simulation.js

"use strict";

var matches = 0;

// 'Borrowed' from http://www.math.ucla.edu/~tom/distributions/binomial.html

function LogGamma(Z) {
  var S=1+76.18009173/Z-86.50532033/(Z+1)+24.01409822/(Z+2)-1.231739516/(Z+3)+.00120858003/(Z+4)-.00000536382/(Z+5);
  var LG= (Z-.5)*Math.log(Z+4.5)-(Z+4.5)+Math.log(S*2.50662827465);
	return LG
}

function Betinc(X,A,B) {
	var A0=0;
	var B0=1;
	var A1=1;
	var B1=1;
	var M9=0;
	var A2=0;
	var C9;
	while (Math.abs((A1-A2)/A1)>.00001) {
		A2=A1;
		C9=-(A+M9)*(A+B+M9)*X/(A+2*M9)/(A+2*M9+1);
		A0=A1+C9*A0;
		B0=B1+C9*B0;
		M9=M9+1;
		C9=M9*(B-M9)*X/(A+2*M9-1)/(A+2*M9);
		A1=A0+C9*A1;
		B1=B0+C9*B1;
		A0=A0/B1;
		B0=B0/B1;
		A1=A1/B1;
		B1=1;
	}
	return A1/A
}

function OddsToReachLimit(w, l, limit, goal) {
    if (w === 0 || l === 0) return 1;
    var X=limit*(1-goal)-l
    var N=limit-w-l
    var P=1-goal
    var bincdf, Betacdf;
		if (N<=0) {
      console.log(`sample size must be positive must be positive ${N} w ${w} l ${l}`)
      return 1;
			// process.exit(1)
		} else if ((P<0)||(P>1)) {
			console.log(`probability must be between 0 and 1 ${P} w ${w} l ${l}`)
      return 1;
			// process.exit(1)
		} else if (X<0) {
			bincdf=0
		} else if (X>=N) {
			bincdf=1
		} else {
			X=Math.floor(X);
			var Z=P;
			var A=X+1;
			var B=N-X;
			var S=A+B;
			var BT=Math.exp(LogGamma(S)-LogGamma(B)-LogGamma(A)+A*Math.log(Z)+B*Math.log(1-Z));
			if (Z<(A+1)/(S+2)) {
				Betacdf=BT*Betinc(Z,A,B)
			} else {
				Betacdf=1-BT*Betinc(1-Z,B,A)
			}
			bincdf=1-Betacdf;
		}
		bincdf=Math.round(bincdf*100000)/100000;
  return bincdf;
}



function LL (x) {
    return 1/(1+Math.pow(10,(-x/400)));
}

function LLR(W, L, elo0, elo1) {
    //if (W==0 || L==0) return 0;
    if (!W) W=1;
    if (!L) L=1;

    var N = W + L;
    var w = W/N, l = L/N;
    var s = w;
    var m2 = w;
    var variance = m2-Math.pow(s,2);
    var variance_s = variance / N;
    var s0 = LL(elo0);
    var s1 = LL(elo1);

    return (s1-s0)*(2*s-s0-s1)/variance_s/2.0;
}

function SPRT(W,L,elo0,elo1, alpha, beta)
//function SPRT(W,L)
{
    //var elo0 = 0, elo1 = 35;
    //var alpha = .05, beta = .05;

    var LLR_ = LLR(W,L,elo0,elo1);
    var LA = Math.log(beta/(1-alpha));
    var LB = Math.log((1-beta)/alpha);

    //console.log(LLR_ + " " + LA + " " + LB);

    if (LLR_ > LB) {
        return true;
    } else if (LLR_ < LA) {
        return false;
    } else {
        return null;
    }
}


function check(w, l) {
  if (_s5 && w+l>=400 && w >= 220 ) return true
  if (_s6 && OddsToReachLimit(w, l, 400, 0.55) < _s7) return false
  return SPRT(w, l, _s1, _s2, _s3, _s4);
  //return SPRT(w, l, -13, 13, .04, .24);
}

function test(success) {
  var win = 0, loss = 0;
  for (var i = 0; i < 400; i++) {
    matches++;
    if (Math.random() < success) {
      win++;
    } else {
      loss++;
    }
    var res = check(win, loss)
    if (res !== null) {
      return res;
    }
  }
  return false; // undecided so we consider this a fail.
}

var trails = 1000

function testPerc(success) {
  var fail = 0;
  for (var i = 0; i < trails; i++) {
    if (test(success) !== true) {
      fail++;
    }
  }
  return fail;
}

function calcResult() {
  matches = 0;
  var falsePass = Array(500)
    .fill()
    .map((x, i) => i / 1000.0)
    .map(e => trails - testPerc(e))
    .reduce(function(a, b) { return a + b; }, 0);

  var falseFail = Array(500)
    .fill()
    .map((x, i) => i / 1000.0 + 0.5)
    .map(e => testPerc(e))
    .reduce(function(a, b) { return a + b; }, 0);
  console.log([matches, falseFail, falsePass].join("|"));
}

function printResult() {
  console.log();
  console.log(`SPRT(${_s1}, ${_s2}, ${_s3}, ${_s4}) cutoff: ${_s5} limit: ${_s6} (${_s7})`);
  console.log();
  console.log("games | falseFail | falsePass");
  console.log("-- | -- | --");
  calcResult();
  calcResult();
  calcResult();
  calcResult();
  calcResult(); 
}

//var _s1 = 0, _s2 = 30, _s3 = .02, _s4 = .9, _s5 = true, _s6 = true;
//printResult()
// var _s1 = 0, _s2 = 35, _s3 = 0.05, _s4 = 0.05, _s5 = true, _s6 = true, _s7 = 0.01;
// printResult()
var _s1 = 0, _s2 = 35, _s3 = 0.05, _s4 = 0.05, _s5 = true, _s6 = true, _s7 = 0.001;
printResult()
// _s1 = 0, _s2 = 35, _s3 = 0.05, _s4 = 0.05, _s5 = true, _s6 = false;
// printResult()
// _s1 = -13, _s2 = 13, _s3 = 0.04, _s4 = 0.24, _s5 = true, _s6 = false;
// printResult()
// _s1 = -13, _s2 = 13, _s3 = 0.04, _s4 = 0.24, _s5 = false, _s6 = false;
// printResult()

// var n = 225
// console.log(check(n,400-n))