&gt; it looks like it would still be fair enough [if it only reaches a portion of the neighboring values at each bounce] due to the fact that there is a large difference in the numbers available &#x27;nearby&#x27; any one spot<p>what is this, NSA logic day?  :-D<p>(This is my way of saying that your argument actually results in really low randomness.  It means the random process has some memory and has far less distribution of states than you would expect.  your argument is like saying a good way to get a random number between 1 and 1,000,000 is to flip a coin, then heads it&#x27;s 170,158; tails it&#x27;s 587,439.  There&#x27;s a large difference between 170,158 and 587,439 but those two numbers wouldn&#x27;t be random AT ALL, because all the other numbers couldn&#x27;t come up.  you&#x27;re saying the die would &#x27;still be fair enough&#x27; because the numbers that can come up are far from each other... well, no...)