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World's incorrect 14-away/6-away pass: Analysis

Posted By: Daniel Murphy
Date: Wednesday, 14 April 2010, at 1:08 a.m.

In Response To: World's incorrect 14-away/6-away pass: Analysis (Matt Cohn-Geier)

I wonder if there isn't a not so complex lesson from the rollouts, which is that a position something like this should in one's reference book. For me, at least, it was a surprise to learn that Team World wins nearly 25% of the time from the 4-cube position at this score. If you could guesstimate that, along with a live cube take point of ~15% and dead cube take point of ~22%, then the take decision would have been easier, no?

I can also add more data:

(1) For money, it's "only" a ~0.100 pass.

(2) For money, Gnubg 0-ply checker play gets nearly the same result for Blue as 2-ply. Comparing match score to money game (0-ply):

White Match Money
Wins (total) 24.5% 21.0%
Wins Gammon on 8-cube 00.3% 00.1%
Wins Gammon on 4-cube 00.0% 00.4%
Wins Single on 16-cube 00.0% 00.6%
Wins Single on 8-cube 05.1% 05.0%
Wins Single on 4-cube 19.4% 14.9%
Loses Single on 4-cube66.1% 73.3%
Loses Single on 8-cube05.6% 01.4%
Loses Single on 16-cube 00.0% 00.6%
Loses Gammon on 4-cube03.2% 03.7%
Loses Gammon on 8-cube00.3% 00.0%
Loses (total) 75.5% 79.0%
Recubes to 8 30.4% 22.3%
Redouble to 8/take 11.3% 14.6%
Redouble to 8/pass 19.1% 07.7%
Redouble to 16/take00.0% 01.2%
Redouble to 16/pass00.0% 01.4%
Redouble to 16/pass00.0% 00.6%

So ... ATS White gets in a redouble 30% of the time, instead of 22%, and 37% of those redoubles are taken, instead of 65% (not too surprising, I suppose, since White's market window on an 8 cube is ~25%-~62% ATS, instead of 50%-~78%).

For example suppose we have a redouble after rolling an ace if Denmark does nothing special

Something like this?

The score (after 0 games) is: World 1, Denmark 7 (match to 15 points)

Move number 57: World on roll, cube decision?

World58


4X5X '3X2X ' ' ' ' ' ' '

2O '1X4O3O2O2O2O ' ' ' '

Denmark75

Position ID: 4902AADvcwMACA Match ID: AgHgARAAOAAA

• World doubles

Cube decision
Rollout cubeless equity -0.184(Money: -0.204)
Cubeful equities:
1.Double, take +0.100
2.Double, pass +1.000 +0.900
3.No double +0.037 -0.063
Proper cube action:Redouble, take
Rollout details
WinW gW bg LoseL gL bgCubelessCubeful
Player World owns 4-cube0.4080.0070.000-0.5920.0270.000 -0.184 +0.037
Standard error0.0020.0010.000-0.0020.0040.000 0.004 0.006
Player Denmark owns 8-cube0.4100.0050.000-0.5900.0300.000 +0.100 +0.100
Standard error0.0030.0010.000-0.0030.0130.000 0.010 0.010
Full cubeful rollout with var.redn.
145 games, Mersenne Twister dice gen. with seed 854265860 and quasi-random dice
Play: 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 20 more moves within equity 0.44
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

Above, another lesson for me: that Team World wins ~41% from here. Supposing that ~27% is from an immediate six, I wouldn't have thought White could pick up another ~14% from other sequences.

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