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Rollout: More subtle than many people think

Posted By: Timothy Chow
Date: Friday, 6 July 2012, at 9:48 p.m.

In Response To: A fairly common type of decision that I rarely see discussed (Timothy Chow)

This post received a lot of views but few comments.

As I said, I don't have a full rollout of the original position, and it doesn't seem necessary, since the truncated rollout isn't close.

However, before you assume that the large equity difference allows one to generalize quickly, take a look at the variant below, which I've done a full rollout for.

If Blue gets a second checker sent back, then his prospects deteriorate drastically. Hitting on the 1pt can be a difficult tradeoff to evaluate.

I'd be interested in seeing more examples of this kind of decision. Thanks to David Levy for providing another one already!





White is Player 1

score: 0
pip: 107
Money session
pip: 60
score: 0

Blue is Player 2
XGID=-aICB----a-a-----abbb-abbA:2:1:1:31:0:0:0:0:10
Blue to play 31

1.Rollout1Bar/22* 2/1* eq: +0.556
Player:
Opponent:
56.86% (G:35.10% B:0.96%)
43.14% (G:9.90% B:0.29%)
Conf: ± 0.012 (+0.544...+0.568)
Duration: 1 minute 16 seconds
2.Rollout1Bar/22* 22/21eq: +0.379 (-0.177)
Player:
Opponent:
52.68% (G:25.65% B:1.09%)
47.32% (G:6.37% B:0.19%)
Conf: ± 0.014 (+0.365...+0.393)
Duration: 2 minutes 01 second
3.Rollout1Bar/22* 3/2eq: +0.200 (-0.356)
Player:
Opponent:
47.46% (G:20.46% B:0.82%)
52.54% (G:10.32% B:0.40%)
Conf: ± 0.023 (+0.177...+0.223)
Duration: 1 minute 49 seconds
1 Truncated at 7 moves using 3 ply.
648 Games rolled with Variance Reduction.
Dice Seed: 2
First 2 moves and cube decisions: 3 ply
Remaining moves: 2 ply, cube decisions: 3 ply

eXtreme Gammon Version: 1.21


Variant:





White is Player 1

score: 0
pip: 109
Money session
pip: 60
score: 0

Blue is Player 2
XGID=-aICB----a-a---a--bbb-abbA:2:1:1:31:0:0:0:0:10
Blue to play 31

1.Rollout1Bar/22* 22/21eq: +0.354
Player:
Opponent:
51.97% (G:27.13% B:1.16%)
48.03% (G:6.51% B:0.21%)
Conf: ± 0.009 (+0.345...+0.363)
Duration: 2 hours 43 minutes
2.Rollout1Bar/22* 2/1* eq: +0.343 (-0.011)
Player:
Opponent:
52.77% (G:29.78% B:0.53%)
47.23% (G:11.73% B:0.45%)
Conf: ± 0.011 (+0.332...+0.354)
Duration: 2 hours 52 minutes
1 2592 Games rolled with Variance Reduction.
Dice Seed: 2
Moves and cube decisions: 3 ply

eXtreme Gammon Version: 1.21

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