A little while ago, Christian posted an article entitled Even more prime time with a position that he said was one of the 3 most interesting positions he'd ever come across. As far as I know, no rollout was ever posted, so I rolled it out myself. See below.
The move I came up with happened to coincide with the move that topped the rollout, but since it's a complicated position I don't know if my reasoning was sound. So let me present my reasoning and people can tell me if I missed something.
The first candidate to consider is bar/24* 13/11. In this kind of position I find it useful to count how many "specific" numbers are needed to hop over the prime. White needs to roll a 1 and two 6's. Blue also needs to roll a 1 and two 6's. Blue has some pips of extra timing because of his outfield checker, but White also has some pips of extra timing because he's on the bar. White's being on the bar means that White has to roll the 1 first before either 6 (bad for White) but it also means that White will not collapse while he's on the bar (good for White). Overall, it looks like all these factors roughly cancel each other, and White may have a slight advantage since he gets first crack at trying to escape. (In principle we also have to think about what happens if either player decides to attack, but overall, attacking looks like a weak strategy that will be adopted only if priming fails, because it carries serious danger of collapsing.)
The second possibility to consider is bar/23 2/1*. White has to roll a 1 and then a 6. Blue needs to roll two 6's. But if Blue gets hit on the 1-point then he will have another checker that he needs to enter from the bar and escape, while White tries to roll his 6. White may collapse while trying to escape, but if Blue is on the bar, this may not be a disaster. If Blue covers the checker on the 1-point then he really needs to roll two 6's or else he'll collapse and be at a serious disadvantage. It's not so hard to roll the two 6's, though, because once he rolls the first 6 he'll buy some extra time to roll the second 6. Overall, the possibility of closing White out and escaping seems to compensate for the risk of getting a third checker sent back. It looks slightly better than bar/24* 13/11.
The third possibility is not hitting; bar/23 4/3 or bar/23 13/11. I don't see too much to choose between these two so I would play bar/23 4/3 since it leaves only a 6-6 joker and doesn't add 6-5 as another joker. The advantage of this move is that if White doesn't roll a 6 then White's position deteriorates real fast. Even if White does roll a 6, we get a direct shot at the fleeing blot (unless White rolls 6-6). Overall this seems best because in most cases we don't have to accomplish the difficult feat of leaping White's prime. Instead we let White's prime collapse before us. Putting White on the bar puts the pressure on ourselves to leap, while White may be calmly dancing as we use up our timing.
Now someone can tell me why I got the right answer just by accident. :-)
| gnubg | 86 |
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| tchow | 107 |
Position ID: ubcNACButwEBSA Match ID: QQkFAAAAAAAA | |
| # | Ply | Move | Equity | |||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| • | 1 | R | bar/23 4/3 | -0.053 | ||||||||||||||||||
| ||||||||||||||||||||||
| Full cubeful rollout with var.redn. | ||||||||||||||||||||||
| 1296 games, Mersenne Twister dice gen. with seed 843569395 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 | bar/23 2/1* | -0.077 ( -0.024) | |||||||||||||||||||
| ||||||||||||||||||||||
| Full cubeful rollout with var.redn. | ||||||||||||||||||||||
| 1296 games, Mersenne Twister dice gen. with seed 843569395 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 | bar/23 13/12 | -0.077 ( -0.024) | |||||||||||||||||||
| ||||||||||||||||||||||
| Full cubeful rollout with var.redn. | ||||||||||||||||||||||
| 1296 games, Mersenne Twister dice gen. with seed 843569395 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 | bar/24* 13/11 | -0.105 ( -0.052) | |||||||||||||||||||
| ||||||||||||||||||||||
| Full cubeful rollout with var.redn. | ||||||||||||||||||||||
| 1296 games, Mersenne Twister dice gen. with seed 843569395 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] | ||||||||||||||||||||||
| 5 | R | bar/24* 4/2 | -0.165 ( -0.112) | |||||||||||||||||||
| ||||||||||||||||||||||
| Full cubeful rollout with var.redn. | ||||||||||||||||||||||
| 1296 games, Mersenne Twister dice gen. with seed 843569395 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] | ||||||||||||||||||||||