{
  "approach": "Uses tiny tick probes, a sub-tick probability filter, and marginal retail-versus-arbitrage sizing to quote one tick inside the competitor. Starting from the exactly reproduced base, adds demand-matched crossing cover at ticks 2-9. When estimated probability is between 2c and 10c and YES inventory is below the desired ordinary ask quantity, a bid rests at floor(100*p), sized to the inventory shortfall, capped by 30% of cash-plus-YES marked wealth and 3000 shares. This gets additional stock on a downward crossing rather than paying the next higher tick, while retaining the base tick-1 reservoir and other quoting rules. Higher fixed-tick reservoirs, broad surplus asks, cash gates, and alternative stock targets were compared on tuning seeds only; selection used the full 600-seed tuning mean. The code was frozen before the holdout.",
  "blocked": null,
  "python_version": "3.12.3",
  "base_mean_edge": 102.33197908899267,
  "score": {
    "mean_edge": 108.63974289615767,
    "retail_edge": 136.2713209771645,
    "arb_edge": -27.63157808101933,
    "simulations": 600,
    "seed_start": 1000,
    "failures": 0
  },
  "holdout": {
    "mean_edge": 97.32763650112,
    "simulations": 600,
    "seed_start": 30000,
    "failures": 0
  },
  "code": "\"\"\"Crossing-funded inventory for passive prediction-market quotes.\n\nUses tiny tick probes, a sub-tick probability filter, and marginal retail-versus-arbitrage sizing to quote one tick inside the competitor. Starting from the exactly reproduced base, adds demand-matched crossing cover at ticks 2-9. When estimated probability is between 2c and 10c and YES inventory is below the desired ordinary ask quantity, a bid rests at floor(100*p), sized to the inventory shortfall, capped by 30% of cash-plus-YES marked wealth and 3000 shares. This gets additional stock on a downward crossing rather than paying the next higher tick, while retaining the base tick-1 reservoir and other quoting rules. Higher fixed-tick reservoirs, broad surplus asks, cash gates, and alternative stock targets were compared on tuning seeds only; selection used the full 600-seed tuning mean. The code was frozen before the holdout.\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\n        # Bridge expected retail demand until another tick crossing is available.\n        if 0.02 < phat < 0.1:\n            ct = max(2, min(99, int(math.floor(ptick))))\n            wealth = state.cash + Y * phat\n            goal = min(1 * qa, 0.3 * max(wealth, 0.0) / phat)\n            if Y < goal and ct < ask_t:\n                amt, qam = ct, min(3000.0, goal - 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": "71d04d586f29bb44ebf387156da6553da332111bdfafb9548c0a1530f52f6594",
  "tried": [
    "Rest covered asks at fixed tick 95 for an upward crossing, all available unreserved YES: seeds 1000-1119 mean_edge=125.48796171475583, retail_edge=153.04677660717581, arb_edge=-27.558814892491668, failures=0.",
    "Rest covered asks at fixed tick 95 for an upward crossing, 200-share cap: seeds 1000-1119 mean_edge=125.47693690978333, retail_edge=153.04677811633417, arb_edge=-27.569841206623334, failures=0.",
    "Rest covered asks at fixed tick 98 for an upward crossing, all available unreserved YES: seeds 1000-1119 mean_edge=125.49686520143584, retail_edge=153.04289923068333, arb_edge=-27.54603402933, failures=0.",
    "Rest covered asks at fixed tick 98 for an upward crossing, 200-share cap: seeds 1000-1119 mean_edge=125.54532360046167, retail_edge=153.04289923068333, arb_edge=-27.497575630303334, failures=0.",
