Monday, April 6, 2015

Yahtzee: a Solved Game

Yahtzee, it's a fun dice game.  If backgammon is in the sweet-spot of skills and luck (which I believe it is) then Yahtzee moves a little more into the luck category, which can be good for drumming up a game.  In Yahtzee if you roll a Yahtzee and no one else does, you're probably going to win.  If you roll two Yahtzees and no one matches it, you ARE going to win.  So the game is really play slots with someone, trying to see who can get the jackpot.

In the other circumstances, when the Yahtzees equalize out (often at no one getting one) there are some important choices to make that can impact competitive equity.  And if you find yourself playing a lot of Yahtzee, realize that those decisions can be objectively rated, and the game can be studied.

Yahtzee, at least in terms of going for the highest score you can is a solved game, meaning all of the combinations have been calculated.

If one wanted to (and I'm not sure I do; I have a lot of gaming interests going at any one time,) then it would be a simple matter to find an implementation of the Optimal Yahtzee Player and use it to figure out "reference points" for certain kinds of common decisions.  If you pick the right ones, you will have the "borderline cases" memorized so that you not only get those decisions right, but you will also know what to do in cases stronger and weaker.

With all that said, if you opponent rolls two unmatched Yahtzees, then you are going to lose.  But learning itself is fun, and it is often nice to do learning play (it's not really work, now is it?) in the space of games because there can be more objective progress, even if you don't necessarily win more games immediately.

I might be talking myself into studying Yahtzee when I get more time, maybe over the Summer Break.

Update:

Nope.  This is a popular post for some reason, though. . .