Letters to the Editor

E-mail me at kwoolsey@netcom.com

Recently it has been discussed here whether to use bearoff formulas or not. While we know that some formulas like the Ward formula can give accurate results, we also know that some special positions are somewhat of the mark. Some days ago I encountered such a position, where these formulas are asthonishingly far away from the truth. Consider the following bearoff situation:

61 51

White money game Blue

This is a position where mostbearoff formulas would indicate double-pass. Rollouts on Jellyfish and Snowie however revealed that with the cube White can win up to 29% of the games, making this position a close double and clear take. Evencubeless White wins almost 27%. I'm sure that many players wouldn't estimate this correctly over the board. The hole on the 5 point of Blue is really a great liability,though Blue can use 3's and 4's well to take off or fill the 2 point. I think this is a very interesting position giving lot of thought.

Michael Higatsberger

The more complex formulas such as Ward and Kleinman make some attempt to takeinto account things such as empty points and extra checkers on the ace point.However, they are not always sufficient to come up with the right answer.This position is a good example.

The key to this position is the way Blue's checkers combine. Five isBlue's bad number, of course. However it is unusually bad because a fiveforces Blue to put yet another checker onto the already overloaded ace point.Thus it is the combination of the empty five point, the checkers on thesix point, and the checkers already on the ace point which makes Blue'sposition considerably worse than the pip count would indicate. In fact,if you move one of the checkers on the ace point BACK to the two point, itturns out that Blue's winning chances increase by 0.2%. Contrast withthe following similar-looking position:

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White money game Blue

In this position, moving a checker back from the ace point to the two pointwould make Blue's winning chances 1.9% less. The difference is that nowfour is the bad number, and for now Blue's fours will be played to thetwo point. Thus, putting another checker on the two point is more costlythan usual.

It would take a very sophisticated and complex formula to take these thingsinto account, and such a formula would probably not be practical to useover the board. We are better using a formula which is simple enough tobe applied over the board, making the proper adjustments when positionssuch as the above arise and are recognized.

Kit Woolsey

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