{
 "approach": "Spread 2 only (every change is under self.s == 2). Measured on the start file: on the step after the arbitrageur fully takes one of our main quotes, the estimate is stale and new orders on that same side are hit again, losing 0.039 a step against 0.0046 on plain steps. Change: the strategy remembers the ids of its main bid and main ask orders (client ids) resting at the end of each step. If at the next step none of the main bid ids is still resting (fully filled, which in practice is the arbitrageur after p crossed it), it places no main bid that step (qb = 0) and no stock or tick-1 cover bids either (qam = 0, q1 = 0). Likewise, if the main ask was fully taken, it places no main ask that step (qa = 0). It holds back for one step only and is quoting normally again the step after. No constants were tuned; the hold length (1 vs 2 steps) and which orders to hold back were chosen on choosing seeds 30000-37999 of spread 2 (first 1000 to find, remaining 977 to check). The file was then frozen and confirmed on all 2011 spread-2 seeds in 90000-97999. It gives up 0.44 a run of retail edge to save 1.06 a run of arbitrage loss.",
 "blocked": null,
 "spread": 2,
 "base_mean_edge": 108.63974289615767,
 "found": [
  "Start file, first 600 spread-2 choosing seeds (30000+), with a logging copy of the engine loop that scores fills the same way: mean edge 83.52644211440901, arb -26.959013174648334 a run.",
  "Jump steps (|score move| > 0.08): 3.25 steps/run, -12.4525 arb/run (-3.8335 a step). Non-jump steps: 1996.75 steps/run, -14.5065 arb/run (-0.00727 a step).",
  "Plain steps (no rival shift of 2+ ticks and no arbitrage fill of a non-probe order in the previous 5 steps, no jump): 1332.38 steps/run, -6.1481 arb/run, -0.00461 a step.",
  "Steps after the arbitrageur filled a non-probe order (non-jump), k = steps since: k1 123.02 steps/run -4.7664/run (-0.03875 a step); k2 106.12, -0.8379 (-0.00790); k3 98.98, -0.6776 (-0.00685); k4 91.08, -0.6091 (-0.00669); k5 83.62, -0.5559 (-0.00665). Jump steps inside these windows add -0.70, -0.59, -0.78, -0.47, -0.17 a run.",
  "Steps after the rival's best quote shifted 2+ ticks (non-jump): k1 61.39 steps/run -0.8828/run (-0.01438 a step); k2 50.08, -0.2328 (-0.00465); k3 43.51, -0.1964; k4 38.78, -0.1629; k5 35.10, -0.1528, so only k1 is above plain.",
  "Steps after a probe was taken: probes are taken on 1994.22 of 2000 steps a run, so this mark does not separate steps (probe_k1 -14.5005 arb/run, which is almost every non-jump step).",
  "Breakdown of the k1-after-arb-fill loss by order: same-side tick-1 stock bids newly placed 3.35 fills/run -1.8128/run; same-side main bids newly placed 4.46 fills/run -1.2826/run; same-side other stock/cover bids 2.59 fills/run -1.0015/run; same-side main asks 3.40 fills/run -0.3706/run; opposite-side main asks/bids -0.1361 and -0.1183/run.",
  "Largest single loss: main asks resting from earlier steps hit on jump steps, 0.80 fills/run -8.2323/run (not addressed here)."
