Hu']))\n                unc = min(unc, ub / (1 - x))\n            q = fl(min(add_a, cov + unc))\n            if q >= 0.01:\n                oid = self._oid('a')\n                out.append(PlaceOrder(side=Side.SELL, price_ticks=ask_t, quantity=q, client_order_id=oid))\n                r = max(0.0, q - cov)\n                self.res[oid] = r\n                free -= r * (1 - x) + 1e-6\n                if ask_t < ca:\n                    self.ahead.add(oid)\n\n        # probes: tiny orders that the arbitrageur removes when p crosses them\n        f = int(math.floor(ptick + 1e-9))\n        r = max(int(P['rmin']), int(math.ceil(2.0 * s * 100)))\n        self.pb = set()\n        self.pa = set()\n        if free > 1.0:\n            for t in range(f, f + r + 1):\n                if cb < t < ca and 1 <= t <= 99:\n                    out.append(PlaceOrder(side=Side.BUY, price_ticks=t, quantity=PROBE))\n                    self.pb.add(t)\n            for t in range(f + 1 - r, f + 2):\n                if cb < t < ca and 1 <= t <= 99:\n                    out.append(PlaceOrder(side=Side.SELL, price_ticks=t, quantity=PROBE))\n                    self.pa.add(t)\n        return actions + out\n",
  "code_sha256": "d68e658732b99a47eb8004f684319f0bc3dc286fe52a066ab019442f8c91aac2",
  "tried": [
    "Measurement only: unchanged upstream base code, no search, no tuning, no parameter or simulator changes. Scorer commit b244530ee2a6247b5f930830eeca9dd950da0e7e, default 2000 steps, CLI --workers 4 --json; seed ranges fixed before inspecting scores.",
    "Scorer reproduction seeds 0-599: {\"simulations\":600,\"failures\":0,\"mean_edge\":102.33197908899267,\"retail_edge\":127.3199510028995,\"arb_edge\":-24.987971913912165,\"standard_deviation\":164.9292142079967,\"standard_error\":6.733206974796292,\"normal_approx_95pct_ci\":[89.13489341839194,115.5290647595934],\"retail_edge_standard_error\":7.309951344710694,\"arb_edge_standard_error\":1.6734816818959528}",
    "Sandbox: base and examples/starter_strategy.py each attempted 20 simulations on seeds 2000-2019; both failed 20/20 before strategy loading with ImportError: Import of 'ntpath' is not allowed in sandbox mode (Python 3.12 pathlib). These infrastructure failures are separate from the unsandboxed scored runs.",
    "Required evaluation seeds 1000-1599 (no tuning): {\"simulations\":600,\"failures\":0,\"mean_edge\":107.2442092237515,\"retail_edge\":135.80165652288784,\"arb_edge\":-28.557447299150834,\"standard_deviation\":171.10497211753423,\"standard_error\":6.98533123568503,\"normal_approx_95pct_ci\":[93.55296000180884,120.93545844569415],\"retail_edge_standard_error\":7.320172854365442,\"arb_edge_standard_error\":2.2846735237859233}",
    "Untuned holdout seeds 30000-30599: {\"simulations\":600,\"failures\":0,\"mean_edge\":96.0405203261775,\"retail_edge\":124.3725985363135,\"arb_edge\":-28.332078210128167,\"standard_deviation\":164.3296874461883,\"standard_error\":6.708731397236731,\"normal_approx_95pct_ci\":[82.89140678759351,109.18963386476149],\"retail_edge_standard_error\":7.09053646141104,\"arb_edge_standard_error\":2.586421042101562}",
