White - Pips 94. Match Score 0/5
Black - Pips 93. Match Score 0/5
Black to Play 3-2
Quote:
Originally Posted by peachpie
Except that in the OP position, black is a big favorite to get a second shot at white's blot after making the 12 point. White escapes entirely with only six rolls. Actually black will get a third shot fairly often.
Right. That is one of the reasons why I qualified my statement by prefacing it with the caveat, “When the gap is high in your board, ...” Here is the whole thing:
When the gap is high in your board, so that escape is easy (and the race is a toss-up after your move), hitting loose is usually better than passive play. Assuming you can safety your blot on the following turn, hitting makes you an instant 70%-to-30% favorite, even when your opponent has a closed board. Letting the opponent escape, of course, leaves the game as a 50%-50% proposition.
70%-30% is an overstatement. In practice, even when you can close out your opponent after he misses the return shot, he will usually still be winning something like 3%-5% of all games. It is probably more accurate, therefore, to say you become a 2-to-1 favorite when you hit. On the other hand, if you have cube access, and can force a pass, then you will have a one-roll position in which you win fully 70% of the games. Covering may never be necessary.
I believe it was Kent Goulding who coined the phrase, “Four in a row is more than you think.” That certainly is relevant here. This gap is not “high in the board,” and escape will be anything but “easy” when Black eschews the hit. The only reason hitting works here is because you get to continue on to the 1pt. If White hits on the 1pt, he will be trapped behind your prime, and if he does not hit, then he will either be on the bar or else right back where he started, and you will have gained half a roll in the exchange.
The other reason I think you have to be careful about applying my “rule” in this position is because of the gammon dangers represented by Black’s two outside blots. With a centered cube in a money game, where you have the protection of the Jacoby rule, they may not be a concern. In a match or some other circumstance where White might suddenly become too good to double after making a return hit, they are definitely a consideration. If this position does not qualify, imagine a similar position where White had a closed board.
Quote:
Originally Posted by peachpie
I am curious, what was the equity difference between 15/12 14/12 and 6/3*/1 ?
Compared to hitting, making the 12pt is almost a 0.08 error. But that is true only if you continue on to the 1pt after hitting. For the reasons you cited (and those discussed above),
making the 12pt actually comes out way ahead of any hitting play that does not continue on to the 1pt. The best of them is 15/13 6/3*, and it trails making the 12pt by more than 0.10!
Here is my 5k XG rollout. It uses my usual unlimited game, no-Jacoby, no-beavers settings. The resulting equities are similar to those generated in
Midiboy’s GnuBg rollout.
Code:
XGID=--BaCBDB------AAabbbabb-b-:0:0:1:32:0:0:0:0:10
Score is X:0 O:0. Unlimited Game
Pip count X: 93 O: 94 X-O: 0-0
Cube: 1
X to play 32
1. Rollout¹ 6/3* 3/1 eq:+0.670
Player: 74.02% (G:9.98% B:0.23%)
Opponent: 25.98% (G:8.19% B:0.23%)
Confidence: ±0.005 (+0.665..+0.675) - [100.0%]
Duration: 9 minutes 27 seconds
2. Rollout¹ 6/1 eq:+0.644 (-0.026)
Player: 68.43% (G:5.34% B:0.13%)
Opponent: 31.57% (G:4.83% B:0.17%)
Confidence: ±0.005 (+0.639..+0.649) - [0.0%]
Duration: 6 minutes 02 seconds
3. Rollout¹ 15/12 6/4 eq:+0.603 (-0.067)
Player: 66.20% (G:5.44% B:0.17%)
Opponent: 33.80% (G:3.76% B:0.08%)
Confidence: ±0.004 (+0.599..+0.608) - [0.0%]
Duration: 5 minutes 13 seconds
4. Rollout¹ 14/11 6/4 eq:+0.600 (-0.070)
Player: 66.80% (G:4.75% B:0.16%)
Opponent: 33.20% (G:3.29% B:0.07%)
Confidence: ±0.004 (+0.596..+0.605) - [0.0%]
Duration: 6 minutes 26 seconds
5. Rollout¹ 15/12 14/12 eq:+0.592 (-0.078)
Player: 67.48% (G:2.39% B:0.04%)
Opponent: 32.52% (G:1.02% B:0.02%)
Confidence: ±0.005 (+0.588..+0.597) - [0.0%]
Duration: 4 minutes 55 seconds
6. Rollout¹ 15/13 14/11 eq:+0.569 (-0.101)
Player: 65.01% (G:5.62% B:0.17%)
Opponent: 34.99% (G:3.26% B:0.05%)
Confidence: ±0.004 (+0.565..+0.573) - [0.0%]
Duration: 4 minutes 22 seconds
7. Rollout¹ 15/10 eq:+0.566 (-0.104)
Player: 65.54% (G:5.41% B:0.17%)
Opponent: 34.46% (G:3.07% B:0.07%)
Confidence: ±0.004 (+0.562..+0.570) - [0.0%]
Duration: 4 minutes 29 seconds
8. Rollout¹ 15/13 6/3* eq:+0.489 (-0.181)
Player: 72.25% (G:12.93% B:0.34%)
Opponent: 27.75% (G:11.99% B:0.41%)
Confidence: ±0.003 (+0.485..+0.492) - [0.0%]
Duration: 10 minutes 08 seconds
¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 14978697
Moves: 3-ply, cube decisions: XG Roller
Rollout by Taper_Mike
2014-Dec-14
eXtreme Gammon Version: 2.10.199.2658
Flashcard PositionID 000933.xgp
Mike
Last edited by Taper_Mike; 12-16-2014 at 05:08 AM.