Problem of the Week #53: Solution


Cash game, Black owns the cube.




Black to play 3-1.


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.

Black has a simple choice in Problem 53: hit with 13/9*, or wait and make a point with 15/12 13/12. Last week we looked at some choices between hitting a blot or making a point in the context of early game play. This week’s position occurs much later in the game, but, as it turns out, the very same principles are still useful. Let’s again list the criteria we explained last time, and see how they apply to this position. Here they are:

> A strong home board favors hitting; a weak home board favors building a point.

> A big disadvantage in the race favors hitting; a close race is neutral.

> The more ground you can gain in the race by hitting, the more correct it’s likely to be. Hitting a blot in your opponent’s inner or outer boards is usually correct; hitting a blot in your own outer board is sometimes a mistake.

> Strong threats for your opponent favor hitting as a tempo play or making a defensive anchor; few threats favor making an offensive point.

> Stacks of checkers favor making a point; no stacks imply plenty of points already, which favors hitting.

Black’s home board isn’t totally undeveloped, but it’s still pretty weak, with just two points and not many point-making rolls on the horizon.

Unlike last week’s problems, here Black trails in the race by 41 pips (149 to 108). That’s certainly a big argument for hitting.

However, hitting here gains only 9 pips in the race. That’s not very much, which is some argument for playing safe.

Right now White has no strong threats; he’s just trying to get his rear checkers home over the course of the next few rolls. That’s an argument for making a point, especially since Black retains good coverage of the outer boards.

Black has a big stack on his 6-point, which is hard to improve at this stage except by dumping checkers in his board and then covering later. That’s a big argument for consolidating first.

One other factor comes into play which wasn’t relevant in our discussion last week: the strength of White’s inner board. Last time we looked at an opening position where White’s board was weak. Now it’s pretty strong. Obviously, that’s also an argument for playing safe, since being hit could be disastrous for Black.

The weight of all these considerations comes down strongly on the side of playing safe this turn with 15/12 13/12. Black still retains plenty of equity in the game since it will take White a while to get his rear checkers around the board safely. Meanwhile, Black can build his home board in peace and wait for a better time to hit.

How much better would Black’s board need to be to make the hit correct? Not much, actually. Just take two checkers from Black’s pile on the 6-point and make any new home board point, even the wretched one-point, and Black’s game is then good enough to hit!


Solution: 15/12 13/12

Your breakdown is extremely in depth and informative, I think this is an excellent post.

I like the hit because we have the 7 point which gives us a chance at making it difficult for white to get out of our base. If we didn't have that they'd just come in and right back out and move around the board too quickly for us to make up on pips. The hit also gives us an even combination roll to make a base point with a 6. 15 can cover the 9 and cannot be hit and while the 9 won't do a good job of preventing the opponent from rounding the board, it does leave him 1 less number to get out of the base.

It seems really close to me either way I'm guessing if you put it in an equity application the correct decision would garner a 2% edge at most but those numbers add up super quickly.