This article originally appeared in the November 2000 issue of GammOnLine.
Thank you to Kit Woolsey for his kind permission to reproduce it here.

More Than One Way to Win

By Alex Zamanian
Here's a position that was played as a take/drop prop in the Boston area recently.


Board image courtesy of GO-Figure

White doubles. Does Blue have a take?

Three intermediate players thought it was a drop, while two expert players thought it was a take. Snowie rollouts indicates that it is in fact an easy take. What is interesting though, was how badly the intermediate players misjudged the position. They all thought it was a not just a pass, but a big pass. But passing this position costs a whopping .4 points, according to the rollouts. What is it about this position that caused three decent players to misevaluate so badly?

When one of the intermediate players was asked why she thought it was a pass, she said something to the effect of, "Three men on the 3 point behind a solid 5 prime indicates a pass. The timing of the priming game is very bad for Blue, that indicates a pass. If Blue gets to attack White, he has to successfully complete the attack and then escape three men from behind a 5 prime, very hard to do. Everything points to passing."

Her analysis is actually quite accurate, in a way. If Blue's only way to win was to win using his 3-point game, then this position would be a good-sized pass. If Blue's only way to win was to win the priming game by containing White's checkers, then this position would be a good-sized pass. If Blue's only way to win was to attack White's checkers as he vacated the 4 point, then extricating his own back checkers, then this position would be a good-sized pass. What she didn't realize was that Blue can win in any of those three ways, and he has good chances to try them all.

For example, if White rolls 6-2 and plays 21/13, Blue can attack with twos, threes, and fours, while escaping with sixes. If White rolls 2-2 and plays 13/5, the timing of the priming game doesn't look too bad for Blue anymore if he can roll a 6 soon. If White rolls well and safely escapes his three back checkers, Blue still retains significant winning chances through the racing and shot hitting chances of his three-point game. Blue has all these different ways to win, and he just needs one of them to come through for him.

This concept comes up with ace-point and deuce-point games quite often. 


White on roll

White's cubeless equity in this position is about .750, which means Blue has a pass of White's double. It's a big pass, but not a monster one, which means if Blue has a well-timed deuce-point game and some other decent way to win, he likely has a take. 


White on roll

For example, from this position, Blue will likely end up with a position similar to his deuce-point game in the previous position. However, that is just about as bad as Blue can do, and he has another real way to win. Over half of White's rolls fail to safety his blot, when Blue might hit and have chances to build a counter-prime. If Blue had to count on one or the other of his two ways to win, he would have to pass White's cube. But since Blue can sometimes try priming, then fall back on his deuce-point game if things go badly, he can comfortably take here.

A holding game can yield two ways to win; racing, or hitting a shot. Often times the racing chances aren't enough to take, but the shot hitting chances compensate for this deficiency.  


White on roll

For example, in the above position, Blue trails in the race by 15% of the leader's pipcount, which usually indicates a pass. Blue's shot hitting chances aren't that great, either. White will usually have two chances to roll a good number to cleanly clear the 10 point, and even if White does leave a shot, Blue still has to hit it. In addition, Blue may be forced to break his board or run with one checker exposing him to attack before he gets a shot. However, he definately has some shot-hitting chances, and Blue's racing chances alone are almost enough for him to take. Here the shot-hitting and racing chances add up to a close take for Blue.

It is often easy to take a look at one bad aspect of a position and conclude that it is a pass. What is more difficult is seeing several bad aspects of a position and recognizing that when put together, they add up to a take.

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