    "Rest covered asks at fixed tick 99 for an upward crossing, all available unreserved YES: seeds 1000-1119 mean_edge=125.5572020224475, retail_edge=153.044467253455, arb_edge=-27.487265231087502, failures=0.",
    "Rest covered asks at fixed tick 99 for an upward crossing, 200-share cap: seeds 1000-1119 mean_edge=125.61652612590333, retail_edge=153.04446762602998, arb_edge=-27.4279415002075, failures=0.",
    "Combine extra cover bids and surplus asks at 10c: seeds 1000-1119 mean_edge=119.6392657812375, retail_edge=153.89130360579833, arb_edge=-34.25203782461001, failures=0.",
    "Extra crossing cover below 5c with 1000-step horizon and 50% wealth cap: seeds 1000-1119 mean_edge=126.5071987455025, retail_edge=153.06573725298, arb_edge=-26.558538507559167, failures=0.",
    "Extra crossing cover below 5c with 1000-step horizon and 50% wealth cap; preserve the original tick-one mechanism: seeds 1000-1119 mean_edge=126.38344417480833, retail_edge=153.04977743928, arb_edge=-26.66633326455417, failures=0.",
    "Extra crossing cover below 10c, 200-step demand horizon and 20% realizable wealth cap: seeds 1000-1119 mean_edge=126.41768243673667, retail_edge=153.82398236262915, arb_edge=-27.406299925954166, failures=0. Full seeds 1000-1599: mean_edge=107.19513571844067, retail_edge=136.719920033584, arb_edge=-29.524784315154168, failures=0.",
    "Extra crossing cover below 10c with 1000-step horizon and 50% wealth cap: seeds 1000-1119 mean_edge=123.34771075891999, retail_edge=154.16195377175833, arb_edge=-30.814243012906665, failures=0.",
    "Extra crossing cover below 10c with 1000-step horizon and 50% wealth cap; preserve the original tick-one mechanism: seeds 1000-1119 mean_edge=123.43153614704667, retail_edge=154.16199036968084, arb_edge=-30.730454222704168, failures=0.",
    "Extra crossing cover below 10c, 200-step demand horizon and 20% realizable wealth cap; preserve the original tick-one mechanism: seeds 1000-1119 mean_edge=126.22688507102416, retail_edge=153.7820642804075, arb_edge=-27.555179209445, failures=0. Full seeds 1000-1599: mean_edge=107.08444607216967, retail_edge=136.66106060689302, arb_edge=-29.576614534734667, failures=0.",
    "Crossing cover from tick two to 10c, preserving tick one and subtracting planned higher-tick stock from its target: seeds 1000-1119 mean_edge=126.2297758216625, retail_edge=153.7820642804075, arb_edge=-27.552288458805, failures=0.",
    "Extra crossing cover below 25c with the same target: seeds 1000-1119 mean_edge=125.10253408251249, retail_edge=153.919959617915, arb_edge=-28.817425535479167, failures=0.",
    "Extra crossing cover below 25c with the same target; preserve the original tick-one mechanism: seeds 1000-1119 mean_edge=124.93046326151332, retail_edge=153.88938980101165, arb_edge=-28.958926539575, failures=0.",
    "Extra crossing cover throughout the book: seeds 1000-1119 mean_edge=124.06650042469583, retail_edge=153.922296400025, arb_edge=-29.855795975399168, failures=0.",
    "Crossing cover from tick two to 10c only when cash is below 60% of marked wealth including locked NO: seeds 1000-1119 mean_edge=126.66050450418084, retail_edge=153.259162086375, arb_edge=-26.59865758227, failures=0. Full seeds 1000-1599: mean_edge=107.52375674383484, retail_edge=136.05966805430768, arb_edge=-28.535911310487336, failures=0.",
    "Crossing cover from tick two to 25c only when cash is below 60% of marked wealth including locked NO: seeds 1000-1119 mean_edge=126.42941100183415, retail_edge=153.36251850214666, arb_edge=-26.933107500391667, failures=0.",