    "REFERENCE methodology: 4000 additional default full-length simulations, seeds 40000-43999, chosen without tuning. SE is sample SD (n-1 denominator) / sqrt(n), across independent seeded simulations; normal 95% CI is mean +/- 1.96 SE. This estimates the simulator seed-distribution mean, not a guarantee about the unknown Paradigm seeds. Subgroups are descriptive associations, not causal effects; marginal groups overlap across axes. Starting price means latent regime.initial_probability, not first executed price; fixed bins [0,0.3), [0.3,0.4), [0.4,0.5), [0.5,0.6), [0.6,0.7), [0.7,1]; chosen using sampled starting probabilities only, before observing reference outcomes, because 20-point end bins contained only 1 and 2 runs. Settlement side is terminal settlement_outcome. Spread is sampled regime.competitor_spread_ticks, not observed bid-ask distance.",
    "REFERENCE_4000 overall: {\"simulations\":4000,\"failures\":0,\"mean_edge\":99.23869339150623,\"retail_edge\":127.07987834308194,\"arb_edge\":-27.8411849515945,\"standard_deviation\":174.98248422377944,\"standard_error\":2.766716003908118,\"normal_approx_95pct_ci\":[93.81593002384632,104.66145675916614],\"retail_edge_standard_error\":2.8934906291383715,\"arb_edge_standard_error\":0.9968729491375384}",
    "REFERENCE_4000 settlement NO: {\"simulations\":2019,\"failures\":0,\"mean_edge\":178.6760201002478,\"retail_edge\":221.54370212011793,\"arb_edge\":-42.86768201988197,\"standard_deviation\":209.2331644709565,\"standard_error\":4.656529557069777,\"normal_approx_95pct_ci\":[169.54922216839103,187.80281803210457],\"retail_edge_standard_error\":4.833568622256416,\"arb_edge_standard_error\":1.2442243486742492}",
    "REFERENCE_4000 settlement YES: {\"simulations\":1981,\"failures\":0,\"mean_edge\":18.277581516216355,\"retail_edge\":30.80402765866214,\"arb_edge\":-12.526446142471631,\"standard_deviation\":65.03486071638828,\"standard_error\":1.461180866520129,\"normal_approx_95pct_ci\":[15.413667017836902,21.14149601459581],\"retail_edge_standard_error\":0.7747493552676384,\"arb_edge_standard_error\":1.4865797054752712}",
    "REFERENCE_4000 competitor_spread_ticks 1: {\"simulations\":1012,\"failures\":0,\"mean_edge\":34.636558971444956,\"retail_edge\":58.56941864486314,\"arb_edge\":-23.932859673441104,\"standard_deviation\":108.3749583040111,\"standard_error\":3.4067376259946602,\"normal_approx_95pct_ci\":[27.959353224495423,41.31376471839449],\"retail_edge_standard_error\":3.6768626972309035,\"arb_edge_standard_error\":2.055290644255973}",
    "REFERENCE_4000 competitor_spread_ticks 2: {\"simulations\":1014,\"failures\":0,\"mean_edge\":78.62034586169882,\"retail_edge\":107.8582269716569,\"arb_edge\":-29.237881109966864,\"standard_deviation\":150.67323699756582,\"standard_error\":4.731699340224055,\"normal_approx_95pct_ci\":[69.34621515485968,87.89447656853797],\"retail_edge_standard_error\":4.987099876667856,\"arb_edge_standard_error\":2.181787075905377}",
    "REFERENCE_4000 competitor_spread_ticks 3: {\"simulations\":1003,\"failures\":0,\"mean_edge\":132.3052700582614,\"retail_edge\":162.4123355647665,\"arb_edge\":-30.107065506517348,\"standard_deviation\":198.7095262774528,\"standard_error\":6.274342492426826,\"normal_approx_95pct_ci\":[120.00755877310483,144.60298134341798],\"retail_edge_standard_error\":6.464829542674944,\"arb_edge_standard_error\":2.046110545868072}",
    "REFERENCE_4000 competitor_spread_ticks 4: {\"simulations\":971,\"failures\":0,\"mean_edge\":153.94372740960227,\"retail_edge\":182.0591627013444,\"arb_edge\":-28.115435291773736,\"standard_deviation\":201.41615085485623,\"standard_error\":6.463751881720962,\"normal_approx_95pct_ci\":[141.2747737214292,166.61268109777535],\"retail_edge_standard_error\":6.774714154184076,\"arb_edge_standard_error\":1.6142769591180643}",
