Optimal play of Pig
May 7th, 2015 at 10:02:12 AM
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For those interested in game mathematics, here's an example of a simple dice game that has a not-so-simple analysis.
http://cs.gettysburg.edu/~tneller/papers/pig.pdf
http://cs.gettysburg.edu/~tneller/papers/pig.pdf
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563
May 7th, 2015 at 12:49:09 PM
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Interesting read.
May 7th, 2015 at 1:01:12 PM
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Wow, that got complicated in a hurry. I think the paper makes more sense if you start with the SKUNK variation, which explains how to maximize points with a limited number of turns rather than with a point goal.
To wrap my head around it, I tried to reason the optimal number of rolls if you wanted to get maximum points in a single turn. If x = # of turns, I think EV = 4*x*(5/6)^x, because 4 is the average scoring outcome, and there is a 1/6 chance you lose your total each turn (by rolling a 1). This yields the optimal strategy of stopping after 5 or 6 rolls to maximize a single round, with both EV=8.03755.
Am I on the right track here?
To wrap my head around it, I tried to reason the optimal number of rolls if you wanted to get maximum points in a single turn. If x = # of turns, I think EV = 4*x*(5/6)^x, because 4 is the average scoring outcome, and there is a 1/6 chance you lose your total each turn (by rolling a 1). This yields the optimal strategy of stopping after 5 or 6 rolls to maximize a single round, with both EV=8.03755.
Am I on the right track here?
May 7th, 2015 at 2:01:56 PM
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Interesting article, goes to show how little it takes to make a game more complex.
Still can't believe that group up in Alberta "solved" heads-up limit hold 'em.
Still can't believe that group up in Alberta "solved" heads-up limit hold 'em.
