Test overshoot

gistfile1.txt

function LL (x) {
    return 1/(1+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-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)
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;
    }
}

var check = (w, l, r) => {
  return Math.max(w*2-l, 5) > r
}

function test(success) {
  var w = 0, l = 0, r = 0, i
  var arr = Array(100)
  arr.fill(null)
  for (i = 0; i < 3000; i++) {
    if (w === 220 || SPRT(w, l) !== null || w + l + r > 399) {
      // console.log("Finished!", w,l,r,i)
      return ({ w, l, r, i});
    }
    if (check(w,l,r)) {
      arr.push(Math.random() < success)
      r++;
    } else {
      arr.push(null)
    }
    var res = arr.shift()
    if (res !== null) {
      if (res) {
        w++;
      } else {
        l++;
      }
      r--;
    }
  }
  // console.log("no result!", w,l,r,i)
  return ({ w, l, r, i});
}

function testAvg(success) {
  var w = 0, ws = 0; // wins and win steps
  var l = 0, ls = 0, lo = 0; // losses, loss steps and loss overshoot
  var inc = 0; // inconclusive
  for (i = 0; i < 2500; i++) {
    var r = test(success)
    if (r.w + r.l + r.r > 399) {
      inc++;
    } else if (r.w === 220 || SPRT(r.w, r.l)) {
      w++; ws += r.i
    } else {
      l++; ls += r.i; lo += r.r;
    }
  }
  return ({success, w, ws, l, ls, lo, inc});
}

function testAvgPrint(success) {
  var r = testAvg(success);
  console.log(`wins: ${r.w}`);
  console.log(`avg win steps: ${r.ws/r.w}`);
  console.log(`losses: ${r.l}`);
  console.log(`avg loss steps: ${r.ls/r.l}`);
  console.log(`avg loss overshoot: ${r.lo/r.l}`);
  console.log(`inconclusive: ${r.inc}`);
}

function makeTable() {
  var arr = [0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9].map(e => testAvg(e))
  console.log("success|wins|losses|inconclusive|avg win steps|avg loss steps|avg loss overshoot")
  console.log("-- | --  | --  | --  | -- | -- | --")
  arr.forEach((e) => 
      console.log(`${e.success}|${e.w}|${e.l}|${e.inc}|${(e.ws/e.w).toFixed(2)}|${(e.ls/e.l).toFixed(2)}|${(e.lo/e.l).toFixed(2)}|`)
    );
}