I sent this cube over quite confidently as I didn’t even know whether it was technically a take. XG dinged me. Here are some evals;
0.749/0.696 No Redouble / Take 3-ply (OMG)
0.840/0.811 No Redouble / Take 4-ply (Better but not close)
0.755/0.660 No Redouble / Take XGR+ (OMG)
0.856/0.840 No Redouble / Take XGR++ (Only slightly better but still way off)
It’s well known that XG2 has trouble evaluating these type of containment postions, seriously underestimating their strength as can be seen by the above evaluations.
I took a look how 3-ply plays the next roll and it’s pretty clueless. Any decent human player could play better. It basically abandons the 24 anchor on too many rolls instead of slotting the back of the prime or spreading checkers in to the outfield.
Here’s an example of when NOT to trust a rollout, 3-ply with GIGANTIC search interval.
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| XGID=--a-BBBBB-----A--A---AhcB-:1:1:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 77.92% (G:0.00% B:0.00%) | 78.24% (G:0.00% B:0.00%) |
| Opponent Winning Chances: | 22.08% (G:7.57% B:0.23%) | 21.76% (G:7.31% B:0.14%) |
| Cubeless Equities | +0.480 | +0.981 |
| Cubeful Equities | ||
| No redouble: | +0.913 | ±0.007 (+0.906..+0.919) |
| Redouble/Take: | +0.895 (-0.017) | ±0.009 (+0.886..+0.904) |
| Redouble/Pass: | +1.000 (+0.087) | |
| Best Cube action: No redouble / Take | ||
| Percentage of wrong pass needed to make the double decision right: 14.2% | ||
| Rollout details | ||
| 5184 Games rolled with Variance Reduction. Moves and cube decisions: 3-ply Search interval:GIGANTIC | ||
| Double Decision confidence: | 99.9% | |
| Take Decision confidence: | 100.0% | |
| Duration: 50 minutes 36 seconds | ||
eXtreme Gammon Version: 2.10
4-ply plays significantly better but still makes too many errors.
WITH GIGANTIC SEARCH INTERVAL XGR+ IMO, plays this postion very well in fact pretty close to XGR++. Where they disagreed on the next roll, the equity differences were small.
So on to the rollouts. Which settings to use? Well based on the above nothing less than XGR+. For this type of position a big search interval is required especially as 3-ply is pretty clueless. It’s obvious that the stronger the settings the more the take decision will shift towards passing as this is basically a skill one-sided position.
A Q&D 4-ply rollout indicated that it was a pass but as I’d got quite interested in this position and as none of the respondents felt it could be a big pass I wanted to get close to the ground truth. To do this I had to make sure the search interval covered as many of what I thought were the “best plays” for the first roll at least.
For XGR+ this would have to be gigantic! Here is the rollout as you can see taking is technically a blunder ~0.098 :
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| XGID=--a-BBBBB-----A--A---AhcB-:1:1:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 80.51% (G:0.00% B:0.00%) | 82.17% (G:0.00% B:0.00%) |
| Opponent Winning Chances: | 19.49% (G:6.01% B:0.67%) | 17.83% (G:5.40% B:0.53%) |
| Cubeless Equities | +0.543 | +1.168 |
| Cubeful Equities | ||
| No redouble: | +0.977 (-0.023) | ±0.014 (+0.963..+0.991) |
| Redouble/Take: | +1.098 (+0.098) | ±0.021 (+1.077..+1.119) |
| Redouble/Pass: | +1.000 | |
| Best Cube action: Redouble / Pass | ||
| Rollout details | ||
| 755 Games rolled with Variance Reduction. Moves and cube decisions: XG Roller+ Search interval:GIGANTIC | ||
| Double Decision confidence: | 99.9% | |
| Take Decision confidence: | 100.0% | |
| Duration: 9 hours 34 minutes | ||
eXtreme Gammon Version: 2.10
How much more of a pass would this be using XGR++? I didn’t want to spend a lot of CPU time rolling this out at XGR++ with gigantic search interval but looking only at the first rolls XGR+ with a gigantic search interval appears to play this better than XGR++ with a huge interval. For rolls 51, 41 and 32, XGR++ huge doesn’t slot the back of the prime.
