A friend of mine just posted on my Facebook wall, linking to this YouTube video about “Grime Dice,” a set of five dice with numbered faces chosen to have some interesting non-transitive properties; the first is that each of the dice will statistically beat two of the other dice, forming two “A beats B beats C beats D beats E beats A” loops, like Rock-Paper-Scissors-Lizard-Spock. The second, more remarkable property, is that if you roll two dice at a time instead of one, and add the totals, one of these loops remains unchanged, while the other reverses in order (so that E beats D beats C beats B beats A beats E).
After writing my last post, about how risk-reward decisions are affected by a game in which the goal is achieving an all-time high score, I got to thinking about more general cases of risk-reward decision-making in games, and how that is, like these Grime dice, a non-transitive thing. If you have the opportunity to see what kinds of risks your opponents are taking, you’re usually going to want to gamble either just a little bit bigger, so as to come out slightly ahead if you both succeed, or – if you feel your opponent’s strategy is too high-risk, play as safely as possible and count on them failing.
Having been reminded of this by the Grime dice, I decided to invent an extremely minimalist dice game to take a closer look at this idea in the abstract.
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