 ],
 "holdout": {
  "mean_edge": 83.84367743895558,
  "retail_edge": 109.57611337547226,
  "arb_edge": -25.732435936500597,
  "failures": 0
 },
 "diff": {
  "mean": 0.6191034334138734,
  "standard_error": 0.11882984237436155,
  "retail": -0.4381141652449529,
  "arb": 1.057217598659672,
  "trimmed": 0.6126937648886989,
  "runs_up": 1378,
  "runs_down": 630
 },
 "others_identical": {
  "runs": 900,
  "identical": true
 },
 "seconds": {
  "start": 74.73294321913272,
  "yours": 75.6162432518322
 },
 "code": "\"\"\"Crossing-cover base with isolated, untuned per-spread overrides stacked: each acts only in runs of its own competitor spread.\"\"\"\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        self.flow_notional = 0.0\n        self.flow_exposure = 0\n        self.last_ask_tick = None\n        self.last_quote_exposed = False\n        self.last_flow_ca = None\n        self.last_flow_cap = 0.0\n        self.last_flow_correction = 1.0\n        self.params = P.copy()\n        self.s2_mb = set()\n        self.s2_ma = set()\n        self.s2_lb = self.s2_la = -99\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            if self.s == 4:\n                # Censored compound-Poisson flow likelihood, using only our fills.\n                self.f4_exposure = [0, 0]\n                self.f4_events = [0, 0]\n                self.f4_weights = [[0.0] * 9, [0.0] * 9]\n                self.f4_means = [2.64 + i * (6.336 - 2.64) / 8 for i in range(9)]\n                # Positive aggregate flow is approximately lognormal; +0.065\n                # accounts for the occasional second arrival in a timestep.\n                self.f4_mu = [math.log(m) - 0.72 + 0.065 for m in self.f4_means]\n                self.f4_last = [None, None]\n                self.f4_rate = 0.1265\n                self.f4_mean = 4.488\n                self.f4_flow = self.f4_rate * self.f4_mean\n                self.f4_extreme = inv(1 - 1e-6)\n            if self.s == 2:\n                self.params.update(dict(W=150, ammo_pmax=0.02, fy=0.7, fu=0.25, Hu=500))\n            if self.s == 1:\n                self.params.update({'dmin': 0.3, 'pfl': 1e-06})\n            if self.s == 3:\n                self.params.update({'flow_prior': 200, 'flow_level': 0.6, 'flow_strength': 1.0, 'flow_safety': 2.0, 'flow_exposure_min': 5.0})\n        P = self.params\n        if self.s == 4:\n            for side, filled, bound in ((0, state.sell_filled_quantity, ca), (1, state.buy_filled_quantity, cb)):\n                last = self.f4_last[side]\n                if last is None:\n                    continue\n                tick, conv, cap, old_bound, ids = last\n                if (side == 0 and bound > old_bound + 1) or (side == 1 and bound < old_bound - 1):\n                    continue\n                # Track only the main quote, excluding probes and stock orders.\n                remaining = sum(o.remaining_quantity for o in state.own_orders if o.order_id in ids)\n                value = max(0.0, cap - remaining * conv)\n                self.f4_exposure[side] += 1\n                if value > 0.01:\n                    self.f4_events[side] += 1\n                    censored = remaining < 0.011\n                    logv = math.log(max(value, 0.01))\n                    weights = self.f4_weights[side]\n                    for i, mu4 in enumerate(self.f4_mu):\n                        z4 = (logv - mu4) / 1.2\n                        weights[i] += math.log(max(1e-12, 1.0 - cdf(z4))) if censored else -0.5 * z4 * z4\n            if state.step % 25 == 0:\n                exposure = sum(self.f4_exposure)\n                events = sum(self.f4_events)\n                event_probability = (events + 80.0 * (1.0 - math.exp(-0.1265))) / (exposure + 80.0)\n                self.f4_rate = max(0.077, min(0.176, -math.log(max(1e-6, 1.0 - event_probability))))\n                weights = [a + b for a, b in zip(*self.f4_weights)]\n                peak = max(weights)\n                weights = [math.exp(w - peak) for w in weights]\n                self.f4_mean = sum(m * w for m, w in zip(self.f4_means, weights)) / sum(weights)\n                self.f4_flow = self.f4_rate * self.f4_mean\n        if self.s == 3 and self.last_quote_exposed and ca <= self.last_flow_ca + 1:\n            self.flow_exposure += 1\n            self.flow_notional += min(self.last_flow_cap, state.sell_filled_quantity * self.last_ask_tick / 100.0) * self.last_flow_correction\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        hitB = hitA = shB = shA = False\n        if self.s == 2:\n            ids = {o.order_id for o in state.own_orders}\n            hitB = bool(self.s2_mb) and not (self.s2_mb & ids)\n            hitA = bool(self.s2_ma) and not (self.s2_ma & ids)\n            if hitB:\n                self.s2_lb = state.step\n            if hitA:\n                self.s2_la = state.step\n            hitB = state.step - self.s2_lb < 1\n            hitA = state.step - self.s2_la < 1\n            if self.pcb is not None:\n                shB = cb < self.pcb - 1\n                shA = ca > self.pca + 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            if self.s == 4:\n                exp = math.exp\n                if self.bc == cs and 1.0 <= wid <= 6.0 and nb == 8 * wid:\n                    # On this stationary grid, spacing is exactly 1/8 tick.