310 lines
15 KiB
C#
310 lines
15 KiB
C#
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using System;
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using System.Collections.Generic;
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using System.Linq;
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namespace Decentralized.Domain
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{
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public enum PredictKind { Event, Faction, Purity, Price }
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public enum PredictResult { Ok, Closed, Amount, Funds, Cap, Opposite, NoPosition }
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/// <summary>
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/// 一个盘口：问一个是非题，开盘当天可以买卖，窗口（FromDay..ToDay）里的结果由游戏或本 mod 的数值决定，ToDay 夜间结算。
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/// 定价用 LMSR：初始价等于先验概率 P0，系统在单盘的最大亏损固定（<see cref="MaxLoss"/>），流动性参数 B 由它反推。
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/// </summary>
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public sealed class PredictMarket
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{
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public int Id;
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public PredictKind Kind;
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/// <summary>事件 / 派系标识；纯度盘是 "gutter" 或 "rust"；行情盘是 "PSC"。</summary>
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public string Key, Title;
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/// <summary>阈值（纯度、价格盘）。</summary>
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public double Param;
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public int OpenDay, FromDay, ToDay;
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public double P0, B, QYes, QNo;
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/// <summary>-1 未结算，0 否，1 是，2 作废（缺观测数据，退还本金）。</summary>
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public int Outcome = -1;
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public double MaxLoss => B * Math.Log(1 / Math.Min(P0, 1 - P0));
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public double ShareCap => Tuning.PredictCap * MaxLoss;
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public bool IsOpen(int day) => Outcome < 0 && day < FromDay;
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public double PYes => 1 / (1 + Math.Exp((QNo - QYes) / B));
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public static double LossFor(int day) => Tuning.PredictLoss0 + Tuning.PredictLossPerDay * day;
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public static PredictMarket Create(int id, PredictKind kind, string key, string title, double param, int openDay, int fromDay, int toDay, double p0)
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{
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p0 = Math.Max(Tuning.PredictPMin, Math.Min(Tuning.PredictPMax, p0));
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double b = LossFor(openDay) / Math.Log(1 / Math.Min(p0, 1 - p0));
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return new PredictMarket { Id = id, Kind = kind, Key = key, Title = title, Param = param, OpenDay = openDay, FromDay = fromDay, ToDay = toDay, P0 = p0, B = b, QYes = b * Math.Log(p0 / (1 - p0)) };
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}
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/// <summary>LMSR 成本函数（数值稳定写法）。</summary>
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public double C(double qy, double qn)
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{
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double m = Math.Max(qy, qn);
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return m + B * Math.Log(Math.Exp((qy - m) / B) + Math.Exp((qn - m) / B));
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}
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/// <summary>某一边买入 shares 份要付的成本（不含手续费）。</summary>
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public double BuyCost(bool yes, double shares) => yes ? C(QYes + shares, QNo) - C(QYes, QNo) : C(QYes, QNo + shares) - C(QYes, QNo);
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/// <summary>某一边卖出 shares 份能收回的金额（不含手续费）。</summary>
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public double SellValue(bool yes, double shares) => yes ? C(QYes, QNo) - C(QYes - shares, QNo) : C(QYes, QNo) - C(QYes, QNo - shares);
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/// <summary>花 cost（不含手续费）能买到的份数：LMSR 成本函数的闭式反解。</summary>
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public double SharesFor(bool yes, double cost)
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{
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double y = yes ? QYes : QNo, o = yes ? QNo : QYes;
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double m = Math.Max(y, o);
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double a = Math.Exp((y - m) / B), oo = Math.Exp((o - m) / B);
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double x = Math.Exp(Math.Min(cost / B, 700)) * (a + oo) - oo;
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return m + B * Math.Log(x) - y;
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}
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public double PriceOf(bool yes) => yes ? PYes : 1 - PYes;
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}
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/// <summary>玩家在某个盘口的持仓（一个盘口只能持有一边）。Insider 是内幕单买入的份数。</summary>
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public sealed class PredictPos
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{
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public int Market;
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public bool Yes;
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public double Shares, Cost, Taint, Basis, Insider;
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}
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/// <summary>结算记录（盘口列表下面的"最近结果"）。</summary>
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public sealed class PredictRecord
