RE: [Bug-gnubg] Odd rollout results of classic reference position

[Ian Shaw]

> From: Ned Cross
> 
> I think this would be a take if all of O's checkers were on 
> the ace and 2
> pts, and even perhaps with 2 on the 3 pt.  I think it's the 
> distribution
> here that makes it a pass for O.  Walter Trice had a good article on
> 1-checker closeouts in Gammon Village about a year or so ago.
> http://www.gammonvillage.com/backgammon/news/article_display.cfm?resourceid=1182


Thanks for the reference, Ned. I couldn't remember O's distribution offhand - 3 
chequers on each of the 1, 2 & 3 points. The same situation applies. GnuBg 
thinks it is a Take on evaluation, but the rollout has it as a pass. The No 
double equity is less than 1.000 this time, even though O still makes bad 
passes if X holds the cube.

Cube analysis
4-ply cubeless equity  +0.552
  0.776 0.000 0.000 - 0.224 0.000 0.000
Cubeful equities:
1. Double, take         +0.959
2. Double, pass         +1.000  ( +0.041)
3. No double            +0.934  ( -0.025)
Proper cube action: Redouble, take

Cube analysis
Rollout cubeless equity  +0.574

Cubeful equities:
1. Double, pass         +1.000
2. Double, take         +1.035  ( +0.035)
3. No double            +0.998  ( -0.002)
Proper cube action: Redouble, pass
Rollout details:
Player Trailer owns 2-cube:
  0.787 0.000 0.000 - 0.213 0.000 0.000 CL  +0.574 CF  +0.998
 [0.000 0.000 0.000 - 0.000 0.000 0.000 CL   0.001 CF  +0.002]
Player Leader owns 4-cube:
  0.789 0.000 0.000 - 0.211 0.000 0.000 CL  +1.157 CF  +1.035
 [0.000 0.000 0.000 - 0.000 0.000 0.000 CL   0.001 CF  +0.002]
Full cubeful rollout with var.redn.
2592 games, seed 1206048640 using quasi-random dice and Mersenne Twister
Play and cube: 2-ply cubeful 100% speed [world class]

> 
> I agree that it seems like X should be able to cash more 
> games later by retaining cube access.  I've seen this show up with GNUBg in 
> other positions
> as well.

I'm concerned that there's a real problem here. Has anyone got a convincing 
explanation as to how one can win more games by relinquishing the cube?

--Ian