\n                    # Equal index distances therefore have bit-identical d*d*k.\n                    # Reuse exp values while retaining the original sum order.\n                    kernel = []\n                    c0 = cs[0]\n                    for ci in self.bc:\n                        d = c0 - ci\n                        d2 = d * d * k\n                        kernel.append(exp(d2) if d2 > -12.5 else 0.0)\n                    kernel = kernel[:0:-1] + kernel\n                    for i in range(nb):\n                        t = uni\n                        start = nb - 1 - i\n                        for wi, e in zip(self.bw, kernel[start:start + nb]):\n                            if e:\n                                t += wi * e\n                        ws.append(t)\n                else:\n                    previous = tuple(zip(self.bc, self.bw))\n                    for c in cs:\n                        t = uni\n                        for ci, wi in previous:\n                            d = c - ci\n                            d2 = d * d * k\n                            if d2 > -12.5:\n                                t += wi * exp(d2)\n                        ws.append(t)\n            else:\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            if self.s == 4:\n                ja = jb = 0.0\n                for p, w in jp:\n                    if x > p:\n                        ja += w * (x - p)\n                    else:\n                        jb += w * (p - x)\n            else:\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            if self.s == 4 and tail <= 1e-6:\n                return min(P['qmax'], math.exp(mu + P['sig_n'] * self.f4_extreme) / px)\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            if self.s == 4 and phat * 100 - t < P['dmin']:\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            if self.s == 4 and t - phat * 100 < P['dmin']:\n                return 0.0\n            a, b = AB(t / 100.0)\n            if t - phat * 100 < P['dmin']:\n                return 0.0\n            if self.s == 4:\n                tail = b * kA / max(self.f4_rate * a, 1e-30)\n                if a <= 0 or tail >= 1.0:\n                    return 0.0\n                return min(P['qmax'], math.exp(math.log(self.f4_mean) - 0.72 + 1.2 * (self.f4_extreme if tail <= 1e-6 else inv(1 - tail))) / (t / 100.0))\n            if self.s == 2 and phat < 0.1:\n                a = max(0.0, a - 0.0015 * (1 - min(1.0, state.yes_inventory / 3000.0)))\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            threshold = max(P['min_ahead'], 20 * 100.0 / comp) if self.s == 3 and step == -1 and 1 <= comp <= 5 else P['min_ahead']\n            if sticky and sum(o.remaining_quantity for o in orders if o.price_ticks == comp and o.order_id in self.ahead) >= threshold:\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        if self.s == 1 and ask_t == 2 and ask_t < ca and phat < 0.01:\n            qa *= 5\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            flow_scale = self.f4_flow / 0.6 if self.s == 4 else 1.0\n            target = min(flow_scale * P['ydem'] * min(H, P['W']) / x, capw)\n            full = min(flow_scale * 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            stock_rate = P['ydf1']\n            if self.s == 4:\n                stock_rate *= self.f4_flow / 0.6\n            if self.s == 3:\n                flow = (self.flow_notional + P['flow_prior'] * P['flow_level']) / (P['flow_prior'] + self.flow_exposure)\n                scale = max(0.5, min(2.0, flow / P['flow_level']))\n                stock_rate *= 1.0 + P['flow_strength'] * (scale - 1.0)\n            q1 = max(0.0, stock_rate * 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        if self.s == 2:\n            if hitB:\n                qb = 0.0\n                qam = 0.0\n                q1 = 0.0\n            if hitA:\n                qa = 0.0\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) or (self.s == 1 and (o.side is Side.SELL) and o.price_ticks <= 2 and o.order_id in self.ahead)):\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                if self.s == 2:\n                    ub = min(ub, max(0.0, free - 200 * min(1.0, H / 50.0)))\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        if self.s == 3:\n            self.last_ask_tick = ask_t\n            self.last_flow_ca = ca\n            exposed_qty = ka + sum(o.quantity for o in out if o.side is Side.SELL and o.price_ticks == ask_t and o.quantity > PROBE)\n            self.last_flow_cap = exposed_qty * ask_t / 100.0\n            self.last_quote_exposed = ask_t / 100.0 > phat + max(0.005, P['flow_safety'] * self.st / 100.0) and self.last_flow_cap >= P['flow_exposure_min']\n            if self.last_quote_exposed:\n                logcap = math.log(self.last_flow_cap)\n                mu_flow = math.log(P['m']) - 0.5 * P['sig_n'] ** 2\n                clipped = P['m'] * cdf((logcap - mu_flow - P['sig_n'] ** 2) / P['sig_n']) + self.last_flow_cap * (1.0 - cdf((logcap - mu_flow) / P['sig_n']))\n                self.last_flow_correction = min(3.0, P['m'] / max(clipped, 0.01))\n        if self.s == 4:\n            self.f4_last = [None, None]\n            # Eligibility is decided before observing fills, so depleted quotes\n            # remain in the sample as right-censored observations.