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{
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public int Day;
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public string Title;
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public int Outcome;
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public double Pnl;
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public bool Held;
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}
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/// <summary>夜间结算发生的事。Kind：win / lose / void / caught。</summary>
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public sealed class PredictEvent
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{
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public string Kind, Title;
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public PredictMarket Market;
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public double Amount, Fraud;
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}
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/// <summary>候选盘口（接入层按游戏当前状态给出）：先验概率按窗口算。</summary>
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public sealed class PredictCandidate
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{
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public PredictKind Kind;
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public string Key, Title;
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public double Param;
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/// <summary>true：只问明天一天（纯度盘）。</summary>
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public bool Tomorrow;
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public Func<int, int, double> Prob;
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}
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public sealed class PredictBook
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{
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public List<PredictMarket> Markets = new List<PredictMarket>();
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public List<PredictPos> Positions = new List<PredictPos>();
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public List<PredictRecord> Recent = new List<PredictRecord>();
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public int Seq;
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/// <summary>每晚观测：当天新出现的事件标识（和 "F:派系"）。窗口里缺任何一天的观测，盘口作废退款。</summary>
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public Dictionary<int, List<string>> Started = new Dictionary<int, List<string>>();
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public List<string> Prev;
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public PredictMarket Find(int id) => Markets.Find(m => m.Id == id);
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public PredictPos PosOf(int id) => Positions.Find(p => p.Market == id);
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private static double Share(Wallet acct, double amount, Func<string, double> price)
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{
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double total = acct.Value(price);
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return total > 0 ? Math.Min(1, amount * price(Assets.CRC) / total) : 0;
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}
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/// <summary>
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/// 买入：花 spend（含 2% 手续费）的 CRC。污点与成本按花掉的价值比例随资金进持仓。insider：这笔单下单时玩家已经知道答案（传闻纸条、派系特权）。
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/// </summary>
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public PredictResult Buy(Wallet acct, PredictMarket m, bool yes, double spend, int day, Func<string, double> pr, bool insider, out double shares)
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{
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shares = 0;
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if (!m.IsOpen(day)) return PredictResult.Closed;
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if (spend <= 0) return PredictResult.Amount;
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if (acct.Avail(Assets.CRC) + 1e-9 < spend) return PredictResult.Funds;
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var pos = PosOf(m.Id);
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if (pos != null && pos.Yes != yes) return PredictResult.Opposite;
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double cost = spend / (1 + Tuning.PredictFee);
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shares = m.SharesFor(yes, cost);
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if ((pos?.Shares ?? 0) + shares > m.ShareCap + 1e-9) { shares = 0; return PredictResult.Cap; }
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double share = Share(acct, spend, pr);
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double taint = acct.Taint * share, basis = acct.Basis * share;
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acct.Add(Assets.CRC, -spend); acct.Taint -= taint; acct.Basis -= basis;
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if (yes) m.QYes += shares; else m.QNo += shares;
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if (pos == null) Positions.Add(pos = new PredictPos { Market = m.Id, Yes = yes });
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pos.Shares += shares; pos.Cost += cost; pos.Taint += taint; pos.Basis += basis;
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if (insider) pos.Insider += shares;
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return PredictResult.Ok;
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}
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/// <summary>全部卖出（盘口关闭前）：收回 LMSR 的卖价减 2% 手续费，污点按比例退回，赚的部分是干净的。返回收回的 CRC。</summary>
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public PredictResult SellAll(Wallet acct, PredictMarket m, int day, out double got)
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{
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got = 0;
