Run a number of tests on a set of dice to see what the average number of rolls is required to have them all land on the first side (represented here with a "0"). Returns the average.

testDice.js

(function (window) {

  // Return a random integer from 0 to `d`
  function r(d) {
    return Math.round(Math.random() * --d);
  }

  // Roll the dice. Returns a string of integers to represent which
  // side each die fell on ("0" is the first side).
  //
  // `m` is the number of dice to roll
  // `d` is the number of sides each die has
  function roll(m, d) {
    return new Array(m).join().split(",").map(function () {
      return r(d);
    }).join("");
  }

  // Run one test of a set of dice. This runs until the `roll`
  // returns a string that matches `s`. Returns the number of
  // rolls.
  //
  // `s` is a string of zeros, with length `m`
  // `m` is the number of dice to roll
  // `d` is the number of sides each die has
  function test(s, m, d) {
    var i = 0;
    while (++i) {
      if (roll(m, d) === s) {
        return i;
      }
    }
  }

  // Run a number of tests on a set of dice to see what the average
  // number of rolls is required to have them all land on the first
  // side (represented here with a "0"). Returns the average.
  //
  // `m` is the number of dice to roll in each test
  // `n` is the number of tests to run
  // `d` is the number of sides each die has
  function testDice(m, n, d) {
    var i, s = new Array(m + 1).join("0"), total = 0;
    for (i = 0; i < n; i++) {
      total += test(s, m, d);
    }
    return total / n;
  }

  window.testDice = testDice;

})(this);