These bad boys are not like any other set of dice you’ve seen before because they don’t follow the traditional rules of transitivity. Let me explain what I mean by that.

In math, a relation is said to be transitive if it satisfies this property: If A is related to B and B is related to C, then A is also related to C. For example, in the context of numbers, less than (<) is a transitive relation because if 3 < 5 and 5 < 7, then we can conclude that 3 < 7 as well. But what happens when you have dice that don't follow this rule? Well, let me introduce you to Efron's dice four intransitive dice invented by Bradley Efron (yes, the same guy who came up with bootstrapping). These dice are a set of four: A, B, C, and D. Here's how they work: each die has six faces, but instead of having numbers like traditional dice, these faces have symbols that represent different outcomes. For example, Die A has four 4's on its faces (because it's a lucky die), while Die B has three 3's and three more 3's (because it's not as lucky). Now, here's where things get interesting: these dice are intransitive! That means that if you roll Die A and then Die B, the outcome of Die A will beat the outcome of Die B with a probability of 2/3. But wait what about when you roll Die C? Well, it beats both Die A and Die B with a probability of 2/3! And finally, there's Die D which is beaten by all three other dice (but still manages to beat itself). So basically, these dice are like the game Rock-Paper-Scissors but in math form. It's crazy stuff, I know! In fact, they might even make your next board game night more interesting (and confusing) than ever before. If you want to learn more about them or try rolling some yourself, head over to mathwithbaddrawings.com and check out Bradley Efron's website.