after 2 slots, nearly all 7,8,10 should be played from mid.
Some players might, but they should not. Five checkers on the bar point give White time to try to clear the midpoint safely. I think these are some reasons why White should not volunteer a shot:
1. I would guess that if Blue promises to miss, then White is a little better off after playing, for example, 52 13/6 than 7/2 6/4, because it is more efficient and because Blue has less chance to hit the checker remaining on the midpoint (but count how many numbers do not clear the checker safely!). But before the roll White is only up 5 pips, with gaps for now on the 2 and 5 points. Blue has good GWC on the race alone.
2. Hitting with 5/3 or 6/2 creates 6 Blue blots. Kind of gammonish. But what about win percentage? If White leaves no shot with 61 52 43 62 54 63 64, his GWC is 62-64%. If White leaves a blot and is hit, White hits from the bar 20/36 = only 55.5%. If White fans, he must pass. White is better off racing.
3. If Blue hits with 4-4, White is royally screwed.
Some rollouts:
The score is: White 2, Blue 9 (match to 15 points). Blue has played 11/9 8/2.
| White | 94 |
|---|
                                  |
| Blue | 99 | |
|---|
Position ID: q+0SAAPZ3AcGAA Match ID: MAHnASAASAAE
|
| # | Ply | Move | Equity |
| • | 1 | R | 7/6 7/1 | +0.4289 |
| | | 0.6222 | 0.0157 | 0.0003 | - | 0.3778 | 0.0128 | 0.0001 | +0.2480 | +0.4289 | | 0.0017 | 0.0024 | 0.0001 | - | 0.0017 | 0.0019 | 0.0002 | 0.0041 | 0.0098 | | |
| | Full cubeful rollout with var.redn. | |
| | 181 games, Mersenne Twister dice gen. with seed 913420271 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 | 13/12 7/1 | +0.3839 ( -0.0450) |
| | | 0.6052 | 0.0130 | 0.0002 | - | 0.3948 | 0.0271 | 0.0002 | +0.1951 | +0.3839 | | 0.0017 | 0.0011 | 0.0001 | - | 0.0017 | 0.0026 | 0.0001 | 0.0043 | 0.0082 | | |
| | Full cubeful rollout with var.redn. | |
| | 181 games, Mersenne Twister dice gen. with seed 913420271 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 | 13/6 | +0.3600 ( -0.0689) |
| | | 0.5884 | 0.0315 | 0.0038 | - | 0.4116 | 0.0286 | 0.0004 | +0.1810 | +0.3600 | | 0.0018 | 0.0023 | 0.0015 | - | 0.0018 | 0.0024 | 0.0001 | 0.0058 | 0.0084 | | |
| | Full cubeful rollout with var.redn. | |
| | 181 games, Mersenne Twister dice gen. with seed 913420271 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] | |
| | 4 | R | 13/12 13/7 | +0.3220 ( -0.1069) |
| | | 0.5797 | 0.0414 | 0.0050 | - | 0.4203 | 0.0312 | 0.0004 | +0.1743 | +0.3220 | | 0.0021 | 0.0017 | 0.0008 | - | 0.0021 | 0.0047 | 0.0001 | 0.0068 | 0.0109 | | |
| | Full cubeful rollout with var.redn. | |
| | 180 games, Mersenne Twister dice gen. with seed 913420271 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] | |
| White | 94 |
|---|
                                  |
| Blue | 99 | |
|---|
Position ID: q+0SAAPZ3AcGAA Match ID: MIHqASAASAAE
|
| # | Ply | Move | Equity |
| | 1 | R | 7/2 6/4 | +0.4351 |
| | | 0.6238 | 0.0194 | 0.0003 | - | 0.3762 | 0.0159 | 0.0004 | +0.2530 | +0.4351 | | 0.0018 | 0.0016 | 0.0001 | - | 0.0018 | 0.0025 | 0.0001 | 0.0040 | 0.0083 | | |
| | Full cubeful rollout with var.redn. | |
| | 180 games, Mersenne Twister dice gen. with seed 913420271 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 | 7/2 4/2 | +0.4274 ( -0.0077) |
