Position #258
Jan 20th, 2010 by vct
White 4, Red 5 (match to 7 points)
White to play 26
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Pip counts: White 71, Red 103
Position ID: 3O2ADQDc7wAABA Match ID: MAH5AEAAKAAA
A position sent in by Kevin. He writes:
My opponent is winning the race and has started to bear off. I’ve sent one man back and am hoping to hit him as he tries to escape. He rolls a 6-2. In the game, he was forced to play the 6 to come into the outer board, but then he played the 2 in his inner board instead of continuing to advance.
Since the odds of getting hit are smaller the closer one is to the attacking checker, I thought he should have played the 2 on top of the 6 (playing 23/15). His reasoning was that fewer numbers hit where he stopped, at 23/17 (he pointed out that if he had moved 2 more pips, the only rolls that miss entirely were doubles 5s and double 6s).
The risk of beeing hit on the 15-point is indeed greater than on the 17-point (Edit: Wrong! see comments). There are two reasons why it still is better to move all the way with 23/15:
* If not hit, it is harder to get the last checker to safety if you stay back, risking yet another double shot.
* 23/17 4/2 leaves another blot in the opponent’s home field. If Red hits, he will very happily slot the ace or 2-point hoping to either make that point or collect the second blot if hit. White will be doubled out if the second blot is hit.
Thanks to Kevin for proposing this position!
| # | Ply | Move | Equity | |||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | R | 23/15 | -0,296 | |||||||||||||||||||
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| Full cubeful rollout with var.redn. | ||||||||||||||||||||||
| 1296 games, Mersenne Twister dice gen. with seed 846310553 and quasi-random dice | ||||||||||||||||||||||
| Play: world class 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| keep the first 0 0-ply moves and up to 8 more moves within equity 0,16 | ||||||||||||||||||||||
| Skip pruning for 1-ply moves. | ||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| Different evaluations after 12 plies: | ||||||||||||||||||||||
| Play: 0-ply cubeful [expert] | ||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| 2 | R | 23/17 4/2 | -0,505 ( -0,210) | |||||||||||||||||||
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||||||||||||||||||||||
| Full cubeful rollout with var.redn. | ||||||||||||||||||||||
| 1296 games, Mersenne Twister dice gen. with seed 846310553 and quasi-random dice | ||||||||||||||||||||||
| Play: world class 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| keep the first 0 0-ply moves and up to 8 more moves within equity 0,16 | ||||||||||||||||||||||
| Skip pruning for 1-ply moves. | ||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| Different evaluations after 12 plies: | ||||||||||||||||||||||
| Play: 0-ply cubeful [expert] | ||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| 3 | R | 23/17 5/3 | -0,514 ( -0,218) | |||||||||||||||||||
|
||||||||||||||||||||||
| Full cubeful rollout with var.redn. | ||||||||||||||||||||||
| 1296 games, Mersenne Twister dice gen. with seed 846310553 and quasi-random dice | ||||||||||||||||||||||
| Play: world class 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| keep the first 0 0-ply moves and up to 8 more moves within equity 0,16 | ||||||||||||||||||||||
| Skip pruning for 1-ply moves. | ||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| Different evaluations after 12 plies: | ||||||||||||||||||||||
| Play: 0-ply cubeful [expert] | ||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| 4 | R | 23/17 3/1 | -0,519 ( -0,223) | |||||||||||||||||||
|
||||||||||||||||||||||
| Full cubeful rollout with var.redn. | ||||||||||||||||||||||
| 1296 games, Mersenne Twister dice gen. with seed 846310553 and quasi-random dice | ||||||||||||||||||||||
| Play: world class 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| keep the first 0 0-ply moves and up to 8 more moves within equity 0,16 | ||||||||||||||||||||||
| Skip pruning for 1-ply moves. | ||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| Different evaluations after 12 plies: | ||||||||||||||||||||||
| Play: 0-ply cubeful [expert] | ||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | ||||||||||||||||||||||


























sure you counted well the hitting numbers on both 15 and 17 point?
I’d echo calumax’s query. My somewhat hasty count:
@15 miss with: 61, 62, 51, 52, 66,55 = 10/36
@17 miss with: 44, 43, 31, 21, 11, = 8/36
@15 another miss is 65, so it is 12/36
You’re right, I miscounted, @15 = 12/36, @17 = 8/36. So 23/17 4/2 is not even safer in that regard. Thanks for the corrections!