A Quick Yahtzee Puzzle

My friend ChefMongoose pointed out this probability question. As with many probability questions, it comes from a dice game. Here, Yahtzee, based on rolling five dice to make combinations. I’m not sure whether my Twitter problems will get in the way of this embedding working; we’ll see.

The question:

Probability help please! You are playing Yahtzee against your insanely competitive spouse. You have two rolls left. You’re trying to get three of a kind. Is it better to commit and roll three dice here? Or split it and roll one die? — Christopher Yost.

Of the five dice, two are showing 1’s; two are showing 2’s; and there’s one last die that’s a 3.

As with many dice questions you can in principle work this out by listing all the possible combinations of every possible outcome. A bit of reasoning takes much less work, but you have to think through the reasons.

Reblog: A quick guide to non-transitive Grime Dice

The bayesianbiologist blog here has an entry just about a special set of dice which allow for an intransitive game. Intransitivity is a neat little property, maybe most familiar from the rock-paper-scissors game, and it’s a property that sneaks into many practical applications, among the interesting ones voting preferences.

A very special package that I am rather excited about arrived in the mail recently. The package contained a set of 6-sided dice. These dice, however, don’t have the standard numbers one to six on their faces. Instead, they have assorted numbers between zero and nine. Here’s the exact configuration:

Aside from maybe making for a more interesting version of snakes and ladders, why the heck am I so excited about these wacky dice? To find out what makes them so interesting, lets start by just rolling one against another and seeing which one rolls the higher number. Simple enough. Lets roll Red against Blue. Until you get your own set, you can roll in silico.

That was fun. We can do it over and over again and we’ll find that Red beats Blue more often than not. So it seems like Red is a pretty good…

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