| | | 0.6208 | 0.0191 | 0.0003 | - | 0.3792 | 0.0149 | 0.0003 | +0.2480 | +0.4274 | | 0.0020 | 0.0015 | 0.0004 | - | 0.0020 | 0.0018 | 0.0001 | 0.0040 | 0.0088 | | |
| | Full cubeful rollout with var.redn. | |
| | 180 games, Mersenne Twister dice gen. with seed 913420271 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 | 7/2 3/1 | +0.3912 ( -0.0439) |
| | | 0.6139 | 0.0179 | 0.0002 | - | 0.3861 | 0.0175 | 0.0002 | +0.2277 | +0.3912 | | 0.0016 | 0.0024 | 0.0004 | - | 0.0016 | 0.0020 | 0.0001 | 0.0043 | 0.0094 | | |
| | Full cubeful rollout with var.redn. | |
| | 180 games, Mersenne Twister dice gen. with seed 913420271 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] | |
| | 4 | R | 13/6 | +0.3597 ( -0.0754) |
| | | 0.5884 | 0.0314 | 0.0031 | - | 0.4116 | 0.0286 | 0.0004 | +0.1810 | +0.3597 | | 0.0018 | 0.0023 | 0.0023 | - | 0.0018 | 0.0024 | 0.0001 | 0.0058 | 0.0084 | | |
| | Full cubeful rollout with var.redn. | |
| | 180 games, Mersenne Twister dice gen. with seed 913420271 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] | |
| White | 94 |
|---|
                                  |
| Blue | 99 | |
|---|
Position ID: q+0SAAPZ3AcGAA Match ID: MAHuASAASAAE
|
| # | Ply | Move | Equity |
| • | 1 | R | 7/4 7/3 | +0.4378 |
| | | 0.6251 | 0.0173 | 0.0002 | - | 0.3749 | 0.0139 | 0.0003 | +0.2550 | +0.4378 | | 0.0018 | 0.0016 | 0.0001 | - | 0.0018 | 0.0020 | 0.0001 | 0.0037 | 0.0088 | | |
| | Full cubeful rollout with var.redn. | |
| | 180 games, Mersenne Twister dice gen. with seed 913420271 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 | 7/4 6/2 | +0.4351 ( -0.0027) |
| | | 0.6238 | 0.0194 | 0.0003 | - | 0.3762 | 0.0159 | 0.0004 | +0.2530 | +0.4351 | | 0.0018 | 0.0016 | 0.0001 | - | 0.0018 | 0.0025 | 0.0001 | 0.0040 | 0.0083 | | |
| | Full cubeful rollout with var.redn. | |
| | 180 games, Mersenne Twister dice gen. with seed 913420271 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 | 13/6 | +0.3597 ( -0.0780) |
| | | 0.5884 | 0.0314 | 0.0031 | - | 0.4116 | 0.0286 | 0.0004 | +0.1810 | +0.3597 | | 0.0018 | 0.0023 | 0.0023 | - | 0.0018 | 0.0024 | 0.0001 | 0.0058 | 0.0084 | | |
| | Full cubeful rollout with var.redn. | |
| | 180 games, Mersenne Twister dice gen. with seed 913420271 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] | |
| | 4 | R | 7/3 4/1 | +0.3468 ( -0.0910) |
| | | 0.5979 | 0.0161 | 0.0003 | - | 0.4021 | 0.0183 | 0.0003 | +0.1947 | +0.3468 | | 0.0021 | 0.0013 | 0.0001 | - | 0.0021 | 0.0029 | 0.0001 | 0.0044 | 0.0093 | | |
| | Full cubeful rollout with var.redn. | |
| | 180 games, Mersenne Twister dice gen. with seed 913420271 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] | |
| White | 94 |
|---|
                                  |
| Blue | 99 | |
|---|
Position ID: q+0SAAPZ3AcGAA Match ID: MAHrASAASAAE
|
| # | Ply | Move | Equity |
| • | 1 | R | 7/1 4/2 | +0.4297 |
| | | 0.6183 | 0.0192 | 0.0004 | - | 0.3817 | 0.0128 | 0.0001 | +0.2434 | +0.4297 | | 0.0021 | 0.0022 | 0.0001 | - | 0.0021 | 0.0029 | 0.0001 | 0.0050 | 0.0085 | | |
| | Full cubeful rollout with var.redn. | |
| | 180 games, Mersenne Twister dice gen. with seed 913420271 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 | 7/1 6/4 | +0.4203 ( -0.0094) |
| | | 0.6191 | 0.0176 | 0.0002 | - | 0.3809 | 0.0153 | 0.0002 | +0.2413 | +0.4203 | | 0.0019 | 0.0013 | 0.0001 | - | 0.0019 | 0.0018 | 0.0001 | 0.0041 | 0.0083 | | |
| | Full cubeful rollout with var.redn. | |