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var pos = PosOf(m.Id);
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if (pos == null) return PredictResult.NoPosition;
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if (!m.IsOpen(day)) return PredictResult.Closed;
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double value = m.SellValue(pos.Yes, pos.Shares);
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got = value * (1 - Tuning.PredictFee);
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if (pos.Yes) m.QYes -= pos.Shares; else m.QNo -= pos.Shares;
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Positions.Remove(pos);
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Pay(acct, pos, got);
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return PredictResult.Ok;
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}
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private static void Pay(Wallet acct, PredictPos pos, double payout)
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{
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double keep = pos.Cost > 0 ? Math.Min(1, payout / pos.Cost) : 0;
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acct.Add(Assets.CRC, payout); acct.Taint += pos.Taint * keep; acct.Basis += pos.Basis * keep;
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}
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/// <summary>
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/// 夜间：先登记今晚的观测，再结算 ToDay 到了的盘口。outcome 由接入层给出（事件 / 派系读观测，纯度和行情读游戏数值），null 表示拿不到数据。
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/// 赢家每份兑付 1 信用点；内幕持仓达到份额上限的 <see cref="Tuning.PredictInsiderShare"/> 后，有概率被查：只退本金，收益的一半记罪证。
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/// </summary>
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public List<PredictEvent> Night(int day, IEnumerable<string> activeNow, Func<PredictMarket, bool?> outcome, Wallet acct, Rng rng)
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{
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var now = activeNow.Distinct().ToList();
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if (Prev != null) Started[day] = now.Where(x => !Prev.Contains(x)).ToList();
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Prev = now;
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foreach (var k in Started.Keys.Where(k => k < day - 12).ToList()) Started.Remove(k);
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var evs = new List<PredictEvent>();
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foreach (var m in Markets.Where(x => x.Outcome < 0 && x.ToDay <= day).ToList())
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{
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bool? res = outcome(m);
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var pos = PosOf(m.Id);
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if (res == null)
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{
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m.Outcome = 2;
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if (pos != null) { Positions.Remove(pos); Pay(acct, pos, pos.Cost); evs.Add(new PredictEvent { Kind = "void", Title = m.Title, Market = m, Amount = pos.Cost }); }
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Record(day, m, 2, 0, pos != null);
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continue;
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}
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m.Outcome = res.Value ? 1 : 0;
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if (pos != null)
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{
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Positions.Remove(pos);
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if (pos.Yes != res.Value)
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{
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evs.Add(new PredictEvent { Kind = "lose", Title = m.Title, Market = m, Amount = pos.Cost });
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Record(day, m, m.Outcome, -pos.Cost, true);
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}
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else
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{
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double payout = pos.Shares, profit = payout - pos.Cost;
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if (pos.Insider >= Tuning.PredictInsiderShare * m.ShareCap && rng.Chance(Tuning.PredictInsiderCatch))
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{
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Pay(acct, pos, pos.Cost);
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evs.Add(new PredictEvent { Kind = "caught", Title = m.Title, Market = m, Amount = profit, Fraud = Math.Min(Tuning.PredictFraudCap, Math.Max(0, profit) * Tuning.PredictFraudShare) });
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Record(day, m, m.Outcome, 0, true);
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}
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else
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{
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Pay(acct, pos, payout);
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evs.Add(new PredictEvent { Kind = "win", Title = m.Title, Market = m, Amount = payout });
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Record(day, m, m.Outcome, profit, true);
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}
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}
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}
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else Record(day, m, m.Outcome, 0, false);
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}
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Markets.RemoveAll(m => m.Outcome >= 0);
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return evs;
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}
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private void Record(int day, PredictMarket m, int outcome, double pnl, bool held)
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{
