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BACKGAMMON BY THE BAY Problem #27 solution		Match to 11 Blue 3, White 8
		Blue to play. Cube action? Candidate plays: Roll Double / Accept Double / Pass

RK:
A tough match doubling decision. Blue has the advantage, with one checker back vs two. She's shooting at a blot from the bar, and if she misses, that blot remains a liability for White. Her numbers that are blocked, 4s and 6s, can make her bar point, so most numbers play OK.

On the other hand, the race and board strengths are close. There's still plenty of room for White to anchor, and White figures to have plenty of counterattacking possibilities. Given a chance to get to the Crawford game, it would be silly for White to pass.

For money, it would be too early to double (which is what the rollouts show), but how about at this match score? There are certainly some incentives to doubling:

• White will virtually never redouble, since Blue will take a 4-cube and rewhip it with more than 6% winning chances.
• White's gammons are worth less than usual.

On the other hand, if you do the math, it turns out that White's take point isn't all that different than for money (it's about 22%, not counting gammons).

The relevant match scores and equities are as follows:

Blue wins 4: 4 away, 3 away: 41% winning chances
Blue wins 2: 6 away, 3 away: 29%
Blue wins 1: 7 away, 3 away: 24%
White wins 1: 8 away, 2 away: 12%
White wins 2: 8 away, 1 away: 6%
White wins 4: match over: 0%

So what does this all mean? If Blue had no market losers, then it wouldd clearly be correct to wait, but there are definitely market losers: Any hit followed by a White fan is a big market loss because of all the blots around. Even some entering numbers, too. Are these enough to make doubling correct? Jellyfish, level 7, which takes the match score into account, doesn't think so. However, it shows Blue with 2% less cubeless equity than the rollouts, so that could make a difference.

Personally, I couldn't criticize a double: I'd envision rolling an ace (or better, 3-3) and losing my market, so I'd take my chances at this score. Blue doesn't have to worry about the cube coming back. And ironically, if Blue doesn't double, and the game turns around, then it's more likely that White will double at some point, so the cube may well end up on 2 anyway.

JF:   No double / Accept (level 7 evaluation)

---

Pip counts:          Blue   136                     White  134

                     Blue                           White              
Level 7 Evaluation   Equity   Win    G/BG    BG     Win    G/BG    BG  
Cubeless             +0.295   60.9%  19.3%   0.8%   39.1%  12.2%   0.2%

Level 5 Rollouts     Equity   Win    G/BG    BG     Win    G/BG    BG  
Cube centered        +0.444   71.2%   3.5%   0.3%   28.8%   1.7%   0.1%
Blue owns cube       +0.531   79.4%   3.8%   0.3%   20.6%   9.6%   0.3%
White owns cube      +0.207   51.1%  19.3%   1.4%   48.9%   2.3%   0.1%
Cubeless             +0.316   61.2%  21.1%   1.5%   38.8%  12.9%   0.4%

Level 6 Rollouts     Equity   Win    G/BG    BG     Win    G/BG    BG  
Cubeless             +0.328   61.3%  22.1%   2.1%   38.7%  13.5%   0.5%

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