Problem of the Week #51: Solution


Cash game, center cube.




Should Black double? If doubled, should White take?


Note: All ‘cash game’ problems assume the Jacoby Rule is in effect. That is, you can’t win a gammon unless the cube has been turned.


Problem 51 shows a bar-point holding game, with a few unusual features. Unlike a normal holding game position, here we have a few extra blots scattered around the board. White has a checker back on his 23-point, which might be a liability later. In addition, his 5-point is only slotted, not made. Black has a vulnerable checker on his 18-point, which won’t be a favorite to get to safety, and another blot on his 9-point, which is pretty easy to safety.

How do all these blots affect our evaluation of the position? To start, let’s move all the bots to safety and see what our underlying benchmark position looks like.




Position 51a: No blots.

When we clean up all the blots we get to a position that should be a familiar benchmark. White holds the bar point with plenty of timing, Black leads in the race by 39 pips. It’s a strong double for Black and just a marginal take/pass for White. The race is key; if Black leads by less, it’s a clear take. If he leads by more and still has plenty of spare checkers (often hard to do) then it’s a pass.

The two key features of our actual position that really matter are Black’s blot back on the 18-point, and White’s blot on our 2-point. The other two blots don’t really matter much. White’s blot on his 5-point only plays a roll if he manages to hit Black before he can cover his own blot. Black’s blot on the 9-point is easy to pick up.

Let’s look at Black’s blot on the 18-point first. Let’s change the position so that Black gets that blot to the midpoint, and we’ll give White an ace to cover the 5-point, resulting in this position:




Position 51b: Black escapes his rear checker.

That change is enough to move the evaluation of the position about ¼ of a point, from a marginal take/pass to a huge pass. (Equity of about +1.23 for Black if White takes a double.) That’s enough to tell us the blot is a solid liability for Black.

Now let’s clean up White’s blot on the 23-point, by moving it to the 18-point, leaving the rest of the original position unchanged. Now we get to Position 51c:




Position 51c: White safeties his rear blot.

Bringing the rear blot to safety is a big deal, reducing Black’s equity by about 0.2 points. It’s now a somewhat close double and an easy take.

So at first it looks like the two changes, picking up Black’s rear blot and picking up White’s as well, look almost equivalent. Does this mean that the starting position, Problem 51, has about the same evaluation as 51a, namely a good double and a marginal take/pass?

No. The problem for White is that Black moves first, making his problems less serious and White’s more serious. Problem 51 is much closer in net equity to 51b than to 51c, and it’s a solid pass. In a bar-point holding game, trailing White blots become a real liability once Black starts to build a board. Couple that with a 36-pip disadvantage in the race, and White’s in too deep a hole.


Solution: Black should double, and White should pass.