\n            for side, tick, bound, conv, distance in (\n                (0, ask_t, ca, ask_t / 100.0, ask_t / 100.0 - phat),\n                (1, bid_t, cb, max(phat, 0.05), phat - bid_t / 100.0)):\n                if distance < max(0.01, 3.0 * self.st / 100.0):\n                    continue\n                if side == 0:\n                    if not (ask_t < ca or any(o.price_ticks == ask_t and o.order_id in self.ahead for o in asks)):\n                        continue\n                    orders = asks\n                    order_side = Side.SELL\n                else:\n                    if not (bid_t > cb or any(o.price_ticks == bid_t and o.order_id in self.ahead for o in bids)):\n                        continue\n                    if (qam > 0 and amt >= bid_t) or (q1 > 0 and bid_t <= 1):\n                        continue\n                    orders = bids\n                    order_side = Side.BUY\n                tracked = {o.order_id: o.remaining_quantity for o in orders if o.order_id in kept_ids and o.price_ticks == tick}\n                tracked.update({o.client_order_id: o.quantity for o in out if o.side is order_side and o.price_ticks == tick and o.client_order_id is not None})\n                cap = sum(tracked.values()) * conv\n                if cap >= 0.5:\n                    self.f4_last[side] = (tick, conv, cap, bound, tracked)\n        if self.s == 2:\n            self.s2_mb = {o.order_id for o in bids if o.order_id in kept_ids} | {o.client_order_id for o in out if o.side is Side.BUY and o.client_order_id}\n            self.s2_ma = {o.order_id for o in asks if o.order_id in kept_ids} | {o.client_order_id for o in out if o.side is Side.SELL and o.client_order_id}\n        return actions + out\n",
 "code_sha256": "963807d6db6ddd2ccf3e594d938edd2c4a7452c7b1172733513b8f013d3688ab",
 "tried": [
  "Step 1: earlier file, 600 sims from seed 1000, --workers 4: mean edge 108.63974289615767 (matches the author's exactly), 61 s wall, so run counts were not halved.",
  "Seeds: 1977 spread-2 seeds in 30000-37999 (find on the first 1000 = A, check on the other 977 = B); 2011 spread-2 seeds in 90000-97999 for confirmation; first 300 seeds of each of spreads 1, 3, 4 from 90000.",
  "Hold the main bid one step after the main bid was fully taken (qb=0): A +0.3999 (SE 0.0565, retail -0.2104, arb +0.6103, 644 up/346 down); B +0.4096 (SE 0.0736, 610/354).",
  "Same, also holding stock and tick-1 cover bids (qb=qam=q1=0): A +0.6019 (SE 0.1015, retail -0.227, arb +0.8289, 630/361); B +0.5735 (SE 0.0938, 606/360).",
  "Both sides, one step (above plus qa=0 after the main ask was fully taken), KEPT: A +0.5653 (SE 0.3274, trimmed 0.6946, retail -0.4345, arb +0.9998, 690/308); B +0.7562 (SE 0.1541, trimmed 0.81, retail -0.483, arb +1.2392, 666/311).",
  "Bid side with stock, held 2 steps: A +0.5661 (SE 0.1448, trimmed 0.4652, 519/480); B +0.5064 (SE 0.1315, trimmed 0.367, 491/486). Rejected: fewer runs gain.",
  "Both sides held 2 steps: A +0.507 (SE 0.3983, retail -1.1326, arb +1.6396, 533/467); B +0.4737 (SE 0.1862, 510/467). Rejected: costs too much retail edge and fewer runs gain.",
  "Confirm (frozen file vs start file, 2011 spread-2 seeds 90000-97999): start mean edge 83.22457400554173, final 83.84367743895558, diff 0.6191034334138734 SE 0.11882984237436155, 0 failures for both.",
  "Other spreads: 300 runs each of spreads 1, 3, 4 (seeds from 90000), every result field identical to the start file: True.",
  "Timing: 200 runs (seeds 90000-90199), serial, one process each, run at the same time: start 74.73 s, final 75.62 s (+1.2%).",
  "The final file computes two shift flags (shB, shA) that nothing uses. They were left in because the file was frozen and confirmed with them, and they do not change any result. A hold-back on rival shifts was not tested."
 ],
 "next": "Try a hold-back on the step after the rival's quote shifts 2+ ticks (k1 loses 0.0144 a step against 0.0046 plain). Try shrinking the held side by a fraction instead of setting it to zero, to win back some of the 0.44 a run of retail edge this gives up. Try the same one-step hold in spreads 1, 3 and 4, each proven on its own seeds. Separately, main asks resting from earlier steps and hit on jump steps cost 8.2 a run in spread 2, which is the largest single loss."
}