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On autopilot, I fell right into the trap. Yeah, I went for safety, and not too bad a position, by picking up the 15pt. That play is only 0.02 behind, but it is the fifth-best option. With two blots in White’s inner board, Blue can afford to take some chances in order to consolidate his position. In many variations, he will add a fifth point to his prime on the next roll, but he needs to get more utility from his builders than the safe R = Run (15/14 15/13) offers. When he rolls an ace, White can make his 3pt, cleaning up both of his blots. That means White’s cover numbers are 1, 2, 3 and 4. Almost anywhere Blue chooses to leave a blot, there is going to be some duplication. As well, Blue is free to drop a blot onto his 10pt. When White hits there, Blue gets a double or triple direct shot from the bar. Slotting the 4pt is a possibility for Blue, but it leaves only 1 direct cover, and doesn’t position the rear checkers very well. Ideally, Blue should hope to make the 9pt or 10pt next turn. When he plays his spare on the 14pt up to the midpoint, as he likely would after slotting, he is not well positioned to do that. e = each (14/13 6/4) is the fourth-best play. The safe Z = Reverse split (14/11) is third best. It creates three builders for the 9pt, and three more for the 10pt. Not a bad play at all. The top two plays both create four builders for the 9pt and 10pt. In fact, D = Down (13/10) slots the 10pt, so most combinations of 6-5-4-1 will make the 9pt (or the 4pt), and 3s can be used to cover the 10pt. This play is only 0.01 back. I am not sure why N = Near (13/11 6/5) does slightly better. After playing N, Blue has combinations of 1 and 2 to make the 4pt, combinations of 6-5-4-2 to make the 9pt, and combinations of 5-4-3-1 to make the 10pt. Is there a bad throw anywhere? Possibly, but I did not count. In case you have not already seen them, Casper and Henrik both give lengthy explanations that are worth a look. Thanks to all who replied. The 31k rollout follows. Mike | ||||||||||||
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| XGID=--c--BDBB---cBAB-b-e-aa---:1:-1:1:12:0:0:3:0:10 | |||||
| Blue to play 12 | |||||
| 1. | Rollout1 | 13/11 6/5 | eq: +0.7005 | |||
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| 2. | Rollout1 | 13/10 | eq: +0.6882 (-0.0123) | |||
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| 3. | Rollout1 | 14/11 | eq: +0.6868 (-0.0137) | |||
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| 4. | Rollout1 | 14/13 6/4 | eq: +0.6819 (-0.0186) | |||
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| 5. | Rollout1 | 15/14 15/13 | eq: +0.6772 (-0.0233) | |||
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| 6. | Rollout1 | 15/13 6/5 | eq: +0.6724 (-0.0281) | |||
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| 1 31104 Games rolled with Variance Reduction. Dice Seed: 62861487 Moves: 3-ply, cube decisions: XG Roller | ||||||
Rollout by Taper_Mike |
eXtreme Gammon Version: 2.03