I’ve put some notes and code I’m writing while trying to figure out John Conway etc’s Winning Ways for your Mathematical Plays (I’m not finding it an easy read).
Work so far is at SWISH -- SWI-Prolog for SHaring
A snag I’ve hit is that according to a theory attributed to Charles Bouton dating back to 1902, the example Nim game I’ve used should always be won by the starting player. My code seems to have some bug because player2 often wins.
Anyways, I thought I’d share my progress so far for anyone interested.
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The rules of the game seem similar to prolog - The game of 23 matches in SWIPROLOG - Stack Overflow which hopefully provides inspiration.
Glad to say both my code and Bouton’s theorem are working fine now.
I misunderstood that winning moves could have nimbers of either 0 or 2. It turns out they can only be 0. (I think the 2 came up in his paper as an example of an even number of ones that become 0 in his aggregation method… I shouldn’t skim through stuff so quickly).
Anyways, I’ve put all four example Nim games provided by Stanford University’s General Game Playing course.
All examples have four heaps labeled a, b, c and d. In the first example, my predicate
playgame([control(player1),heap(a,1),heap(b,5),heap(c,4),heap(d,2)], Moves).
player1 has a move with a nimber of 0, so always wins.
In Example 2 player1 has no 0 nimber move, so player2 does and always wins. (I have no idea why that his true, but a long line of famous mathematicians agree, and my code gives that result).
playgame([control(player1),heap(a,2),heap(b,2),heap(c,10),heap(d,10)], Moves).
I’ve also included Stanford’s other two examples at SWISH -- SWI-Prolog for SHaring
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