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Yahtzee» Forums » Strategy

Subject: yahtzee calculator. rss

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peter stack
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hi,

i'm pretty much a yahztee enthusiast and i just wondered if it's possible to write a program that lets you play perfect the game every step of the way. maybe it already exists?. i know it will destroy the fun of the game, but i'm just curious. it's a game based on probability and the mathematical formula is rather simpel.
 
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Justin Case
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There is indeed a computer program that plays a perfect game, and does so in a rather interesting manner.

Looking at the game from the beginning, it is simply too complex, there are too many routes to the ending, for any calculating machine to work through it all, and trying to write an algorithm for perfect play is nigh impossible.

But then the developer had an insight. Looking at the game from the ending, on a player's last turn there are only 13 score boxes that can be open, and the Yahtzee bonus is either in play or it is not, so it is possible to calculate a perfect strategy for playing that one final turn.

But if you know the perfect strategy for the last turn, then it becomes possible to calculate a perfect strategy for the next to last turn as well. And so the computer was able to work out a perfect play algorithm by working backwards from last turn to first. It's still far too complex for humans to make the best possible play on every turn and every roll, but guidelines have emerged from the computer program that human players can use to improve their play.

meeple
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Justin Case
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2097 wrote:
But if you’ve been playing perfectly, but through bad luck you’re behind, it might make sense to play a little more risky if it could possibly pay off more, right? That’s why I wanted the algorithm to know about the other players’ scores.

Otherwise you’re just playing solo games.


Well there's not a whole lot of defense in Yahtzee anyway, unless you put the pads on and play full contact! laugh

But of course you are right about adjusting one's play at the end of the game, taking opposing scores into account. However, when you stop to think about it, that decision is pretty cut and dry far more often than not, assuming that the only choice is between winning or not winning. So the programming shouldn't be too difficult -- calculate the probable score of the opponent, and calculate the most likely way to exceed that score.

Things get a lot more complicated, and there is a great deal of room for a "fiddle factor" incorporating the programmer's preferences, when multi-player games are being played. Just from your personal point of view, in a 4 or 5 player game where you are on your next to last turn and looking at a likely second place finish, would you play for the very slim chance of a win that is more likely to knock you back to third place, or would you play for the average outcome that gives up the win but will probably lock up second place?

For myself, I would lock up that second place finish just about every day of the week, and would program a robot player the same way, but that's entirely me. I think the bottom line is that once you move away from the "perfect solitaire play" model to adjusting for opposing scores, you've entered an uncertain area where the preferences of the programmer will be the major factor.

Still, though, the programming shouldn't be difficult from the coding aspect, especially since the best play algorithm would always be right there as well.

meeple
 
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