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Recent.Add(new PredictRecord { Day = day, Title = m.Title, Outcome = outcome, Pnl = pnl, Held = held });
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while (Recent.Count > Tuning.PredictHistory) Recent.RemoveAt(0);
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}
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/// <summary>读观测：窗口里每一天都有记录才能判断；有任何一天缺就返回 null（作废）。</summary>
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public bool? Happened(PredictMarket m)
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{
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string tag = m.Kind == PredictKind.Faction ? "F:" + m.Key : m.Key;
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bool any = false;
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for (int d = m.FromDay; d <= m.ToDay; d++)
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{
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if (!Started.TryGetValue(d, out var list)) return null;
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if (list.Contains(tag)) any = true;
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}
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return any;
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}
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/// <summary>
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/// 每天开门后补盘：开放的盘口少于下限时补到下限，之后每天再随机新开一两个，总数不超过上限。同类同键的盘口不重复开。
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/// 返回新开的盘口。
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/// </summary>
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public List<PredictMarket> Refill(int day, Rng rng, IList<PredictCandidate> candidates)
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{
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var made = new List<PredictMarket>();
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int open = Markets.Count(m => m.Outcome < 0);
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int want = open < Tuning.PredictOpenMin ? Tuning.PredictOpenMin - open : 0;
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want = Math.Max(want, rng.Range(1, Tuning.PredictNewPerDay));
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want = Math.Min(want, Tuning.PredictOpenMax - open);
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var pool = candidates.Where(c => !Markets.Any(m => m.Outcome < 0 && m.Kind == c.Kind && m.Key == c.Key)).ToList();
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while (want-- > 0 && pool.Count > 0)
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{
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var c = pool[rng.Range(0, pool.Count - 1)];
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pool.RemoveAll(x => x.Kind == c.Kind && x.Key == c.Key);
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int from = c.Tomorrow ? day + 1 : day + 1 + rng.Range(0, 1);
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int to = c.Tomorrow ? from : from + rng.Range(0, 2);
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var m = PredictMarket.Create(++Seq, c.Kind, c.Key, c.Title, c.Param, day, from, to, c.Prob(from, to));
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Markets.Add(m); made.Add(m);
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}
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return made;
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}
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}
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/// <summary>盘口先验概率：事件按游戏的掷骰规则，纯度按均匀分布，行情按本 mod 的价格过程。</summary>
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public static class PredictMath
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{
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/// <summary>某个常规事件在窗口里出现的概率：每天先过"有事件"这一关（chance），再按权重在可选事件里抽中。</summary>
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public static double EventProb(double dayChance, double odd, double totalOdd, int days)
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{
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double p1 = totalOdd > 0 ? dayChance * odd / totalOdd : 0;
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return 1 - Math.Pow(1 - p1, days);
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}
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public static double FactionProb(int days) => 1 - Math.Pow(1 - Tuning.PredictFactionDaily, days);
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|
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|
/// <summary>均匀整数 lo..hi 里不低于 threshold 的概率。</summary>
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|
|
public static double PurityAtLeast(double threshold, int lo, int hi)
|
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|
|
{
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|
|
double n = hi - lo + 1, k = hi - Math.Ceiling(threshold) + 1;
|
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|
|
return Math.Max(0, Math.Min(1, k / n));
|
|||
|
|
}
|
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|
|
|
|||
|
|
public static double Phi(double x)
|
|||
|
|
{
|
|||
|
|
double t = 1 / (1 + 0.2316419 * Math.Abs(x));
|
|||
|
|
double d = 0.3989423 * Math.Exp(-x * x / 2);
|
|||
|
|
double p = d * t * (0.3193815 + t * (-0.3565638 + t * (1.781478 + t * (-1.821256 + t * 1.330274))));
|
|||
|
|
return x > 0 ? 1 - p : p;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// 价格在 nights 个夜晚之后（每晚向锚回归 revert、加 vol 的对数噪声，每个早上再加 vol/2 的开门波动）不低于 threshold 的概率。
|
|||
|
|
/// 对数价格近似正态；锚按今天的值外推（事件和减半的变化不计）。
|
|||
|
|
/// </summary>
|
|||
|
|
public static double PriceAtLeast(double price, double anchor, double vol, double revert, int nights, double threshold)
|
|||
|
|
{
|
|||
|
|
double m = Math.Log(price), la = Math.Log(anchor), v = 0;
|
|||
|
|
for (int i = 0; i < nights; i++)
|
|||
|
|
{
|
|||
|
|
m += revert * (la - m);
|
|||
|
|
v = (1 - revert) * (1 - revert) * v + vol * vol + vol * vol / 4;
|
|||
|
|
}
|
|||
|
|
double sd = Math.Sqrt(Math.Max(v, 1e-12));
|
|||
|
|
return 1 - Phi((Math.Log(threshold) - m) / sd);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|