Intransitive games

[pokerfan]

Last edited Wed Jul 4, 2012, 05:54 PM - Edit history (1)

So cool...

Let's play a dice game. I have three dice. They are similar to regular six-sided dice except they have slightly different numbers on them. Each die is different. I'll label them Red, Green, and Blue so that we can differentiate them. The meshes for the three dice are shown here.



We're going to choose and roll one of the dice. I'll even let you choose first. You are free to select any die you like (Red, Green or Blue), then I'll pick one of the two remaining dice. We then enter into a battle: We both roll our dice, and the highest scoring number wins a point. We'll roll twenty times and declare a winner as the one with the most points. Simple?

It might not be a surprise to my suspicious readers, but I'm going to predict that I'm probably going to win the battle. In fact I'll go as far to say that I think I'll win the battle over 98% of the time! (Even if, in the event of a tie at ten points each, I concede the win to you). OK, you say, I somehow forced you into picking one of the dice? No problem, let's do it again.

You can chose to keep the same die, or select another one (you can even have the die I just rolled if you like!) I predict I'm going to win again. We can keep going all day. It does not matter which of the dice you choose, I'll select one of the other dice and win over 98 times in every 100 games. Huh, what's going on? That does not make sense! What's the trick?

http://lifehacker.com/5923186/how-to-use-math-and-win-free-drinks-from-your-friends

[eppur_se_muova]

1. Read something similar to this recently ...

in Paulos' Innumeracy -- Efron's dice. There's also a set of nontransitive dice with numbers 1 through 6 -- these could easily be passed off as standard dice.