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Rollout, and where this problem came from

Posted By: Timothy Chow
Date: Tuesday, 2 February 2010, at 1:50 a.m.

In Response To: Money-play endgame: Blue to play 3-1 (Timothy Chow)

I'm slightly surprised this problem hasn't gotten more nibbles because I think it's one of the more interesting problems I've posted recently.

The position is a variant of one on page 95 of Backgammon Boot Camp, where it is posed at DMP. Trice writes that the closeout is a Big Blunder because it leaves too many blotting numbers, and that either of the safer plays 6/5 4/1 or 5/4 5/2 is superior, with 5/4 5/2 taking a slight edge. Then he remarks that if it were a money game with Blue holding the cube, then 4/3*/off would be best. He says that 4/3*/1 is "not a particularly mysterious play" though "few would find it over the board."

I thought that there was more to this position than Trice was letting on so I started experimenting with variations. Trice is right about 5/4 5/2 or 6/5 4/1 being best at DMP. But the money-play situation is a little subtle. Trice considers what happens when Blue holds the cube, but I find this to be a somewhat contrived scenario. Technically, Blue might be just a hair too good to redouble, but in practice I think most people (including myself) would cash here, if indeed we somehow got this far without redoubling earlier. The more practical scenario, in my opinion, has White holding the cube, as I posted. Then we get a rather delicate tradeoff between extra games lost and extra gammons won. The closeout wins the most gammons and happens to come out on top in this particular position. The DMP plays 5/4 5/2 and 6/5 4/1 win almost no gammons. The pick-and-pass plays 4/3*/off and 6/3*/2 win an intermediate number of gammons and lose an intermediate number of games. Bring White's outfield checkers closer to home and 4/3*/off overtakes 6/3* 4/3 because it becomes harder to win enough gammons to justify the extra risk. All in all, I found this to be a very rich problem to study.

gnubg86


2X2X2X2X2X2X ' '1X ' ' '

3O3O1X3O2O4O ' ' ' ' '1X

tchow55

Position ID: 27YRAgh3bg8AAA Match ID: QYkMAAAAAAAA

# Ply Move Equity
• 1 R 6/3* 4/3 +0.843
0.8810.1110.000-0.1190.0000.000 +0.874 +0.843
0.0010.0020.000-0.0010.0000.000 0.001 0.001
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 843474456 and quasi-random dice
Play: supremo 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]
2 R 5/4 5/2 +0.816 ( -0.028)
0.9160.0090.000-0.0840.0000.000 +0.842 +0.816
0.0000.0010.000-0.0000.0000.000 0.001 0.001
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 843474456 and quasi-random dice
Play: supremo 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]
3 R 6/5 4/1 +0.813 ( -0.030)
0.9150.0100.000-0.0850.0000.000 +0.840 +0.813
0.0000.0000.000-0.0000.0000.000 0.001 0.001
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 843474456 and quasi-random dice
Play: supremo 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]
4 R 4/3*/off +0.809 ( -0.034)
0.8960.0520.000-0.1040.0000.000 +0.844 +0.809
0.0010.0010.000-0.0010.0000.000 0.001 0.002
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 843474456 and quasi-random dice
Play: supremo 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]
5 R 4/off +0.801 ( -0.042)
0.9090.0120.000-0.0910.0000.000 +0.830 +0.801
0.0010.0010.000-0.0010.0000.000 0.001 0.001
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 843474456 and quasi-random dice
Play: supremo 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]
6 R 6/3*/2 +0.795 ( -0.048)
0.8900.0470.000-0.1100.0000.000 +0.828 +0.795
0.0010.0010.000-0.0010.0000.000 0.001 0.001
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 843474456 and quasi-random dice
Play: supremo 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]
7 R 6/2 +0.781 ( -0.063)
0.8990.0110.000-0.1010.0000.000 +0.809 +0.781
0.0000.0010.000-0.0000.0000.000 0.001 0.001
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 843474456 and quasi-random dice
Play: supremo 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

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