| | 180 games, Mersenne Twister dice gen. with seed 913420271 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 | 7/1 3/1 | +0.3251 ( -0.1046) |
| | | 0.5915 | 0.0122 | 0.0001 | - | 0.4085 | 0.0196 | 0.0003 | +0.1745 | +0.3251 | | 0.0021 | 0.0021 | 0.0006 | - | 0.0021 | 0.0026 | 0.0001 | 0.0050 | 0.0082 | | |
| | Full cubeful rollout with var.redn. | |
| | 180 games, Mersenne Twister dice gen. with seed 913420271 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] | |
| | 4 | R | 13/7 6/4 | +0.3027 ( -0.1270) |
| | | 0.5765 | 0.0323 | 0.0027 | - | 0.4235 | 0.0415 | 0.0004 | +0.1474 | +0.3027 | | 0.0024 | 0.0026 | 0.0010 | - | 0.0024 | 0.0026 | 0.0002 | 0.0068 | 0.0138 | | |
| | Full cubeful rollout with var.redn. | |
| | 180 games, Mersenne Twister dice gen. with seed 913420271 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] | |
| White | 94 |
|---|
                                  |
| Blue | 99 | |
|---|
Position ID: q+0SAAPZ3AcGAA Match ID: MAHzASAASAAE
|
| Cube decision |
| 2-ply cubeless equity | +0.2796 | (Money: +0.2814) |
| | 0.6408 0.0129 0.0001 - 0.3592 0.0131 0.0002 |
| Cubeful equities: |
| 1. | No double | +0.4458 | |
| 2. | Double, pass | +1.0000 | +0.5542 |
| 3. | Double, take | +0.3887 | -0.0570 |
| Proper cube action: | No double, take (9.3%) |
| # | Ply | Move | Equity |
| • | 1 | R | 7/3 7/1 | +0.5069 |
| | | 0.6404 | 0.0158 | 0.0008 | - | 0.3596 | 0.0136 | 0.0002 | +0.2841 | +0.5069 | | 0.0015 | 0.0018 | 0.0005 | - | 0.0015 | 0.0015 | 0.0001 | 0.0039 | 0.0086 | | |
| | Full cubeful rollout with var.redn. | |
| | 180 games, Mersenne Twister dice gen. with seed 913420271 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 | 7/1 6/2 | +0.4973 ( -0.0097) |
| | | 0.6392 | 0.0167 | 0.0003 | - | 0.3608 | 0.0128 | 0.0002 | +0.2825 | +0.4973 | | 0.0016 | 0.0017 | 0.0001 | - | 0.0016 | 0.0020 | 0.0001 | 0.0041 | 0.0092 | | |
| | Full cubeful rollout with var.redn. | |
| | 180 games, Mersenne Twister dice gen. with seed 913420271 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 | 13/3 | +0.4530 ( -0.0539) |
| | | 0.6196 | 0.0303 | 0.0026 | - | 0.3804 | 0.0233 | 0.0002 | +0.2502 | +0.4530 | | 0.0017 | 0.0025 | 0.0055 | - | 0.0017 | 0.0024 | 0.0001 | 0.0050 | 0.0127 | | |
| | Full cubeful rollout with var.redn. | |
| | 180 games, Mersenne Twister dice gen. with seed 913420271 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] | |
White 2, Blue 9 (match to 15 points). After White 64 13/3 ... Blue 53 20/12. White on roll
| White | 96 |
|---|
                                  |
| Blue | 91 | |
|---|
Position ID: q+0SAQK5uQ8AQA Match ID: MAH7ASAASAAE
|
| Cube decision |
| 4-ply cubeless equity | -0.0406 | (Money: -0.0215) |
| | 0.4380 0.2315 0.0284 - 0.5620 0.1554 0.0022 |
| Cubeful equities: |
| 1. | No double | +0.0448 | |
| 2. | Double, pass | +1.0000 | +0.9552 |
| 3. | Double, take | -0.0693 | -0.1141 |
| Proper cube action: | No double, take (10.7%) |
Leading to ...
| White | 96 |
|---|
                                  |
| Blue | 91 | |
|---|
Position ID: ubkPAECr7RIBAg Match ID: cAngASAASAAE
|
| Cube decision |
| 4-ply cubeless equity | +0.8654 | (Money: +0.8457) |
| | 0.8640 0.1497 0.0010 - 0.1360 0.0320 0.0010 |
| Cubeful equities: |
| 1. | Double, pass | +1.0000 | |
| 2. | Double, take | +1.5848 | +0.5848 |
| 3. | No double | +0.8948 | -0.1052 |
| Proper cube action: | Double, pass |