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| XGID=baDCCCB---------a--bbcb-b-:0:0:1:53:6:0:1:7:10 | |||||
Original position | |||||
| 1. | Rollout1 | 6/1* 4/1 | eq: +0.762 | |||
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| 2. | Rollout1 | 5/Off 4/1* | eq: +0.673 (-0.089) | |||
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| 3. | Rollout1 | 6/3 6/1* | eq: +0.638 (-0.123) | |||
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| 4. | Rollout1 | 5/Off 3/Off | eq: +0.629 (-0.132) | |||
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| 1 1296 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller | ||||||
David's rollout of his original position appears above.
To make the "Bagai" play (P = Point) work, after-life is a vital factor, of course. To take the extreme case, if White's board is closed (i.e., her 9pt and 6pt checkers are on her 2pt), then H (Hit, 5/off 4/1*) is better than 0 (5/off 3/off) by .075, C (Clear, 6/3 6/1*) is a double-whopper, and P (Point, 6/1* 3/1*) swings from best-by-far into a triple-whopper. Likewise if White has a six-point prime anywhere.
What if -- compared to the original position above -- White's 1pt is open instead of her 2pt? In that case, P is still best, but 0 jumps from 4th place to 2nd place, it's error size cut in half (to .064). If, in addition, you advance White's 9pt and 4pt checkers to the 3pt and 2pt (i.e., best five points with spares on 2pt and 3pt), 0's error size reduces to .028.
If White has only ONE checker on the bar and a closed board, it is very wrong for Blue to play anything other than 0 (Off), even if White's spare is advanced all the way to her 1pt (and even for money, regardless of cube position). H (the loose hit) may seem tempting, but it is slimed too often when White hits with an ace, even when she subsequently cracks with ace-non6.
However, if White has ONE checker on the bar and her original formation (see diagram above), then the best play depends on where else on the board we put that checker (i.e., other than the bar). Here is the representative AtS cusp:
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| XGID=aaDCCCB--a------a--bbcb-b-:0:0:1:53:6:0:1:7:10 | |||||
AtS Cusp (Compared to original, White's roof-checker is moved to her 16pt) | |||||
| 1. | Rollout1 | 5/Off 3/Off | eq: +0.662 | |||
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| 2. | Rollout1 | 6/1* 4/1 | eq: +0.662 (0.000) | |||
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| 3. | Rollout2 | 5/Off 4/1* | eq: +0.595 (-0.067) | |||
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| 4. | Rollout2 | 6/3 6/1* | eq: +0.557 (-0.105) | |||
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| 1 5184 Games rolled with Variance Reduction. Dice Seed: 60048472 Moves: 3-ply, cube decisions: XG Roller 2 1296 Games rolled with Variance Reduction. Dice Seed: 60048472 Moves: 3-ply, cube decisions: XG Roller | ||||||
If White's "floating checker" is on her 18pt, P (Point, Bagai) is best by .006. If it is on her 17pt, then P is best by .003 (rollouts not shown). If moved one more pip to her 16pt, we have the position above where 0 and P are in a dead heat.
For every pip we continue to move that checker forward from the 6pt, 0's edge over P becomes larger and larger (and on a slightly increasing curve). For example, by the time it gets to the 6pt, 0's edge over P grows to .048 (rollout not shown).
For Money (because Blue is paid for gammons and backgammons), we need to advance White's floating checker from the 16pt to the 10pt (actually the 10 1/2 pt!) to reach the cusp:
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| XGID=aaDCCCB--------aa--bbcb-b-:1:-1:1:53:0:0:3:0:10 | |||||
Money Cusp (Compared to original, White's roof-checker is moved to her 10pt) | |||||
| 1. | Rollout1 | 5/Off 3/Off | eq: +1.008 | |||
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| 2. | Rollout1 | 6/1* 4/1 | eq: +1.004 (-0.004) | |||
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| 3. | Rollout2 | 5/Off 4/1* | eq: +0.955 (-0.053) | |||
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| 4. | Rollout2 | 6/3 6/1* | eq: +0.763 (-0.245) | |||
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| 1 5184 Games rolled with Variance Reduction. Dice Seed: 60048472 Moves: 3-ply, cube decisions: XG Roller 2 1296 Games rolled with Variance Reduction. Dice Seed: 60048472 Moves: 3-ply, cube decisions: XG Roller | ||||||
In short, P (the Bagai, when keeping a five-point board) is a "no-brainer" when putting a third checker in the air (except against a six-prime). It's often right when putting only a second checker in the air, but it is sensitive to the strength of White's board/prime and her timing (and to Blue's exact distribution).
Nack