KfChatDotNet/KfChatDotNetBot/Services/Cecil.cs

using MathNet.Numerics;
using MathNet.Numerics.Distributions;
using RandN;
using RandN.Compat;

namespace KfChatDotNetBot.Services;

public static class Cecil
{
    private static readonly RandomShim<StandardRng> Rand = RandomShim.Create(StandardRng.Create());
    public static double Consult(Skew skew, double minThreshold = 0)
    {
        var r = Rand.NextDouble();
        if (r < skew.LossRate)
        {
            return 0;
        }

        var winRate = 1 - skew.LossRate;
        var scaledR = (r - skew.LossRate) / winRate;

        double baseResult;
        switch (skew)
        {
            case BetaSkew betaSkew:
                baseResult = Beta.InvCDF(betaSkew.Weight, betaSkew.Beta, scaledR) * betaSkew.CalibratedMaxWin;
                break;
            case GammaSkew gammaSkew:
                baseResult = Gamma.InvCDF(gammaSkew.Weight, gammaSkew.Weight, scaledR);
                break;
            default:
                return 0;
        }

        baseResult /= winRate;
        
        if (minThreshold == 0) return baseResult;

        var limit = (skew is BetaSkew b) ? b.MaxWin : double.MaxValue;
        
        return Math.Min(Round(baseResult, minThreshold), limit);

        double Round(double baseR, double minT)
        {
            var lower = Math.Floor(baseR / minT) * minT;
            var upper = lower + minT;
            var roundChance = (baseR - lower) / minT;
            return (Rand.NextDouble() < roundChance) ? lower : upper;
        }
        
    }
}

public abstract class Skew
{
    public double Weight;
    public double LossRate;
    protected double TargetEv = 1;
    public abstract void Calibrate(double winRate);

    public void Rig(double desiredEv, double lr)
    {
        TargetEv = desiredEv;
        Calibrate(1-lr);
    }
}

public class BetaSkew : Skew
{
    public readonly double MaxWin;
    public double CalibratedMaxWin;
    public double Beta;
    public double Alpha;

    public BetaSkew(double vol, double mw, double lr)
    {
        MaxWin = mw;
        Weight = vol;
        LossRate = lr;
        Rig(1, lr);
    }

    public override void Calibrate(double winRate)
    {
        CalibratedMaxWin = MaxWin * winRate;
        var normalizer = TargetEv / CalibratedMaxWin;
        Alpha = normalizer * Weight;
        Beta = (1 - normalizer) * Weight;
    }
}

public class GammaSkew : Skew
{
    public double Alpha;
    public double B;

    public GammaSkew(double wght, double lr)
    {
        Weight = wght;
        LossRate = lr;
        Alpha = Math.Pow(Weight, Weight) / SpecialFunctions.Gamma(wght);
        Rig(1, lr);
    }

    public override void Calibrate(double winRate)
    {
        B = (Weight / TargetEv) * winRate;
    }
}