The Most Powerful Dice

[krusader74]

The Most Powerful Dice -- Numberphile



In this 6 minute 33 second YouTube video on the Numberphile channel, Tadashi Tokieda asks us to consider the following game:

Two players choose a die from a set of dice and roll them against each other. Whichever comes up higher wins. Here is the set of the dice players can use and their face values:

Green Die: 6 6 2 2 2 2

Red Die: 5 5 5 1 1 1

Yellow Die: 4 4 4 4 0 0

Blue Die: 3 3 3 3 3 3

Rank the dice. Which is stronger, which is weaker?

One die is stronger than the other die if that die has a higher probability of winning against the other die.

The rankings are

Green > Red > Yellow > Blue > Green

This is a simple example of a non-transitive cycle in probabilistic comparison.

BTW, you can purchase a set of non-transitive dice at mathsgear.co.uk

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[tkdco2]

Nice video!

The most powerful dice are the ones that you can throw at obnoxious players and stun them with one blow.

What?

[Scott Anderson]

The most powerful dice are the ones thrown by Hulk Hogan, everyone knows that

[krusader74]

Incidentally, if someone wished to experiment with the probability of one die scoring higher than another and the relative strength of dice using Palamedes, you could enter the following code, one line at a time, on the main page:

Green <-[6, 6, 2, 2, 2, 2]
Red <- [5, 5, 5, 1, 1, 1]
Yellow <- [4, 4, 4, 4, 0, 0]
Blue <- 6#3
probWins <- sum(map(hold(_1 > _2), _1 cross _2))/sum(map(1, _1 cross _2))
stronger <- probWins(_1, _2) > probWins(_2, _1)
stronger(Green, Red)
stronger(Green, Blue)
probWins(Green, Blue)


But I've already created a more elaborate script to analyze this game. The script is here. You can run it with this link. And here is a screenshot of the output. (Note I've only tested this in Firefox 49 so far.)