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BACKGAMMON BY THE BAY Problem #24 solution		Match to 11 Blue 1, White 8
		Blue to play 21 Candidate plays: 24/21 21/18 18/15 18/16 24/23 18/16 6/5 8/6 24/23 6/3* 6/4 24/23

RK:
Blue has a few reasonable choices with this 21. The main themes are:

• Hitting loose with 6/3*
• Advancing the anchor with 21/18
• Keeping the anchor and moving the spare back checkers in some combination.

Hitting is attractive because of Blue's superior board and White's lack of an anchor. On the down side:

• Blue risks losing significant racing equity. White hits on the 3 point with 17 numbers, costing Blue 22 pips in a close race. White can also return hit on the 18 point with several additional numbers, reducing Blue's chances of covering the 3 point. And 33, 63 and 31 hit twice, which is quite costly.
• White's lack of builders means that he's not threatening to do much this roll, so a hit isn't urgent. Blue may be able to hit more profitably later.
• Even if Blue escapes being hit and covers the 3 point, she still doesn't have the game won but would have to make some more progress to claim.

If Blue doesn't hit, what's the best play? If Blue keeps the 21 point, she should reduce shots by moving 18/15. This checker also provides increased coverage of her outfield, should White run there. The checker on the 24 point should be able to advance later.

So, is it better to have the 21 point or 18 point? The 21 point guards against immediate jokers like 44, 24 and 22, as well as providing long-term insurance against a closeout. It also runs a bit more risk of being hemmed in, in case White gets lucky and makes his 5, 7, 9 and/or 10 points. If White had escaped his back checkers, staying back on the 21 point provides more defensive possibilities. But in a mutual holding game, which this could easily become, timing is important. The more advanced the rear anchor, the more pips the other spare checkers have to play with before having to break something important. It's also a bit easier to convert to a race if Blue rolls big doubles. Even if Blue gets pointed on, she still has plenty of room to enter, and the 18 point provides some security.

Frankly, I wouldn't have thought the choice of anchors made a significant difference and would have played 18/15, to avoid the jokers. I'd also want more coverage in case White runs into my outfield, so I don't have to break the midpoint. However, the rollouts showed a clear preference for the bar point, which surprised me. I decided to run a quick level 6 rollout to confirm (216 games each, standard deviation around 2%). I found that 18/15 improved, with .104 equity, while 21/18 was .083 and 6/3* was .033. While this isn't conclusive, it seems to show that 18/15 is reasonable if not best. JF should be playing better on level 6 than on level 5, although I'm not sure why it would be playing the 18/15 position badly in the first place. Comments are welcome (karr@best.com).

---

Pip counts:          Blue   166                     White  160

                     Blue                           White              
Level 5 Rollouts     Equity   Win    G/BG    BG     Win    G/BG    BG  
21/18                +0.091   52.7%  13.7%   0.3%   47.3%  10.0%   0.2%
18/15                +0.048   50.6%  13.7%   0.4%   49.4%  10.1%   0.3%
6/3*                 +0.030   50.5%  13.6%   0.4%   49.5%  11.6%   0.5%
18/16 6/5            +0.026   50.7%  13.8%   0.4%   49.3%  12.4%   0.5%
18/16 24/23          +0.026   50.0%  12.6%   0.3%   50.0%  10.0%   0.3%
24/21                +0.019   49.7%  11.8%   0.3%   50.3%   9.2%   0.2%
6/4 24/23            -0.015   48.7%  11.9%   0.3%   51.3%  10.9%   0.3%
8/6 24/23            -0.033   48.0%  12.0%   0.3%   52.0%  11.4%   0.4%

                     Blue  
Level 6 Rollouts     Equity
18/15                +0.104
21/18                +0.083
6/3*                 +0.033

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