Ok, well not CHRIS Bray analysis. More "bray" as in the sound a donkey makes. But the original post yielded such a lack of interest I felt I had to spice it up a bit. Unfortunately I suspect it will be like trying to spice up a Denny's Grand Slam breakfast by adding tabasco sauce and cayenne pepper, with the end result somehow being even more unpalatable than the original.
And, Stick, there is definitely math involved! It may not be math like Bob Koca does but come on, nobody really understands that shit anyway, if a man's being honest. "Math" may be the wrong word actually. More like "guessing". Whatever. Tomato, tomato.
I probably should have rolled the original position out before racing to post it, as the rollout showed it was a clear blunder to take (as I did), but what intrigued me (besides just the sheer fascination of the position itself, God dammit!) was that at ++ the numbers didn't make sense to me. Allow me to demonstrate:
Original position rolled out:
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| XGID=-BDDB-aa---------aacbbd--A:1:-1:-1:00:0:0:0:5:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 74.70% (G:0.00% B:0.00%) | 76.57% (G:0.00% B:0.00%) |
| Opponent Winning Chances: | 25.30% (G:3.11% B:0.04%) | 23.43% (G:4.74% B:0.16%) |
| Cubeless Equities | +0.453 | +1.177 |
| Cubeful Equities | ||
| No redouble: | +0.872 (-0.128) | ±0.003 (+0.870..+0.875) |
| Redouble/Take: | +1.085 (+0.085) | ±0.006 (+1.080..+1.091) |
| Redouble/Pass: | +1.000 | |
| Best Cube action: Redouble / Pass | ||
| Rollout details | ||
| 2592 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller+ Search interval: Huge | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 1 hour 27 minutes | ||
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
Here is the original position at ++ analysis:
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| XGID=-BDDB-aa---------aacbbd--A:1:-1:-1:00:0:0:0:5:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in XG Roller++ | No redouble | Redouble/Take |
| Player Winning Chances: | 74.87% (G:0.00% B:0.00%) | 75.78% (G:0.00% B:0.00%) |
| Opponent Winning Chances: | 25.13% (G:3.12% B:0.04%) | 24.22% (G:4.35% B:0.06%) |
| Cubeless Equities | +0.456 | +1.145 |
| Cubeful Equities | ||
| No redouble: | +0.865 (-0.135) | |
| Redouble/Take: | +1.034 (+0.034) | |
| Redouble/Pass: | +1.000 | |
| Best Cube action: Redouble / Pass | ||
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
As Phil said, in order to solve this one needs to know the chances of winning with 2 checkers off against a perfectly closed board so that you can then use "math" to determine what the chances are here. Having learned those numbers from Phil, and then forgetting them and relearning them from Stick, and then forgetting them, and then relearning them from Stick again I knew that we'd have about a 6% chance. So, what are our chances here? We're favored to enter (by a small amount) and he's not favored to make the 2-point (by a small amount), but he MIGHT be favored to make the 1 OR the 2-point (which is where Koca math could come in handy to determine but c'est la vie) so I "calculated" that I could pull this off about 25% of the time. Maybe. I knew, again from the two previously mentioned esteemed gentlemen, that the take point for a recube at 5a 5a was 25% so this would be close. What decided it for me was the small but real chance of getting a gammon. I knew that the gammon value had to be pretty small at this score but if it raised our chances by even 1% (which is about what it did) that could swing it into my favor. What threw me at the ++ analysis was that it says we win 24.22% of the time and win 4.35% gammons. With gammons being worth about 0.25 we were clearly better than 25% so why was it a small pass? Phil answered that question in his post by explaining that the real takepoint is a little higher than 25% (Stick uses 26%) so the original point of this post was sort of lost. Obviously, as Fatboy (basically) pointed out, it's a huge take at an initial double (take point here being lower than money and GV being higher):
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| XGID=-BDDB-aa---------aacbbd--A:0:0:-1:00:0:0:0:5:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in XG Roller++ | No double | Double/Take |
| Player Winning Chances: | 75.68% (G:0.00% B:0.00%) | 75.71% (G:0.00% B:0.00%) |
| Opponent Winning Chances: | 24.32% (G:3.99% B:0.06%) | 24.29% (G:3.63% B:0.05%) |
| Cubeless Equities | +0.476 | +0.892 |
| Cubeful Equities | ||
| No double: | +0.767 | |
| Double/Take: | +0.745 (-0.022) | |
| Double/Pass: | +1.000 (+0.233) | |
| Best Cube action: No double / Take | ||
| Percentage of wrong pass needed to make the double decision right: 7.9% | ||
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
For what it's worth, one more checker off makes it a big take:
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| XGID=-BCDB-aa---------aacbbd--A:1:-1:-1:00:0:0:0:5:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 72.55% (G:0.00% B:0.00%) | 73.26% (G:0.00% B:0.00%) |
| Opponent Winning Chances: | 27.45% (G:5.18% B:0.14%) | 26.74% (G:5.67% B:0.22%) |
| Cubeless Equities | +0.381 | +1.014 |
| Cubeful Equities | ||
| No redouble: | +0.844 (-0.067) | ±0.006 (+0.838..+0.850) |
| Redouble/Take: | +0.911 | ±0.009 (+0.902..+0.919) |
| Redouble/Pass: | +1.000 (+0.089) | |
| Best Cube action: Redouble / Take | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller+ Search interval: Huge | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 48 minutes 38 seconds | ||
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
Now sometimes these positions are all very interesting in a sort of how-many-angels-can-dance-on-a-head-of-a-pin sort of way (42), but how well do they really apply as we go out into the world of backgammon to do battle? Well, it just so happens that the following position came up for me this morning. For those of you who haven't taken lessons or even bought Phil's video on doubling (and seriously, come on, you really should), our take point here at 7a 6a with a recube is about 21% and our GV is about 0.5. (Note: If Stick has different numbers go with them.) You now have all kinds of useful reference positions to answer the question, should I have taken this cube? Obviously, things are a little different, but I'd say it's in the same species as the original so, knowing what we know now, do a little math and decide what you'd do OTB:
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| XGID=-DbG-------aaa-----cbbba-A:1:-1:-1:00:0:1:0:7:10 | |||||
| Blue on roll, cube action? | |||||
eXtreme Gammon Version: 2.10
Ok. There's no happy ending. That's life. So sue me.