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| Minimizing shots, 5/1 3/1, leaves only 11 shots, but an awkward distribution. Even when he is missed, Blue will leave a single shot next turn when he rolls 22 54 64 65, and a double shot when he rolls 41 51 61 32 43 53 63.
The alternative is to play two checkers from the 5pt, 5/3 5/1, leaving 20 shots. Only 22 and 33 force exposure next time. Over the board, I concluded that leaving two blots now, and only 20 shots, would just about guarantee a victory when I was missed. The alternative seemed likely to blot again, even when my opponent missed his first shots. So, on a play where a monkey would have a 50/50 chance to be right, I misplayed! Inspired by John O’Hagan, I have done some counting now. For simplicity, I assumed that White could hold his rear guard. Imagine, for instance, that White’s spare on his 6pt were moved back to his 19pt. In the actual position of this problem, of course, White’s timing difficulties favor safer play. Unfortunately, I don’t feel that I have the skill to do this sort of counting at the table in a clocked match, so I’ll have to go by the seat of my pants when a similar position arises in future. When I do hone my counting skills, however, John’s method of approximation is clearly the way to go. |
| Description | Blue plays 5/1, 3/1 | Blue plays 5/3, 5/1 |
|---|---|---|
| White hits immediately. | 11/36 (any 1) | 20/36 (any 1 or 3) |
| White misses, but Blue leaves a single shot at a single blot next turn. | 7/36 (22 54 64 65) | 1/36 (22) |
| White misses, but Blue leaves a double shot at a single blot next turn. | 6/36 (43 53 63) | 1/36 (33) |
| White misses, but Blue leaves a double shot at two blots next turn. | 8/36 (41 51 61 32) | 0/36 |
| When Blue leaves a single shot at one blot, White’s chance to hit next turn. | 11/36 (any 1) | 11/36 (any 1) |
| When Blue leaves a double shot at one blot, White’s chance to hit next turn. | 20/36 (any 1 or 3) | 20/36 (any 1 or 3) |
| When Blue leaves two blots, White’s chance to hit one or both blots next turn. | 20/36 (any 1 or 3) | — |
| White hits this turn or next. | 11/36 + 25/36 * (7/36 * 11/36 + 14/36 * 20/36) = 23181/46656 = 17.9/36 | 20/36 + 16/36 * (1/36 * 11/36 + 1/36 * 20/36) = 26416/46656 = 20.4/36 |
| Mike |
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| XGID=-DbBaC-------------cbabbb-:2:-1:1:42:0:0:3:0:10 | |||||
| Blue to play 42 | |||||
| 1. | Rollout1 | 5/1 3/1 | eq: +0.574 | |||
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| 2. | Rollout1 | 5/3 5/1 | eq: +0.535 (-0.039) | |||
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| 1 5184 Games rolled with Variance Reduction. Dice Seed: 81618050 Moves: 3-ply, cube decisions: XG Roller | ||||||
eXtreme Gammon Version: 2.03