Problem of the Week #35: November 1


Cash game. White owns the cube. Black on move.




Black to play 4-3.

Something a little different this time. Identify the worst of these three plays:

(a) 11/7 5/2

(b) 11/4

(c) 7/4 6/2.

11/7 5/2.
Black wants to clear outside points, create a good distribution that will allow him to rip off checkers and up his gammon rate.
Bonus question..
What is the best play?

First of all, I think that with White's board already crushed, Black's in very good shape and can play aggressively for the gammon without much risk.

That said, at first glance, covering the bar point looks good, creating a nice 5-prime. But since we'll have to break that prime real soon, I don't think it is that good. Black's goal is probably to wait for White to leave an anchor (which could happen soon after White bears in his last outfield checker) and then try to close the point where there's a blot left. By letting the bar point open (or slotted), White's 4s will eventually fore him to leave his 3-pt anchor.

In order to attack an eventual blot, Black must keep his checkers in front of White as much as possible. So putting a checker deep on the 2-pt is probably not a good idea, so (a) or (c) would be the worst play for me, but which one?

With (a), you leave 2 spares on the 6-pt, but none on the 5 and 4 pts. With (c), you have a spare on each of the 6, 5 and 4 pts, which seems more flexible. Plus you can handle an awkward 6 with 11/5 next turn if you don't get hit. (Note that getting hit here isn't really bad for Black, since you will recirculate easily and maybe hit another blot on the way.) In order, I prefer (b), (c) and (a), so my pick for worst move is:

(a) 11/7 5/2

I agree with the others -- 11/7 5/2 both wins fewer gammons and with an awkward distribution might even lead to future problems winning the game.

The prime has already done its job, now your goal is to keep a flexible distribution and be ready to either attack or bear off quickly.

11-7 5-2 is the worst, 11-7 8-5 the best ( if white hits we can easily attack is blot ), just slightly better than 7-4 6-2 ( that gives us good distribution ).

In Problem 35, White’s backgame has run out of time. He has a busted board, and although mathematically a possibility, it is unlikely that he will ever remake it. Black leads in the race 85 to 127. More importantly, White’s gammon count is 78. After this turn, White’s gammon count will exactly match Black’s pip count.

White’s primary strategy should be to save the gammon. Winning is still a possibility, however, without an effective prime, White must resolve himself to minimizing his losses. Conversely, Black’s main aim should be to increase his chance for the double game. As the gammon count shows, it’s a close thing, and in the long run Black will be rewarded for the extra risks he takes here.

The best thing going for White is his timing. It looks like he was able to release a backman on the previous move, so he has twelve pips to move before he crashes further. Black will be forced to begin dismantling his outside points before White kills another checker. This being the case, Black should be reluctant to make his bar point. As the shot counts below demonstrate, however, he may not have anything better.

• (a) 11/7, 5/2 - Black will leave a double shot on his next turn if he rolls 65, and a single shot with 54.
• (b) 11/4 - White can hit with any 4 or 6 (20 shots). If White misses, Black will leave another shot if he rolls 66, 65, 64, 63, 62 or 44 (10 shots).
• (c) 7/4, 6/2 - White can hit with any 2, 64, 44 and 11 (15 shots). If White misses, Black will leave another shot if he rolls 65 or 44 (3 shots).

Clearly, making the bar point is Black’s safest play. But look at the inflexible result. After 11/7, 5/2, Black is stripped everywhere except the two and six points. He will need some lucky rolls to clear the outfield block he just set up. Furthermore, if White abandons one of his rear points, Black doesn’t want to be stripped; he needs to have some builders at the ready.

Even if he is able to bear in safely, the stripped five point presents some special problems against a one-three backgame. During the bear-off, it is the only point from which Black can play a three or five. Black will have a lot of forced moves, and can easily get into trouble downstream, when the cost of being hit is much greater than it is now.

Another subtle disadvantage to making the bar point comes after Black clears his eight point. He will then have no sixes. Instead of racing home to win the gammon, he will have slowed himself down.

For these reasons, play (a) is Black’s worst move in Problem 35. Of the others, play (b) is probably best, as it forces White to abandon one of his backgame points to hit. If Black finds himself on the bar after play (b), he’ll have many return shots. Even when he misses those, he’ll be heavily favored to scamper home to victory.

My solution: Play (a), 11/7, 5/2, is Black’s worst.

For the Record
I am so often wrong that I like to post my record in these messages. It's kind of a truth-in-advertising thing. I have been answering these problems without the use of a bot, and before checking the excellent solutions of others, since Problem 28. My record at this writing is 44% correct.
Correct: 28(a), 29, 30, 32
Incorrect: 28(b), 31, 33(a), 33(b), 34

a) 11/7, 5/2 is the worst because it leaves you with the worst home board structure. It gets a checker behind the enemy and black will have to break the 7 and/or 8 point very soon. 11/4 looks best here. Black doesn't mind getting hit if it will cause white to break one of this anchors.

the first one is obviously the worst one

I agree 11/7 5/2. Clearing the back points and playing for the gammon are fundamental principals. I like this problem bc my first inclination was to make that play. But after further analysis, it occurred to be the worst.

I know it's only a detail, but the gammon count is in fact 79, since you need to bear off at least one.

Ok, I'm picky...

And so it is. Thank you, Uberkuber.

What about Crossovers?
Another reason play (a) is the worst: at a time when Black is trying to win a close gammon, play (a) doesn't make any crossovers.