Problem of the Week #138: Solution


Money game, White owns the cube, Black on roll.




Black to play 6-1.



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 138 shows an interesting blitz position. White’s been caught with a checker on the bar, another exposed blot in Black’s home board, and a third blot in his own outfield. Black has a three-and-a-half point board plus a few builders on hand. If White were helpless, Black would have a strong attack. Unlike the case with an opening blitz, however, White actually has a position here, with a strong board and a four-point block. If Black’s blitz fails, White will get the upper hand very quickly.

Black has four reasonable and distinct choices with his 6-1:

(a) Closing a fourth point in his board with 9/2.

(b) Hitting the outside blot with 22/15*.

(c) Hitting inside and picking up, with 10/4*/3.

(d) Hitting inside and leaving two blots, with 10/4* 9/8 or 10/4* 3/2.


Blitz positions tend to be tricky. In general, your top priority is to hit blots and make points. If you can do only one of these things, you’ve got a nice, easy decision. If you can do both, you’ve probably got a tough decision. If you can’t do either, you’ve got a choice between bringing down builders and moving your back men, and those can also be tough decisions.

I like to categorize blitz problems based on the strength of my inner board. (Assuming I’m the one doing the blitzing!) With a 2-point board, hitting blots tends to trump making a third point, because the third point still doesn’t make the board all that strong. With a 3-point board, a play that makes the fourth point is relatively very powerful. The same improvement occurs when going from a 4-point board to a 5-point board. In this area, making the extra point (all other things being equal) often trumps hitting another blot.

The other question to consider is just how valuable it is to hit the next blot. If you’re only attacking one checker, hitting a second checker is very important. If you already have two checkers on the bar, hitting a third is a low priority. Additional checkers have an even lower priority.

With those ideas in place, let’s look at our actual problem. First let’s note that among the hitting plays, 22/15* trumps both 10/4*/3 and 10/4* 3/2. Picking and passing leaves Black with a semi-dead checker on the 3-point, while leaving two blots is just too risky in light of White’s board. Another point to notice is that unlike the case in a normal blitz, we’re already a solid underdog in this position: no matter what play we make, our winning chances are only about 40%.

So our choice is between 9/2 and 22/15*. We have a 3.5-point board, so making the fourth point would normally be our default play in the absence of other factors. Here most of the other factors also point to building our board. White’s position is much stronger than in a normal blitz, so getting hit back could be immediately fatal. Hitting and escaping is nice, but we still have two more checkers to extract, and White has 21 very strong numbers (2s, 4s, and 55) on his very first shot.

For all these reasons, the best play is the simple 9/2, and rollouts confirm this. 22/15* is very slightly better at double match point, but 9/2 both wins more gammons and loses fewer gammons than any other play, moving it to the top spot in a cash game. The plays that hit in the inner board are much worse.


Can we tweak the position a little to make 22/15* the better choice? Let’s do some experimenting and see what happens.

Let’s start by relieving some of the pressure on Black. We’ll move two of his back checkers out to the midpoint.




Problem 138a: Black to play 6-1.

This change puts Black ahead in the race by 20 more pips. The count is now 121-147 in favor of Black. In addition, he now has more builders at his disposal that can reach his inner board pretty quickly. Is this enough to tip the balance in favor of one of the hitting plays?

Alas, no. Black’s raw winning chances have now risen into the low-50% range, so at least he’s a favorite in the position. However, 9/2 is still better than 22/15*, although the difference is closer. Once again, 22/15* is slightly better at double match point, but 9/2 wins more gammons and loser fewer, making it the overall winner.

Let’s give Black a little more help. This time we’ll bust up White’s board a bit.




Problem 138b: Black to play 6-1.

We’ve taken away White’s 5-point, moving the checkers back a bit. Now Black’s doing even better in the race, and has less to worry about if he does get hit. Does this change the evaluation?

Nope. In fact, 9/2’s edge over 22/15* is now even greater! The difference is that when Black covers the 2-point and White throws his best number – something containing a 4 – Black’s in much less danger of losing than before. Covering the 2-point is now the best play at double match point, and it still wins more gammons and losers fewer than before.

Let’s make one more try. From Position 138b, we’ll strengthen Black’s board by moving two checkers from his midpoint to his 5-point. Here’s the new position:




Position 138c: Black to play 6-1.

Does that change anything? Actually it does, a little. Making the 2-point is right by an even wider margin than in any of the other positions, but now we have a new runner-up: 22/15* has slid into third place, and 10/4*/3 has moved into a solid second place. This makes perfect sense. The closer Black gets to the actual closeout, the more important it becomes to eliminate White’s chance for an anchor. White’s blot on the 15-point is now increasingly irrelevant to the outcome of the game.

The moral of the problem: don’t underestimate the value of simply closing points in your board when conducting a blitz.


Solution: 9/2