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BACKGAMMON BY THE BAY Problem #30 solution		Match to 11 Blue 9, White 7
		Blue to play. Cube action? Candidate plays: Roll Double / Accept Double / Pass

RK:
This is a classic match cube decision. For money, of course, it looks like an easy double/drop. Blue has a big gammon threat, with all of White's outfield checkers frozen (temporarily at least). But it's not too good to double, because White can easily enter and hit something, thus turning the tables.

At this match score, though, things are completely different. If White drops, it'll be Crawford game, so she'll have to win three games, or win a gammon plus a plain game. This works out to around 17% winning chances. So as long as her winning chances in the game exceed 17%, she should take and redouble, putting the match on the line.

Does she have 17%? It's not so easy to estimate. Blue has to safety the checker on 18, then clear the midpoint and other outfield checkers, while White is a favorite to come in soon, so she figures to have a bunch of indirect shots. On the other hand, a hit isn't a win, given White's non-solid board, but it certainly helps. The point is, it's not that hard to get 17% wins, and the rollouts show about 19%. So White really should take this.

Now: should Blue double? The general rule of thumb, when two away from victory (and leading) is: Don't double if you have a significant gammon threat.

In a sense, Blue can have his cake and eat it too by not doubling. First, if he wins a gammon, he wins the match without doubling (while if he doubles, he kills his own gammons; that is, he gets no extra value from a gammon). Second, he's not risking having White win the match by getting lucky in this game. Worst case, if White turns the game around, Blue usually escapes with a one or two point loss.

So Blue should play on. If the gammon threat disappears, he can wait for a time when he's close to White's take point (which means he has 83% winning chances) before he needs to double.

JF:   No double / Accept (level 7 evaluation)

---

Pip counts:          Blue   113                     White  130

                     Blue                           White              
Level 7 Evaluation   Equity   Win    G/BG    BG     Win    G/BG    BG  
Cubeless             +0.780   77.5%  27.0%   0.2%   22.5%   4.0%   0.0%

Level 5 Rollouts     Equity   Win    G/BG    BG     Win    G/BG    BG  
Cube centered        +0.969   90.7%  15.8%   0.1%    9.3%   0.4%   0.0%
Blue owns cube       +1.002   93.1%  16.0%   0.1%    6.9%   2.0%   0.1%
White owns cube      +0.851   75.9%  34.0%   0.3%   24.1%   0.9%   0.0%
Cubeless             +0.916   80.4%  34.6%   0.3%   19.6%   4.0%   0.1%

Level 6 Rollouts     Equity   Win    G/BG    BG     Win    G/BG    BG  
Cubeless             +0.929   80.8%  34.6%   0.4%   19.2%   3.6%   0.1%

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