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Very subtle bearoff play: Analysis

Posted By: Timothy Chow
Date: Thursday, 3 October 2019, at 11:58 p.m.

In Response To: Very subtle bearoff play (Timothy Chow)

First let's take a look at the rollouts. We find that 6/off 2/off is the clear winner at DMP and for money, but 6/4 6/off comes out a hair ahead ATS.





White is Player 2

score: 4
pip: 27
7 point match
pip: 48
score: 0

Blue is Player 1
XGID=aBBBBBC-----------------b-:1:-1:1:22:0:4:0:7:10
Blue to play 22

1.Rollout16/4 6/Offeq: -0.707
Player:
Opponent:		17.41% (G:0.00% B:0.00%)
82.59% (G:0.00% B:0.00%)		Conf.: ± 0.002 (-0.709...-0.705) - [100.0%]
Duration: 1 minute 45 seconds
2.Rollout16/Off 2/Offeq: -0.712 (-0.005)
Player:
Opponent:		18.45% (G:0.00% B:0.00%)
81.55% (G:0.00% B:0.00%)		Conf.: ± 0.002 (-0.714...-0.710) - [0.0%]
Duration: 4 minutes 41 seconds
3.Rollout24/Off(2)eq: -0.740 (-0.033)
Player:
Opponent:		15.81% (G:0.00% B:0.00%)
84.19% (G:0.00% B:0.00%)		Conf.: ± 0.003 (-0.744...-0.737) - [0.0%]
Duration: 1 minute 04 seconds
4.Rollout26/Off 5/3eq: -0.752 (-0.045)
Player:
Opponent:		15.31% (G:0.00% B:0.00%)
84.69% (G:0.00% B:0.00%)		Conf.: ± 0.003 (-0.756...-0.749) - [0.0%]
Duration: 1 minute 01 second
1 5184 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller+
Search interval: Large

2 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller+
Search interval: Large

eXtreme Gammon Version: 2.19.207.pre-release, MET: Kazaross XG2
White is Player 2

score: 0
pip: 27
Unlimited Game
pip: 48
score: 0

Blue is Player 1
XGID=aBBBBBC-----------------b-:1:1:1:22:0:0:0:0:10
Blue to play 22

1.Rollout16/Off 2/Offeq: -0.571
Player:
Opponent:		18.61% (G:0.00% B:0.00%)
81.39% (G:0.00% B:0.00%)		Conf.: ± 0.005 (-0.576...-0.566) - [100.0%]
Duration: 4 minutes 22 seconds
2.Rollout16/4 6/Offeq: -0.593 (-0.022)
Player:
Opponent:		17.54% (G:0.00% B:0.00%)
82.46% (G:0.00% B:0.00%)		Conf.: ± 0.004 (-0.597...-0.588) - [0.0%]
Duration: 38.8 seconds
3.Rollout16/Off 5/3eq: -0.636 (-0.065)
Player:
Opponent:		15.55% (G:0.00% B:0.00%)
84.45% (G:0.00% B:0.00%)		Conf.: ± 0.004 (-0.640...-0.632) - [0.0%]
Duration: 1 minute 12 seconds
4.Rollout14/Off(2)eq: -0.636 (-0.065)
Player:
Opponent:		15.86% (G:0.00% B:0.00%)
84.14% (G:0.00% B:0.00%)		Conf.: ± 0.005 (-0.641...-0.632) - [0.0%]
Duration: 55.1 seconds
1 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller+
Search interval: Large

eXtreme Gammon Version: 2.19.207.pre-release

IMO Sam gave a good explanation of why 6/off 2/off is best at DMP. It has the usual characteristics one looks for in this type of position—bearing off fast, keeping a good board.

But what about ATS? Since gammons and backgammons are obviously irrelevant, it can only be the cube action that nudges 6/4 6/off into first place.

This is the sort of thing for which the "Rollout statistics" available in the pre-release version of XG can provide some insight. In particular, the statistics tell us how often Blue wins the game without giving White the opportunity to redouble. Let's call these "smooth-sailing" wins. It turns out that ATS, 6/4 6/off gives Blue significantly more smooth-sailing wins than 6/off 2/off does, at the cost of giving White more RD/P opportunities. Given the various match equities at stake, this tradeoff turns out to be worth it.

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