Would these make any difference? What I couldn’t quantify was how much loss in strength from the smaller search interval would be counterbalanced by XGR++ finding some better plays and cube decisions down the line. Here’s the rollout:
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| XGID=--a-BBBBB-----A--A---AhcB-:1:1:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 80.03% (G:0.00% B:0.00%) | 81.72% (G:0.00% B:0.00%) |
| Opponent Winning Chances: | 19.97% (G:6.06% B:0.52%) | 18.28% (G:5.39% B:0.41%) |
| Cubeless Equities | +0.535 | +1.153 |
| Cubeful Equities | ||
| No redouble: | +0.970 (-0.030) | ±0.012 (+0.958..+0.982) |
| Redouble/Take: | +1.063 (+0.063) | ±0.016 (+1.047..+1.079) |
| Redouble/Pass: | +1.000 | |
| Best Cube action: Redouble / Pass | ||
| Rollout details | ||
| 739 Games rolled with Variance Reduction. Moves and cube decisions: XG Roller++ Search interval: Huge | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 1 day 00 hour 28 minutes | ||
eXtreme Gammon Version: 2.10
OK so I’d come this far so I might as well go all the way and roll it out with XGR++ gigantic. Still too much variance but looks like an improvement on huge search interval. Here’s the rollout:
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| XGID=--a-BBBBB-----A--A---AhcB-:1:1:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 79.73% (G:0.00% B:0.00%) | 81.88% (G:0.00% B:0.00%) |
| Opponent Winning Chances: | 20.27% (G:6.14% B:0.54%) | 18.12% (G:5.32% B:0.46%) |
| Cubeless Equities | +0.528 | +1.160 |
| Cubeful Equities | ||
| No redouble: | +0.955 (-0.045) | ±0.012 (+0.943..+0.968) |
| Redouble/Take: | +1.081 (+0.081) | ±0.018 (+1.063..+1.099) |
| Redouble/Pass: | +1.000 | |
| Best Cube action: Redouble / Pass | ||
| Rollout details | ||
| 747 Games rolled with Variance Reduction. Moves and cube decisions: XG Roller++ Search interval:GIGANTIC | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 1 day 12 hours 14 minutes | ||
eXtreme Gammon Version: 2.10
Having looked at all the checker play / search interval scenarios unfortunately there is no way to eliminate XG2’s cube misevaluations which could obviously effect the rollout results. The no double equity looks too high based on many bad takes on the next roll, My rough calculations allowing for those would indicated the no double equity closer to 0.93. Also is the XGR+ gigantic result being skewed by poorer cube evaluations down the line?
How close to perfect does XG2 XGR++ play?
Who knows but IMO there’s still some improvement possible. Have a look at this after blue doubles and has 43 to play. XGR++ likes 24/21 17/13. Breaking from the 24 point looks wrong. It also breaks on 42 which also might be wrong.
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| XGID=--a-BBBBB-----A--A---AhcB-:1:-1:1:43:0:0:3:0:10 | |||||
| Blue to play 43 | |||||
| 1. | Rollout1 | 17/13 14/11 | eq: +0.524 | |||
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| 2. | Rollout1 | 21/18 17/13 | eq: +0.503 (-0.021) | |||
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| 3. | Rollout1 | 17/10 | eq: +0.498 (-0.026) | |||
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| 4. | Rollout1 | 24/21 17/13 | eq: +0.480 (-0.044) | |||
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| 1 190 Games rolled with Variance Reduction. Moves and cube decisions: 4-ply Search interval: Huge | ||||||
eXtreme Gammon Version: 2.10
So in conclusion we can be 100% sure it’s technically a pass and quite confident it’s a big pass. I’ll extend the XGR++ gigantic rollout and report back.
An interesting reference postion for the bots and also something for humans to aim for when trying to perfect their containment play.
And finally, it’s positions like this that make me wish the search intervals were configurable as in GNUBG.
Comments and scrutiny of my work welcome :-)
Michael