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Walter Trice
Posted By: Tom Keith
Date: Wednesday, 3 September 2014, at 4:03 p.m.
In Response To: Thoughts on solving hypergammon (Tom Keith)
I just happened upon an r.g.b post Walter Trice wrote in 1995. I was struck by how similar his description of solving backgammon was to the one I gave above.
Here's a simple way to completely solve the game of backgammon.
For any position you can express the equity in terms of the equities of immediate successors. Checker play decisions are handled by taking the maximum equity from the set of all legal plays for each roll. You can also incorporate cube action into the equation (cube location matters, but cube value does not.)
The equations are then solved iteratively. You initialize all nonterminal equities to zero (or whatever suits your fancy) and equities for terminal states to their actual values. Then you run through all legal positions and calculate equities using whatever values you have. When you're all done you repeat the process. You continue until convergence occurs.
This sounds awfully simpleminded, but I do know that it works for 1checker backgammon. I used this method to solve that game 6 years ago, at a time when people were naive enough to play 1checker backgammon for money. My guess is that Hugh Sconyers did something like this for 3checker backgammon. I believe (but have not proven) that in principle the method would work for any number of checkers, though the number of positions increases so rapidly that the limit of one's computing capacity is quickly reached.
I encourage those interested in this stuff to actually write a 1checker backgammon program. Using the method I have outlined here it's really very simple.

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