The Variance of High Production Hexes in Catan

It always bugs me when I have a set up which is just as good as someone else’s, and then one of their numbers rolls twice as many times as an equivalent one of mine,  even though their expectation is, in theory, the same. Like when the 6’s roll twice as many times as the 8’s, and, ironically, you happen to be on a 6 and not on an 8, so you just sit there watching that stream of resources going to someone else throughout the whole game.

This bothered me so much that I started using the balanced dice option featured in, and the difference was very noticeable. Given the implementation of a ranking system in Colonist, I’ve since started playing rated games, and these only feature the usual “random” dice, much to my frustration.

In a (likely futile) attempt to convince others to abandon the “random” dice in favor of their balanced counterpart I wrote this small article that compares the probabilities of these specific imbalances occurring. And guess what, the chances of one of the high hexes (5 pips or 4 pips) rolling at least twice as many times as it’s counterpart is roughly 37%, i.e. more than one in three…

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