How to cheat at settlers by loading the dice (2017)

Summary

how to cheat at settlers by loading the dice (and prove it with p-values) posted on 2017-12-14 tl;dr This post shows how to create loaded dice, and how to use these dice to gain between 5-15 additional resource cards per game of Settlers of Catan. Surprisingly, we’ll prove that standard scientific tests are not powerful enough to determine that the dice are unfair while playing a game. This essentially means that it’s impossible for your opponents to scientifically prove that you’re cheating. This impossibility is due to methodological defects in the current state of scientific practice, and we’ll highlight some ongoing work to fix these defects. Loading the dice My copy of Settlers of Catan came with two normal wooden dice. To load these dice, I placed them in a small plate of water overnight, leaving the 6 side exposed. The submerged area absorbed water, becoming heavier. My hope was that when rolled, the heavier wet sides would be more likely to land face down, and the lighter dry side would be more likely to land face up. So by leaving the 6 exposed, I was hoping to create dice that roll 6’s more often. This effect is called the bias of the dice. To measure this bias, my wife and I spent the next 7 days rolling dice while eating dinner. (She must love me a lot!) In total, we rolled the dice 4310 times. The raw results are shown below. 1 2 3 4 5 6 number of rolls 622 698 650 684 666 812 probability 0.151 0.169 0.157 0.165 0.161 0.196 Looking at the data, it’s “obvious” that our dice are biased: The 6 gets rolled more times than any of the other numbers. Before we prove this bias formally, however, let’s design a strategy to exploit this bias while playing Settlers of Catan. A strategy for loaded dice The key to winning at Settlers of Catan is to get a lot of resources. We want to figure out how many extra resources we can get using our biased dice. First, let’s quickly review the rules. Each settlement is placed on the corner of three tiles, and each tile has a n...