    "REFERENCE_4000 starting_probability [0.0,0.3): {\"simulations\":352,\"failures\":0,\"mean_edge\":195.03828936736647,\"retail_edge\":240.65578719249604,\"arb_edge\":-45.6174978251804,\"standard_deviation\":252.95411083531144,\"standard_error\":13.482499408796219,\"normal_approx_95pct_ci\":[168.61259052612587,221.46398820860708],\"retail_edge_standard_error\":13.291084702494366,\"arb_edge_standard_error\":5.005275271879887}",
    "REFERENCE_4000 starting_probability [0.3,0.4): {\"simulations\":834,\"failures\":0,\"mean_edge\":139.52531020740744,\"retail_edge\":182.12867098971836,\"arb_edge\":-42.6033607823193,\"standard_deviation\":226.6645720019036,\"standard_error\":7.848752226421596,\"normal_approx_95pct_ci\":[124.14175584362111,154.90886457119376],\"retail_edge_standard_error\":7.764072705110629,\"arb_edge_standard_error\":3.2744309559304954}",
    "REFERENCE_4000 starting_probability [0.4,0.5): {\"simulations\":807,\"failures\":0,\"mean_edge\":108.0767117059756,\"retail_edge\":135.75655257942353,\"arb_edge\":-27.679840873454896,\"standard_deviation\":161.77572311295035,\"standard_error\":5.6947751645145495,\"normal_approx_95pct_ci\":[96.91495238352708,119.23847102842412],\"retail_edge_standard_error\":6.200746888851364,\"arb_edge_standard_error\":1.4314938802380086}",
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    "REFERENCE_4000 joint settlement/spread/starting_probability; bin index 0-5 as above; small cells noisy: 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    "REFERENCE_4000 tail concentration: {\"median_edge\":32.07245863765,\"min_edge\":-1406.3841329516,\"max_edge\":1347.7492544137,\"top_10pct_share_of_total_edge\":0.5265243835574145,\"top_1pct_share_of_total_edge\":0.09136857602322396,\"negative_edge_simulations\":410}",
    "REFERENCE_4000 consecutive 200-seed batch means (20 batches, not confidence limits): {\"means\":[120.1459997637355,80.268713494352,108.2180275208605,104.9447442617015,99.606137844652,99.56484566393951,104.4527777986555,83.30346229194299,99.702828050003,106.56194963288449,86.96853670120099,117.993678912772,97.54432494387649,118.35928546291,91.6543671921895,114.39312363795051,74.351438568571,95.247337874639,74.1665619190715,107.3257262942165],\"sd_of_batch_means\":14.016230022806354,\"expected_200_run_mean_standard_error\":12.37313011835025}",
    "Final candidate (only candidate; unchanged base): {\"score\":{\"simulations\":600,\"failures\":0,\"mean_edge\":107.2442092237515,\"retail_edge\":135.80165652288784,\"arb_edge\":-28.557447299150834,\"seed_start\":1000},\"holdout\":{\"mean_edge\":96.0405203261775,\"simulations\":600,\"failures\":0,\"seed_start\":30000},\"code_sha256\":\"d68e658732b99a47eb8004f684319f0bc3dc286fe52a066ab019442f8c91aac2\"}"
  ],
  "next": "The reference shows strong NO-settlement and low-starting-probability dependence; narrow competitor spreads are much less profitable. The top decile contributes over half the total edge, and a 200-run mean has estimated SE about 12.37, so leaderboard-sized unpaired differences are noisy. Use seeds 40000-43999 as a fixed paired reference, never a tuning set; compare per-seed edge differences with paired SE, then freeze each candidate before an independent final holdout."
}