    "Crossing cover from tick two to 10c only when cash is below 80% of marked wealth including locked NO: seeds 1000-1119 mean_edge=126.24315447582667, retail_edge=153.45372964926167, arb_edge=-27.210575173511664, failures=0. Full seeds 1000-1599: mean_edge=107.11443583689316, retail_edge=136.23093143414567, arb_edge=-29.116495597267168, failures=0.",
    "NO-aware cash-gated crossing cover, with the same joint inventory target: seeds 1000-1119 mean_edge=126.24315447582667, retail_edge=153.45372964926167, arb_edge=-27.210575173511664, failures=0.",
    "Crossing cover from tick two to 25c only when cash is below 80% of marked wealth including locked NO: seeds 1000-1119 mean_edge=126.28099518631417, retail_edge=153.47799264674083, arb_edge=-27.196997460515835, failures=0.",
    "Crossing asks above 2c only when cash is below 30% of liquid wealth; retain 40% as stock value and cap each sale at 1000 shares: seeds 1000-1119 mean_edge=125.17263907656834, retail_edge=153.04067831998086, arb_edge=-27.86803924349417, failures=0.",
    "Same cash-shortage crossing asks, restricted above 10c: seeds 1000-1119 mean_edge=125.20000929480167, retail_edge=153.04067831998086, arb_edge=-27.840669025260834, failures=0.",
    "Combine NO-aware cash-gated cover bids with cash-shortage crossing asks: seeds 1000-1119 mean_edge=125.3330197896875, retail_edge=153.44962658773, arb_edge=-28.116606798119168, failures=0.",
    "Crossing cover below 5c sized to 1 times the desired ordinary ask quantity: seeds 1000-1119 mean_edge=127.3657544021375, retail_edge=152.64922409915167, arb_edge=-25.283469697085003, failures=0.",
    "Crossing cover below 10c sized to 3 times the desired ordinary ask quantity: seeds 1000-1119 mean_edge=127.4957334561225, retail_edge=153.79978604834, arb_edge=-26.304052592274168, failures=0.",
    "Crossing cover below 10c sized to 1 times expected retail demand before a one-tick exit: seeds 1000-1119 mean_edge=126.49547112263333, retail_edge=153.17960496440583, arb_edge=-26.684133841847498, failures=0.",
    "Crossing cover below 10c sized to 4 times expected retail demand before a one-tick exit: seeds 1000-1119 mean_edge=127.66510019837166, retail_edge=153.54789994938, arb_edge=-25.882799751076668, failures=0.",
    "Crossing cover below 25c sized to 1 times expected retail demand before a one-tick exit: seeds 1000-1119 mean_edge=126.68996268607249, retail_edge=153.17444221667918, arb_edge=-26.484479530685835, failures=0.",
    "Move planned cover bids to floor(p) from tick two upward, preserving original tick-one region: seeds 1000-1119 mean_edge=125.87612201603, retail_edge=152.152743122655, arb_edge=-26.276621106709168, failures=0.",
    "Move planned cover bids to floor(p), including tick one: seeds 1000-1119 mean_edge=121.48689090252749, retail_edge=150.5227051237925, arb_edge=-29.035814221340836, failures=0.",
    "Move ordinary bids to floor(p) below 5c and remove eager cover: seeds 1000-1119 mean_edge=127.69295347953417, retail_edge=151.00918713820585, arb_edge=-23.316233658741666, failures=0. Full seeds 1000-1599: mean_edge=108.27719320275384, retail_edge=133.846136182565, arb_edge=-25.568942979825167, failures=0.",
    "Move ordinary bids to floor(p) below 10c and remove eager cover: seeds 1000-1119 mean_edge=127.69295347953417, retail_edge=151.00918713820585, arb_edge=-23.316233658741666, failures=0.",
    "Move bids below fair value only when cover is deficient below 10c: seeds 1000-1119 mean_edge=125.88556886273334, retail_edge=152.1630605610142, arb_edge=-26.277491698366667, failures=0.",
    "Move bids below fair value only when cover is deficient below 5c: seeds 1000-1119 mean_edge=125.88556886273334, retail_edge=152.1630605610142, arb_edge=-26.277491698366667, failures=0.",
