Problem of the Week #152: September 30


(a) Cash game, center cube.




Black to play 6-1.


(b) Cash game, center cube.




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.

Black will be slotting in one of these positions, while he plays safe in the other, but I have not yet figured out which is which. Over the board, I likely would have overlooked the slot, playing 13/7 8/7 in both.

Against one checker back, Black is losing the timing battle. That motivates him to slot. Working against that is the possibility that he could change gears, switching from a priming game plan to one of attack.

If his slot is hit, however, Black is better off when White has two checkers back. When White has only one checker back, the tempo gained by the hit may be just what White needs to complete his escape.

I'll post again after I think about this some more.

I think I would play 13/7 13/12 in both. My thinking is that covering on 7 is pretty clear, so the question is what to do with the 1? I can't come up with any compelling reason why 8/7 is better than 13/12... the advantage 13/12 has is that we at least crossover a quadrant which might prove useful down the line. Maybe I'm missing something?

a. 13/7, 6/5

b.13/7, 8/7

This is my answer as well.

"Prime an anchor, blitz a blot!"


Against the straggler, the slot is antithematic. You make the 3 even better for scrambling home. Hitting on the five, even open is much better. The open 5 point is an overprotected point. I want to wait for the stragller. In the meantime, i want to hold my material for an attack.

Against the anchor, it is a different story. Centercube. After the slot, and a miss, is it a take? My estimation is: if the slot survives, white is cooked. if we don't slot, it isn't a double.

a) 13/7 8/7

b) 13/7 6/5

When one of them has to be slotted, i would slot (a), because being hit is good for timing, and when the one checker manages to escape he is very much favourite. But with so little covering material i would opt for 13/12.

Grunch.

a) 13/7 6/5. We need a prime here. The lone checker escapes we are in pretty bad shape, with white in a controlled, well(ish) timed and dangerous position with the three checkers on the 14. Our counter shot if the checker escapes after we play 13/7 8/7 is not even that effective with such a weak board, with any five a huge number for them even if we do hit.

This spot looks like an illusion of strength with only two home board points made and so much to do running our own men out. We need to gamble a little for real strength. If hit, so be it, we have a backgame.

b) 13/7 8/7. White is in imminent danger of a severe(ish) positional collapse here without the extra man on the 14 they have in a). Even if they run one of the two men back, they still have to get the other which is a relatively longtail event in this spot. If we get hit we are in pretty poor shape, and the risk/reward here looks way off for a slot imo. Just play safe and watch white's position worsen.

+1

Wamy, this may be a longshot, but are you studying for a statistics exam currently?

One of these days, Bill will present a two-part problem where both answers are the same. Today, however, does not seem to be that day.

In Part (a), White has a big advantage in timing. With 3 checkers on his 11pt, and 3 spares inside, he can probably outwait Black in this prime-versus-semi-prime situation. I like the slot.

In Part (b), White’s timing is significantly worse. Except for 63, his 6s play poorly already. In addition, even if Black does not make his 5pt right away, and White manages to escape with one checker, Black will still have the other trapped. There is less urgency to make the 5pt here than there is in Part (a). I’ll try the safe play.

My Solutions
Part (a): 13/7, 6/5
Part (b): 13/7, 8/7

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. My record at this writing is 54%.

No sadly. Why?

"longtail event" phrase from original post.

(a) Pip count: Black 145 - White 137
If we don't close the bar point, White can escape the back checker (at least to the outerfield) with 9 rolls(63,53,54,55,65) and can escape partially with 8 other rolls (41,32,51,52) for a total 17 rolls, almost half of his rolls.

If we cover the bar point, White can now only escape with 4 rolls (63,53), a significant improvement. I don't hitting him loose will gains us a lot compared to a containment move, even if usually the guidelines say "contain many checkers" and "attack the lone checker".

Now, which containment roll is better? We have these options:

1) 22/16 8/7
2) 13/7 8/7
3) 13/7 13/12
4) 13/7 6/5

(1) seems too risky as White can pound of us with several rolls. (4) is also risky, but there is a big benefit if we're not hit and we can cover the 5-pt: a nice 5 or 6-prime! Black will cover with 23 rolls (any 3,any 4,62,22). The downside is a 20-pip loss in the race and a 3rd man sent back. I'm not sure if it's worth it. QF makes me think it is, but otherwise, I think I would discard slotting the 5-pt. For once, I'll ride the QF and slot.

13/7 6/5

(b) Pip count: Black 145 - White 149

Now, Black has the small race lead and has White with 2 men back as well, so slotting is not in my mind. It would then be between 8/7 and 13/12 for the ace after 13/7. 13/12 will give Black one less roll to hit if White was to escape (although White could be more inclined to keep his anchor). On the other side, is the spare better on the 8-pt or on the bar point? I don't see much of a difference, but the slightest of differences could top one play over the other. I keep the extra roll to hit.

13/7 8/7