Problem of the Week #21: July 26


Cash game. Center cube. Black on roll.




Part (a): Should Black double? If Black doubles, should White take, drop, or beaver?



Part (b): Should Black double? If Black doubles, should White take, drop, or beaver?



When contemplating a middle game double, don’t make the mistake of looking only at your position. Remember to look just as carefully at the weaknesses in your opponent’s position. It may be his weakness, rather than your strength, that gives you a good double.

Part (a) is a perfect case in point. Black has escaped his back checkers and built a little structure, while White has grabbed your 5-point. In most positions of this general type, Black’s advantages wouldn’t even add up to an initial double. But now look at White’s position:

> His back men are split and vulnerable to potential blitzing rolls like 66, 55, and 44, both now and on subsequent rolls. If his two back checkers were anchored on the 23-point or the 22-point, the position wouldn’t be a double.

> His front position is still chaotic and will be for a couple of turns. If he had a small 4-prime or even a good board with, say, the 4-point and 5-point made, he’d have a threat to contain any checker hit on the next couple of turns, and Black wouldn’t have a double.

But with both these weaknesses, White’s game is toothless enough so that Black has a very solid double. White still has a clear take of course.


In Part (b), Black is off to a decent start. He’s got a good defensive anchor, while on the offensive side he has – well – something. He’s got some great points slotted, and next turn he might actually cover one or two of them.

The key to the position is not Black’s game but White’s. While Black has something, White has a bit less than nothing. No points, just blots. Something versus nothing is a good prescription for an early double, especially if the defender doesn’t have an anchor. Without an anchor, there will always be variations where things go terribly wrong and Black’s messy position turns into a powerful blitz. Did you stop to guess what Black’s cubeless gammon chances were in Part (b)? If you did, did you realize they’re over 25%? Numbers like that almost always guarantee not just an initial double, but a strong and mandatory initial double. Black’s checkers aren’t just passive slots. They’re also potential attackers, which can be activated by a single good sequence. Couple that with a rock-solid defensive anchor, and Black has a great double.

Clear take, of course. There are plenty of variations where things don’t go so well and White recovers quickly.


Solution:

Part (a): Black should double, and White should take.

Part (b): Ditto.

In part A, if white has a clear take, what's the rush for Black to double? If Black improves and White doesn't, Black can always turn the cube then. Even if it's a drop, it won't usually be by much, and I'd be happy as Black to cash in my win at that point.

Edit: Plus White may very well take incorrectly later in these types of positions, where I'd hardly ever expect him to make a mistake now by dropping.

Black is near White's dropping point already, and he has a few enormous market-losers (44, 55, and 66). So double now.

"My opponent will make a mistake later" is, for most players, an enormous leak in their game, leading them to postpone doubling in positions they consider murky, but which are, in fact, excellent doubles. "When in doubt, double" is a slogan that's much more likely to lead to something approaching correct play in unclear positions.

After posting my answer in the problem thread (a. no double, b. double/take for the record) I did GNU rollouts on these positions. No double on a) is about the -0.050 mark, while b) is more like -0.100. So those who answered like I did can take some consolation from the fact that b) is a much stronger double.

So it's a clear but thin take? In that case, I cannot disagree with a double.

I don't recall advocating this approach in general.

In this *specific* position, there is value in waiting a bit vs. *typical* players IMO (i.e., good but not world-class), and that won't show up in a rollout.

Wow. I think this just might be the first set of problems he has ever posted where I got the right answer and most of the logic

You'll get used to it