We left Black in this position last week, trailing 0-4 to 7 with the cube on White's side and apparently up the creek without a paddle. What is the correct cube action?
This is a handy reference position, easy to remember as White wins 88% of the games and 8 of those are gammons. At this score Black needs about 10% to take and redouble for the match, because that will be his equity if he passes and trails 7-away, Crawford. We can do lots of calculations to see whether White should redouble, but let me simplify it for you. At this score, it's almost impossible for White to have a correct redouble while there is a chance of a gammon.
Even leaving gammons out entirely, White's doubling window is so small, between 87 and 90% roughly, that her chances of ever being in it are minute. She'll either be not good enough, or she'll have a cash. Doubling now kills White's gammons and puts the match on the line, so playing on until those gammon chances have gone and then cashing is always the plan. In real terms, if White redoubles for the match, she'll be 88%. If she plays on and never redoubles she'll be 87.8%, but clearly she can do a lot better than that by using the cube to cash in all the games where her gammon chances disappear and retaining her 65% match equity in the horror games where she loses.
Player skills come into this. If Black is a world class player playing an intermediate, he should probably pass this, as his theoretical ME of 10% going into the Crawford game will be a lot better than that, because he will outplay White, which he can't really do if he takes this. From this it follows that intermediate White should turn the cube.
However, doubling does have one big plus for White. Humans hate to take and put the match on the line, so if White redoubles here, she will get a lot of wrong passes, from those who underestimate Black's winning chances and from those who know that the take is theoretically correct, but would rather try to win from 7-away, Crawford. In this match White (eberlein a very strong player) doubled and Black (me) feebly passed!
Doh! Tomorrow, if it ever comes, I have some lovely quiz positions for you, all of which were sent to me from Croatia. I forecast that this country has a very bright BG future, with a lot of good players improving fast and the Croatian Backgammon Federation - Hrvatski backgammon-tavla savez, up and running to promote the game there.
Until then, wherever you are, enjoy the game!
1 comment:
I was curious enough about this to roll it out. As i expected, both Cubing and dropping are whoppers (.1 EMG errors) I like to lok at cube decisions in MWC rather than EMG, so here are the numbers.
Cube analysis
Rollout cubeless MWC 88.12% (Money: +0.848)
Cubeful equities:
1. No double 89.43%
2. Double, pass 90.72% ( 1.29%)
3. Double, take 88.07% ( -1.36%)
Proper cube action: No redouble, take (51.2%)
Rollout details:
Player O owns 2-cube:
0.876 0.094 0.003 - 0.124 0.001 0.000 CL 88.12% CF 89.43%
[0.001 0.004 0.001 - 0.001 0.000 0.000 CL 0.02% CF 0.07%]
Player X owns 4-cube:
0.881 0.115 0.001 - 0.119 0.012 0.000 CL 94.06% CF 88.07%
[0.001 0.006 0.001 - 0.001 0.003 0.000 CL 0.06% CF 0.13%]
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 934800214 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]
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