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BGonline.org Forums
The Curious Case of Benjamin's Button -- SOLUTIONS
Posted By: Philippe Michel In Response To: The Curious Case of Benjamin's Button -- SOLUTIONS (Nack Ballard)
Date: Monday, 20 November 2017, at 10:22 p.m.
The problem may be due to the variance reduction computations. That wouldn't require misplays, merely misevaluations of the gammons percentages.
FWIW, GNUbg does rate the moves as tied :
Unlimited game, Jacoby rule
GNUbg 87
You 17 Position ID: cveqAAA6AgAAAA Match ID: QQkHAAAAAAAA
# Ply Move Equity 1 R 6/off 2/1 +1.478306
1.000000 0.478306 0.000000 - 0.000000 0.000000 0.000000 +1.478306 +1.478306 0.000000 0.000380 0.000000 - 0.000000 0.000000 0.000000 0.000381 0.000381 Full cubeful rollout with var.redn. 1296 games, Mersenne Twister dice gen. with seed 1 and quasi-random dice Play: 4ply 4-ply cubeful prune [4ply] keep the first 0 0-ply moves and up to 16 more moves within equity 0.32 Skip pruning for 1-ply moves. keep the first 0 2-ply moves and up to 4 more moves within equity 0.08 Skip pruning for 3-ply moves. Cube: 4-ply cubeful prune [4ply] 2 R 6/off 3/2 +1.478303 (-0.000003)
1.000000 0.478303 0.000000 - 0.000000 0.000000 0.000000 +1.478303 +1.478303 0.000000 0.000168 0.000000 - 0.000000 0.000000 0.000000 0.000169 0.000168 Full cubeful rollout with var.redn. 1296 games, Mersenne Twister dice gen. with seed 1 and quasi-random dice Play: 4ply 4-ply cubeful prune [4ply] keep the first 0 0-ply moves and up to 16 more moves within equity 0.32 Skip pruning for 1-ply moves. keep the first 0 2-ply moves and up to 4 more moves within equity 0.08 Skip pruning for 3-ply moves. Cube: 4-ply cubeful prune [4ply] with an equity between XG's 2/1 and 3/2 plays.
Maybe XG plays the White checkers (closer to) perfectly after 2/1, GNUbg does not as well, but errs identically after both plays, and XG after 3/2 does worse.
But it looks more likely to me that both programs play the checkers accurately but XG gammons evaluations are slightly off, with variance reduction then adding some noise to the base rollout.
Note that GNUbg has some post-processing after its neural networks to detect situations where gammons (or wins, or backgammons) are either certain or impossible while the bare neural net output is essentially never 0% nor 100%. XG may not do this.
You could try to do some rollouts without variance reduction and see what happens. It would need a lot more trials, but even 36^6 of them, for instance, wouldn't take much time.
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