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New XG rollouts statistics shed light on Neil Robins's position

Posted By: Timothy Chow
Date: Monday, 13 April 2015, at 2:14 p.m.


XG's rollout statistics provide some insight into the very interesting position that Neil Robins posted recently.

First, here's a 200,000-trial rollout of the position.





White is Player 2

score: 4
pip: 30
7 point match
pip: 21
score: 1

Blue is Player 1
XGID=-ECBA---------------bbbbb-:1:-1:1:42:1:4:0:7:10
Blue to play 42

1.Rollout14/Off 2/Offeq: +0.018
Player:
Opponent:		52.38% (G:0.00% B:0.00%)
47.62% (G:0.00% B:0.00%)		Conf.: ± 0.000 (+0.018...+0.018) - [100.0%]
Duration: 59.2 seconds
2.Rollout14/2 3/Offeq: +0.017 (-0.001)
Player:
Opponent:		52.46% (G:0.00% B:0.00%)
47.54% (G:0.00% B:0.00%)		Conf.: ± 0.000 (+0.017...+0.017) - [0.0%]
Duration: 1 minute 01 second
1 200000 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller++
Search interval: Gigantic

eXtreme Gammon Version: 2.19.208.pre-release, MET: Kazaross XG2



Next, here are the rollout statistics for the two plays: 

 

4/Off 2/Off Non VR Equity: +0.016 (Cost: +27.32%) 

Cube	Win BG	Win G	Win S	Cash	Pass	Lose S	Lose G	Lose BG	D/T	D/P	Take %	D/T	D/P	Pass %	 

2			97,009		51,039	15,693						36,259	51,039	41.53%	 

4			3,539	2		11,890			20,828	2	99.99%				 

8			3,423			17,405									 

 

 

4/2 3/Off Non VR Equity: +0.016 (Cost: +27.31%) 

Cube	Win BG	Win G	Win S	Cash	Pass	Lose S	Lose G	Lose BG	D/T	D/P	Take %	D/T	D/P	Pass %	 

2			97,226		50,520	15,691						36,563	50,520	41.99%	 

4			3,565	15		11,942			21,041	15	99.93%				 

8			3,357			17,684


There are three possible cube values: 2, 4, and 8. The 4-cube level might seem surprising at first since Blue has an autorecube, but sometimes White bears off all her checkers before Blue can get in the autorecube, and it seems that XG doesn't autorecube if Blue is gin. (I'm not sure if the extremely rare instances where Blue cashes a 4-cube are due to roundoff error or whether there are actually some cases where Blue's cash is not optional.)

The Kazaross XG2 MET gives the following MWC values: 6a Crawford = 11.27%; 4a3a = 42.85%; 2a3a = 59.95%. The non-VR MWC (expressed as a percentage) after 4/off 2/off can therefore be calculated as:

(97009*42.85 + (51039 + 15693)*11.27 + (3539 + 2)*59.95 + 3423*100)/200000 ~ 27.32

Of course, a similar calculation applies to 4/2 3/off:

(97226*42.85 + (50520 + 15691)*11.27 + (3565 + 15)*59.95 + 3357*100)/200000 ~ 27.31

Now comes a key observation. If we compare the two expressions above term by term, then we find that the MWC of 4/2 3/off is better at the 2-cube and 4-cube levels, and the advantage of 4/off 2/off kicks in only at the 8-cube level. In other words, the reason 4/off 2/off squeaks out ahead ATS is that it leads to more takable 8-cubes that Blue then wins.

This is not a complete explanation of the situation, of course, because it's still not totally clear why 4/off 2/off leads to more takable 8-cubes. But the rollout statistics have given us an important insight that tells us what to look for if we want to investigate further. For example, it seems to me that positions like the one below are a little more likely to occur after 4/off 2/off than after 4/2 3/off.





White is Player 2

score: 4
pip: 10
7 point match
pip: 7
score: 1

Blue is Player 1
XGID=-D-A----------------a-a-b-:1:-1:-1:00:1:4:0:7:10
White on roll, cube action?

Analyzed in XG Roller++ No redouble Redouble/Take
Player Winning Chances: 88.08% (G:0.00% B:0.00%) 88.08% (G:0.00% B:0.00%)
Opponent Winning Chances: 11.92% (G:0.00% B:0.00%) 11.92% (G:0.00% B:0.00%)
Cubeless Equities +0.762 +1.261
Cubeful Equities
No redouble:+0.809 (-0.150)
Redouble/Take:+0.959
Redouble/Pass:+1.000 (+0.041)
Best Cube action: Redouble / Take

eXtreme Gammon Version: 2.19.208.pre-release, MET: Kazaross XG2







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