Thanks for the comments. I was hoping that there would be a viewpoint that makes this problem easy but I'm not sure there is. What I feel I can say for sure is this.
1. We don't really need to consider 21/10 because 21/15 12/7 shares essentially all the advantages of 21/10 with lower risk (fewer shots).
2. If Blue plays 21/15 12/7 then 15 rolls hit, and leave White with a strong advantage because White has a 4-point board and Blue has another blot dangling. If Blue is missed then Blue has a very strong advantage because of his threat to lock up the race, perhaps even hitting White along the way.
3. If Blue plays 12/1 then 24 rolls hit, but except for the three pointing rolls they still leave Blue with an even game or even a slight advantage because White must either leave a return shot or bury another checker. If Blue is missed then Blue has a strong advantage but nowhere near as strong as after playing 21/15 12/7 and being missed.
It's difficult to weigh a volatile play against a less volatile play, but here the gain from 21/15 12/7 when things go well is very large and the loss when things go poorly is smaller because 21/15 12/7 leaves significantly fewer shots than 12/1. This conclusion is robust over a variety of match scores and cube locations.
As a side remark, I think that there is a tendency among many players, myself included, to think that playing with just one blot is a safer route to winning. Keeping track of two blots, and coping with the worry that both of them might get hit, is a psychological challenge. But this position illustrates that getting both checkers poised to come home can be a lot more powerful than getting one of them home for sure and leaving the other one stranded. So the gains and losses have to be weighed carefully.
| gnubg | 75 |
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| tchow | 66 |
Position ID: 77gxAAJ37wABBA Match ID: UYn6AAAAAAAA | |
| # | Ply | Move | Equity | |||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| • | 1 | R | 21/15 12/7 | +0.353 | ||||||||||||||||||
| ||||||||||||||||||||||
| Full cubeful rollout with var.redn. | ||||||||||||||||||||||
| 1296 games, Mersenne Twister dice gen. with seed 851982813 and quasi-random dice | ||||||||||||||||||||||
| Play: supremo 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| keep the first 0 0-ply moves and up to 16 more moves within equity 0.32 | ||||||||||||||||||||||
| Skip pruning for 1-ply moves. | ||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| 2 | R | 21/10 | +0.266 ( -0.087) | |||||||||||||||||||
| ||||||||||||||||||||||
| Full cubeful rollout with var.redn. | ||||||||||||||||||||||
| 1296 games, Mersenne Twister dice gen. with seed 851982813 and quasi-random dice | ||||||||||||||||||||||
| Play: supremo 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| keep the first 0 0-ply moves and up to 16 more moves within equity 0.32 | ||||||||||||||||||||||
| Skip pruning for 1-ply moves. | ||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| 3 | R | 12/1 | +0.244 ( -0.109) | |||||||||||||||||||
| ||||||||||||||||||||||
| Full cubeful rollout with var.redn. | ||||||||||||||||||||||
| 1296 games, Mersenne Twister dice gen. with seed 851982813 and quasi-random dice | ||||||||||||||||||||||
| Play: supremo 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| keep the first 0 0-ply moves and up to 16 more moves within equity 0.32 | ||||||||||||||||||||||
| Skip pruning for 1-ply moves. | ||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | ||||||||||||||||||||||