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BACKGAMMON BY THE BAY
Problem #25 solution
Match to 11
Blue 1, White 8
Blue to play.
Cube action?Candidate plays:
Double / Pass
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RK:
Blue has a definite edge here. The race is even, but White has a checker on the bar, while Blue has a better board and is a favorite to make it even better by covering the 3 point. However, once Blue covers the point (assuming she does), her board isn't likely to get much better for a while, because of a lack of builders. She'll probably start moving some of her back checkers, and most likely White will have enough time to enter and anchor and hope for some kind of counterattack. In other words, it's a fairly easy take for White.Is it a double, though? Blue is way behind in the match, so some aggression is justified. If she's going to win the match, she must get lucky sometime, so maybe this is the time to jack up the stakes. Some players get a bit too cautious when leading and drop when they really still have a take. Any chance White would pass? Seems unlikely. Therefore, there's actually an advantage to waiting till the position gets a little better and hoping for an error from White then.
Are there any market losers? Yes. If Blue rolls 66 or 55, and White fans, Blue's equity is around .68, a clear drop, although not an overwhelming market loser. Most of the other cover-fan sequences, though, show Blue with a more marginal market loss if any, which gives some argument for waiting til then to double. Blue will rarely lose her market by much, and of course there are many sequences where she might regret having doubled.
The rollout data don't take into account the match score, so we can't really be sure just by looking at those raw numbers. However, Jellyfish's level 7 evaluation does take into account the match score when computing whether to double, and it says "No double". And JF's cubeless evaluation of .354 is extremely close to both sets of cubeless rollouts, so its cube evaluation should be trusted.
For further evidence, we can look at the match equities. The following shows the possible outcomes of doubles and gammons in this game, followed by Blue's probability of winning the match.
- Blue wins 1 point (9 away: 3 away): 16%
- Blue wins 2 points (-8:-3): 20%
- Blue wins 4 points (-6:-3): 29%
- White wins 1 point (-10:-2): 7%
- White wins 2 points (-10:-1): 3%
- White wins 4 points (match over): 0%
If Blue doubles, White stands to gain 13% by taking, while risking 4% (not counting gammons). This is a bit better than the money 3-1 ratio, although it's offset by the fact that White will almost never redouble. But the point is that the take point is not very different from money.
How about gammons? With the cube on 2, Blue gains 9% by winning a gammon instead of a plain game, while losing instead of winning costs 17%. Again, this is very close to the money ratio of 1/2, so gammons aren't much more costly than usual for White.
Since White gets virtually no redouble equity, he would be expected to pass with an equity worse than -.50. Here the equity is somewhere between -.35 and .37, so it's an easy take. These figures lend credence to the fact that, despite being behind in the match, Blue should wait for her position to improve a bit before doubling.
JF: No double / Accept (level 7 evaluation)
Pip counts: Blue 163 White 163 Blue White Level 7 Evaluation Equity Win G/BG BG Win G/BG BG Cubeless +0.354 60.6% 21.1% 0.7% 39.4% 7.4% 0.2% Level 5 Rollouts Equity Win G/BG BG Win G/BG BG Cube centered +0.481 73.5% 1.8% 0.1% 26.5% 0.8% 0.0% Blue owns cube +0.571 80.1% 2.0% 0.1% 19.9% 4.9% 0.3% White owns cube +0.218 50.6% 21.2% 0.9% 49.4% 1.4% 0.1% Cubeless +0.352 60.3% 22.5% 1.0% 39.7% 8.5% 0.4% Level 6 Rollouts Equity Win G/BG BG Win G/BG BG Cubeless +0.371 60.9% 23.3% 1.1% 39.1% 8.8% 0.3%
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