plinko-maths.js

// let payouts be the array payouts details (like from /bets/custom)
// let details.outcome be the final outcome of the bet

// Given the outcome, find out how many times it went right
var rights = payouts.findIndex(function(p) {
  return details.outcome >= p.from && details.outcome < p.to;
});

assert(rights >= 0);

var directionCombinations = binom(choices, rights);

// Now we will convert from where details.outcome lies in the range
var payoutsRange = payouts[rights].to - payouts[rights].from;

var ith = ((details.outcome - payouts[rights].from) / payoutsRange) * (directionCombinations-1);
assert(ith >= 0, ith <= directionCombinations-1);
ith = Math.round(ith);


// path is the path!
var path = bitseq(choices, rights, ith);


function binom(n,k) {
  k = Math.min(k, n - k);
  assert(k >= 0);

  var r = 1;
  for (var i = 0; i < k; ++i)
    r = (r * (n - i)) / (i + 1);
  return r;
}

// n is how many layers
// k is how many rights it made
// i it the ith value
function bitseq(n, k, i) {
  if (k > n || k < 0) return null;
  if (n === k && i == 0) return Array.apply(null, new Array(n)).map(String.prototype.valueOf, 'R').join('');
  if (n === k) return null;

  var m = binom(n-1, k);

  if (i < m) {
    var seq = bitseq(n-1, k, i);
    if (seq === null) return null;
    return 'L' + seq;
  }

  var seq = bitseq(n-1, k-1, i-m);
  if (seq === null) return null;
  return 'R' + seq;
}