    "Remove eager planned cover purchases: seeds 1000-1119 mean_edge=127.53152849497168, retail_edge=150.83056869929584, arb_edge=-23.299040204396665, failures=0.",
    "Surplus crossing asks above 5c only with cash below 400: seeds 1000-1119 mean_edge=125.40647071590416, retail_edge=152.89705443883335, arb_edge=-27.490583723005, failures=0.",
    "Crossing asks for surplus YES above 10c: seeds 1000-1119 mean_edge=121.533789128135, retail_edge=153.08335888854333, arb_edge=-31.549569760464166, failures=0.",
    "Surplus crossing asks above 10c only within 0.15 tick of fair value: seeds 1000-1119 mean_edge=123.614885661505, retail_edge=152.9916611009975, arb_edge=-29.376775439564167, failures=0.",
    "Pre-position at fixed bid tick 2 while p is up to five ticks higher; stock demand to maturity, 20% cash cap: seeds 1000-1119 mean_edge=126.56666559444334, retail_edge=152.51814850302333, arb_edge=-25.951482908662502, failures=0. Full seeds 1000-1599: mean_edge=107.03697050449567, retail_edge=135.36314182796767, arb_edge=-28.32617132348817, failures=0.",
    "Pre-position at fixed bid tick 2 while p is up to five ticks higher; stock demand to maturity, 50% cash cap: seeds 1000-1119 mean_edge=125.95758734141833, retail_edge=152.50482580936418, arb_edge=-26.547238468028336, failures=0.",
    "Pre-position at fixed bid tick 3 while p is up to five ticks higher; stock demand to maturity, 20% cash cap: seeds 1000-1119 mean_edge=124.74668935907083, retail_edge=152.75332903130084, arb_edge=-28.006639672308335, failures=0.",
    "Pre-position at fixed bid tick 3 while p is up to five ticks higher; stock demand to maturity, 50% cash cap: seeds 1000-1119 mean_edge=123.7354409057075, retail_edge=153.017117355075, arb_edge=-29.281676449450835, failures=0.",
    "Pre-position at fixed bid tick 4 while p is up to five ticks higher; stock demand to maturity, 20% cash cap: seeds 1000-1119 mean_edge=124.65645558580083, retail_edge=153.11856650653752, arb_edge=-28.462110920813334, failures=0.",
    "Pre-position at fixed bid tick 5 while p is up to five ticks higher; stock demand to maturity, 20% cash cap: seeds 1000-1119 mean_edge=123.794516259975, retail_edge=153.77297037957584, arb_edge=-29.978454119664164, failures=0.",
    "Sandbox: final strategy and examples/starter_strategy.py each checked on 20 simulations; both fail before strategy loading because Python 3.12 pathlib imports ntpath, which the simulator sandbox disallows. Unsandboxed scores are reported above.",
    "Scorer verification: supplied base on seeds 0-599 mean_edge=102.33197908899267, retail_edge=127.3199510028995, arb_edge=-24.987971913912165, failures=0; exactly matches the supplied reference. Unchanged base on tuning seeds 1000-1599 mean_edge=107.2442092237515, retail_edge=135.80165652288784, arb_edge=-28.557447299150834, failures=0.",
    "Selected Crossing cover below 10c sized to 1 times the desired ordinary ask quantity (cover10x1), frozen before accessing holdout: seeds 1000-1599 mean_edge=108.63974289615767, retail_edge=136.2713209771645, arb_edge=-27.63157808101933, failures=0; seeds 30000-30599 mean_edge=97.32763650112, failures=0."
  ],
  "next": "Test using the desired ask quantity to govern the original eager ammunition purchases as well as the added crossing bids, while preserving the tick-1 reservoir. Split acquisition cost into ordinary crossings and jumps through the bid, and distinguish stock funding from protection of tiny probes against retail fills. Validate on fresh seeds; do not tune to this holdout."
}