Problem of the Week #67: June 13


Cash game, center cube.




Black to play 4-2.


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 only two real choices to consider in Problem 67.

• Advance a backman: 24/20, 13/11
• Play safe: 13/7

White leads by 11 pips, 140 to 151.

Advance a Backman
Advancing invites an attack from White. After a Black split, White can hit and cover on the 20 point with 16 rolls (11, 22, 33, 44, 12, 13, 16, 23, 26, 36). In addition, he can hit and cover on the 24 point with 3 shots (66, 65). If fact, 66 plays quite well for White, allowing him to hit twice while making the 24 point and slotting the 20.

With a roll of 24, White can play 18/20*/24*, hitting twice. Similarly, the roll 14 gives White a double hit when he plays 19/20*/24*. Other loose hits occur with 6 rolls (15, 25, and possibly 35).

Even if we ignore loose hits on the 24 point, the only rolls that don't hit Black somewhere are 45, 46, 55, and possibly 34. Of these, 55 is a great roll for White, whether Black has split or not.

Play Safe
On the other hand, playing safe is no cup of tea. White still gets 16 chances to make the 20 point, while the roll 24 makes the 21 point. Otherwise, White has slightly worse timing than Black. He'll probably be forced to abandon his midpoint before Black leaves his. Black won't last much longer, however, and will end up burying checkers behind White's anchor if he tries to wait him out.

It's a close call, but sitting back seems like a sure path to second place. White's advanced anchor allows him to play aggressively. He'll be working to complete his prime. Black should challenge him.

My solution: 24/20, 13/11.

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. Grunch: I have been answering these problems without the use of a bot, and before checking the excellent solutions of others, since Problem 28. Including the tossups 39a and 62, my record at this writing is 47% correct.
22 Correct: 28a, 29, 30, 32, 35, 36, 38, 39a, 39b, 42b, 43, 44, 45, 47, 48a, 48b, 50, 52b, 53, 57, 62, 66. 25 Incorrect: 28b, 31, 33a, 33b, 34, 37, 40a, 40b, 41, 42a, 46, 48c, 49, 51, 52a, 54, 55, 56, 58, 59, 60, 61, 63, 64, 65.

13/7 is the obvious move and over the board, that's what I would do without thinking twice. Looking a little harder at the position, I'm struggling to find anything better. Black would like to make some progress toward bringing home the checkers from the 24 point. But, what can he do? 24/20 is already kind of sucky as there are a bunch of rolls that will point on his head. The only 2 that makes sense is 13/11. I suppose it is unlikely that white will roll the 5/2 or 6/1 to hit. Even if white does hit, he is really weakening himself by breaking the anchor and he'd be giving black a chance to anchor on the 20 point.
The only nice feature of 24/20 is that if white misses, his blot on the 14 point will come under some pressure and he'll either have to move the blot to safety or give black a direct shot.

Since black is going to have to move up at some point to prevent himself from getting stuck behind a prime, I'll go with 24/20, 13/11

If you make an anchor on the 5 (or escape a guy cleanly or hit the outfield blot), your chances go way way up, and I'm not really sure what your plan is otherwise. If you just sit there, you're giving him a free hand in the outfield to prime you. I can't really find wins by sitting there without rolling some perfect numbers on command (like 33/44 next turn, etc). And like the last problem, any number that points on your head is bad for you anyway if you sit back. And since there's no cube, there isn't much difference between getting 2 guys closed out onto the bar (although you're doubled out long before here of course) or getting primed into a crappy ace-point game where you're also just going to get doubled out.

24/20 13/11

24/20 is automatic for me. Look at where your spares are! You've got one spare on the midpoint and two spares on your 6 point. You've got to get moving otherwise you're going to mess up your prime (and your game). You also can't let white have free reign in the outfield.

Once this is done, there's no choice for the 2.

I see 2 alternatives to consider here: a) 13/7 b)13/11 24/20.

After 13/11 24/20 white has a lot of hits: 61,62,63,65,31,32,D3,21,D1,D2,D4 (18/36)
31,32,36 and 65 don’t play so nice in a).
The numbers 51,52,41 and 42 are awkward in a) but even-chance hits in b)
The numbers D6,64,54 and 43 are awkward in b) but small risk in a).

Conclusion: I would play 13/7

I know it comes under fire, but I still like 24/20 13/11. any other play just looks unnatural to me. 13/7 just doesnt seem productive enough.

24/20 13/11. have to get the back pips moving, and increases hits if white breaks out from 4 prime with the extra outfield pip.

The real question in my mind: when white doubles next turn is this a take or drop?

If we are doubled next turn, it would be a big take. all we have to do is anchor or escape and the game is equal again. when we are pointed on here, white will still only have a three point board and a fairly stripped distribution in most variations. Even though white is even money to point on us here if we split 24/20, (either pointing the front or rear checker with 18 numbers) some leave the midpoint completely stripped with 44 and 55.

I always have trouble with positions like this (Black’s low anchor vs a building prime, White high anchor vs a 4-prime in this case), but I will give it a shot.

Pip count is 151-140 in favor of White, 145-140 after the roll. Since there are 2 back men for each side, that very slight leading race for White is irrelevant.

Assuming neither side will roll a double for a while, White has more timing before having to either leave one back man alone behind or leave the midpoint. So that means that Black could well be squeezed out of his ace-point anchor, unless he wants to eventually leave his own midpoint or break his 4-prime. For instance, he could play 7/5 7/3 right now, but it would only delay the inevitable.

Therefore, his only viable 2 in my opinion is 13/11. That would leave two options for the 4: 24/20 or 11/7. White has a good chance to make his 5-pt next turn. Is it worse for Black to get pointed on that 5-pt or to be slowly primed? I say that in both cases it’s bad, so let’s try the play with the most hope and advance under the gun. Who knows, White could throw a 5 or a 6 and be forced to hit loose?

Let’s see if I learned something from the previous problem. My take:

24/20 13/11

(I wonder if the cube had been turned if that play would be too dangerous gammon-wise.)

Easy take. I don't even think white should double.

13/7. Keep the magical ace point

I do not quite agree that we only have two choices in the position. I am trying to get in the habit of looking at all possible moves. And I think it is important to do so in this position. Even if the alternatives look quite ugly at first glance.
If you move 24/20 13/11 we will probably be hit on the 20. As White has a high anchor he should not fear hitting lose. The safe play 13/7 may be prematurely striping the midpoint. So if white runs we will have to break it to hit. Our board is not strong enough that white would probably not have much trouble reestablishing a point in our home board.
Either of these moves seems okay even with their drawbacks.
I think we should also consider 6/2 13/11 yes I know it looks weird. But although 6/2 seems to put a man out of play, it does start a point. If we can make it having a board advantage might help us. Moving 13/11 puts a builder in a better place than 13/7. Since I would like to try to make the 9. (13/9 13/11 is a bit much even for me) And I would think that I might not mind if either of these men where picked up. A little recirculation might not be a bad thing in this position. I think this move might have the greatest chance of maintaining my structural integrity for the longest time.

I am also influenced by asking myself why Mr. Robertie would have a problem that seems to only have two possible alternatives. So although I am sometimes criticized for excessive love of the big play. And I am almost embarrassed because it looks a bit ugly.
I am stick my neck out a answer.
6/2 13/11

Grunch; 13-7.