           
 
         
 | | White is Player 2
score: 0
pip: 82 | Unlimited Game
Jacoby Beaver | pip: 119
score: 0
Blue is Player 1 |
|
| XGID=--BBABB---AAdB----B-acbbc-:1:-1:1:61:0:0:3:0:10 |
| Blue to play 61 |
| 1. | Rollout1 | 13/7 5/4 | eq: -0.361 |
| Player:
Opponent: | 39.80% (G:6.50% B:0.18%)
60.20% (G:3.42% B:0.06%) | Conf.: ± 0.002 (-0.364...-0.359) - [100.0%]
Duration: 2 hours 44 minutes |
|
| 2. | Rollout1 | 13/7 11/10 | eq: -0.370 (-0.009) |
| Player:
Opponent: | 39.36% (G:6.51% B:0.19%)
60.64% (G:3.52% B:0.05%) | Conf.: ± 0.003 (-0.373...-0.367) - [0.0%]
Duration: 2 hours 37 minutes |
|
| 3. | Rollout1 | 13/7 10/9 | eq: -0.376 (-0.014) |
| Player:
Opponent: | 39.52% (G:7.07% B:0.24%)
60.48% (G:4.48% B:0.08%) | Conf.: ± 0.003 (-0.378...-0.373) - [0.0%]
Duration: 2 hours 06 minutes |
|
| 4. | Rollout1 | 13/6 | eq: -0.377 (-0.016) |
| Player:
Opponent: | 39.07% (G:6.47% B:0.19%)
60.93% (G:3.43% B:0.05%) | Conf.: ± 0.002 (-0.380...-0.375) - [0.0%]
Duration: 2 hours 16 minutes |
|
| 5. | Rollout1 | 11/4 | eq: -0.379 (-0.018) |
| Player:
Opponent: | 38.79% (G:5.68% B:0.17%)
61.21% (G:2.09% B:0.01%) | Conf.: ± 0.002 (-0.381...-0.377) - [0.0%]
Duration: 1 hour 02 minutes |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 57611092
Moves and cube decisions: 4-ply
Search interval: Large
|
While all respondents discovered the theme of forcing 61 to leave a double shot, none backed the breaking/blotting the midpoint with a whole heart. Mike assumed it was correct only because of QF, while Havard, Tim and Robert (the latter two of whom ironically being the only ones that stated—correctly—how the ace should be played, to activate a third builder) decided not to support breaking the midpoint even with QF. David Renne voted for breaking the mid, though it's not clear he would have had he realized that White's 61 is Blue's sole gainer. The imaginary gainer of her 51 actually costs Blue equity due to his non-covered fifth inside point.
What the 13/7 5/4 and 11/4 moves have in common is that the ace is played 5/4. The choice of playing 13/7 (instead of covering the inside point with 11/5) is almost entirely about the tactical tradeoff between (a) White's much worse 61, and (b) her less costly 51 and better 11.
According to XGR++ evaluation, if Blue plays 13/7 instead of 11/5, White's equity on 61 drops from +.348 to –.117, her equity on 51 turns positive from –.002 to +.077, and her equity on 11 (played 13/12*(3) 5/4) rises from +.273 to +.392. Dividing each scenario by its appropriate 1/18 or 1/36, White's net loss, which is Blue's net gain, is .018. This happens to be the exact margin in the 4-ply rollout, though for a proper comparison it is better to reconcile to the XGR++ evaluation of .023.
There are other factors. For example, after 13/7 (5/4), Blue will fail to cover his 5pt with 43, and if he rolls small he might prefer to have been able to keep two checkers on the midpoint another roll. However, such effects are tiny. For example, as White should not hit with 41 31 or 21, her gain (after dividing by 18) on those three rolls combined (due to Blue's slight positional sacrifice) is only half of .001. Still, if we hypothecize that 41 31 21 is a light sample and that the other 21 numbers (not counting 55 44 33 22, which make Blue's 61 play irrelevant) favor the solid 11/5 on average by just a fifth of .001 each, that gets us (from .018) up to the XGR++ evaluation margin of .023.
Have a look at the first two variants diagrammed below (which are side by side if you widen your window or zoom out with Ctrl-). White's midpoint is reduced to three checkers, and to two checkers, respectively. By XGR++ evaluation, the .023 advantage of breaking the midpoint deteriorate into (respective) disadvantages of .024 and .210. It is a matter of timing; Blue has better prospects to obtain a clean double shot, a scenario that playing 13/7 belies. By contrast, in the original position, Blue is unlikely to keep the midpoint long enough to get that double shot, while leaving a single checker on the midpoint may gain little or nothing. (White might not have a blot in her board, or hitting might help her off the hook.)
Going the other way, the final two variants (also side by side) show a fifth and sixth checker on White's midpoint. This time (again by XGR++ eval), the .023 advantage of breaking the midpoint is (respectively) reduced to .010 and reversed to –.025. Blue is less desperate to resort to the immediate tactic of 13/7 because the race is closer, which also means that White can gain equity by hitting with more aces—add 41 in the five-on-mid position and 51 41 31 21 in the six-on-mid position (and she loses less when she hits with 61).
Nack
| 1. | XG Roller++ | 11/4 | eq: -0.285 |
| Player:
Opponent: | 42.54% (G:5.61% B:0.17%)
57.46% (G:2.93% B:0.01%) | |
|
| 2. | XG Roller++ | 13/7 5/4 | eq: -0.309 (-0.024) |
| Player:
Opponent: | 43.47% (G:7.14% B:0.27%)
56.53% (G:7.82% B:0.10%) | |
|
| 1. | XG Roller++ | 11/4 | eq: -0.061 |
| Player:
Opponent: | 51.22% (G:7.42% B:0.27%)
48.78% (G:3.58% B:0.02%) | |
|
| 2. | XG Roller++ | 11/5 10/9 | eq: -0.254 (-0.192) |
| Player:
Opponent: | 45.17% (G:5.22% B:0.18%)
54.83% (G:7.00% B:0.05%) | |
|
| 3. | XG Roller++ | 13/7 5/4 | eq: -0.272 (-0.210) |
| Player:
Opponent: | 45.64% (G:6.56% B:0.28%)
54.36% (G:13.13% B:0.17%) | |
|
| 1. | XG Roller++ | 13/7 5/4 | eq: -0.227 |
| Player:
Opponent: | 45.25% (G:10.49% B:0.25%)
54.75% (G:6.20% B:0.19%) | |
|
| 2. | XG Roller++ | 11/4 | eq: -0.238 (-0.010) |
| Player:
Opponent: | 44.21% (G:7.75% B:0.10%)
55.79% (G:1.86% B:0.01%) | |
|
| 1. | XG Roller++ | 11/4 | eq: -0.102 |
| Player:
Opponent: | 49.92% (G:8.69% B:0.09%)
50.08% (G:1.53% B:0.01%) | |
|
| 2. | XG Roller++ | 13/7 5/4 | eq: -0.127 (-0.025) |
| Player:
Opponent: | 48.92% (G:12.22% B:0.23%)
51.08% (G:5.45% B:0.21%) | |
|
