Problem of the Week #24: August 16


Cash game. White owns cube. Black on roll.




Part (a): Black to play 5-4.




Part (b): Black to play 5-4.




Part (c): Black to play 4-3.

a i go 13-4, bring down another checker to try to close out our board

b i go 15-10 15-11, gives us good chances of making the 8-point or hitting if he manages to run one of his back checkers out, or moving into position to make the 3-point next roll

c i think i go 5-2 4-off, although there's probably something i've missed that leaves us less bad numbers

The key theme in all of these positions is gammon.

With that in mind my play in each position is

a) 7/2* 13/9, I'm not afread of getting hit and attacking makes gives plenty of numbers that make the 2 or 3 point in the next roll.

b) I want to make the 3 point in this position, so to give myself ammunition to close the point, I lift the 13 point and play to 8 and 9.

c) I want to win gammon and because the opponents home board do scare me at all, I quickly take 2 checkers off. The single win is almost certain even if I get hitted.

Wow stunning first post. This seems absolutely right to me. I'm wondering if all these positions are from the same game actually.

Good observation. The three positions are all indeed from different stages of the same game.

Grunching...

In (a), what are the reasonable candidates?

21/16 13/9: Play on both sides. Get the back checkers moving with a big racing lead, the better structure, and a blot loose in Villain's home board. Meanwhile, bring down a builder for both the front and back of the prime. The back checkers stay connected, and 4s are duplicated to hit.

13/8/4: Stay safely buttoned up and create another builder/attacker.

13/8 13/9: With a close to dominating position, set up your checkers to try to finish Villain off.

7/2* 13/9: Seize the moment and attack now.

OK, now, what to play? 7/2* seems like the least useful option, with few additional builders available and White not threatening much of anything anyway. Again because White has few threats, going nuclear with 13/8 13/9 seems too loose. 13/8/4 seems solid enough, but now Hero has no spares for high numbers, and may be forced to play several awkward rolls while White continues to improve his front position.

So, we're left with 21/16 13/9. Which seems like the best option to me.

On to (b)...

15/10 15/11: Completely safe play, in a dominating position. Why goof around? You'll win your share of gammons without trying to catch another checker.

13/8 13/9: White's not dead yet, so maximize your chance to complete the prime and/or attack a slot. Meanwhile, give White some awkward rolls by continuing to hold vs. his midpoint.

15/10 13/9 or 15/11 13/8: We are dominating and the only remaining question is to maximize gammon chances by trying to catch another checker. So leave a double-shot at Villain's midpoint. If we are hit, so what?

No real additional analysis at this point, but 15/10 15/11 seems most reasonable to me.

On to (c)... just minimizing shots with 4/o 5/3 seems obvious to me. There are a ton of bad rolls after 4/o 3/o.

I think it's worth noting that your gammon chances are just fine in all variations after the "safer" moves. In (c) in particular, the best way to win a gammon is to not get hit IMO. Sure, taking two off gets you to an even number of checkers left, but you are still going to have to roll very well to not miss once.

Meanwhile it's not just your next roll that leaves far more shots, if you take two off. You also get a ton of repeating shots happening.

a) 21/16 13/9. We are way ahead in the race and now seems like a good time to get off the anchor. We have the stronger board and a 4 prime and white has a blot in his home board and his midpoint is stripped. If we wait we are likely to have to leave the anchor a few rolls down the road with white having a stronger board.

b) 13/8 13/9. I really want that 3 point. Slotting it seems unnecessary and risky. Getting hit would give white a good opportunity to grab it and significantly reduce his gammon chances. Getting hit by an indirect shot is not a disaster with whites home board. Clearing the 15 point seems too passive, and leaves us without ammunition if white rolls a deuce.

c) 4-off 3-off. Gammon looks close and again whites board means that we're still in great shape to win if we leave a shot and get hit.

*g*

a) 13->4
b) 13->8, 13->9
c) 5->2, 4 off

a) 13/4
b) 15/10, 15/11
c) 4/off, 5/2

a) It looks like white's position will collapse in a few rolls. Breaking the anchor on 21 is unnecessary and looks quite dangerous. I'd just go with 13/4 and await developments

b) In this case, I like the slotting play and there is very little that can go wrong. So, 13/8, 7/3

c) 4/off, 5/2
You want to try and avoid an odd number of checkers on your highest point because there will be a lot of rolls that give you trouble on your next roll. Bearing off the extra checker is not worth the risk. You still have a decent chance at a gammon provided you don't get hit.

Surprised that no one likes the slotting play for part b. It seems like a routine move in this type of position where white will have a very difficult time starting an attack.

I'm attacking here. White's home board blot plus black's anchor means that there's not much of a downside to the attack. Also, white's ace point anchor is blocked. I'm looking to prevent white from seeing daylight by inching the anchor forward.

After playing 7/2*, 13/9 is automatic to maximize covers.

This seems pretty simple. Break the 13 point and give yourself ammunition to make the 3 point. This also gives you an opportunity to see white's midpoint broken and potentially giving you yet another checker back two or three rolls from now.

Breaking the 15 point accomplishes neither goal as well as breaking the 13 point. Slotting the 3 point is silly. Save the attacker for when white rolls a 2 and moves up.

Take two checkers off. White has already crunched, so you're playing for the gammon. Even numbers of checkers are better than odd numbers (since odd numbers are wasteful), so shuffling the checkers around to avoid leaving a shot isn't as valuable. I think you had an odd number of checkers, you might prefer to shuffle and minimize shots (depending on how close you were to winning the gammon, etc).

You don't have immediate covers in the next roll, and about 1/3 of the time white is going to attack that blot when he rolls a 2. This will set you back a good number of rolls because you've got to bring checkers around to try to stamp out that blot. In the meantime, white is likely to roll another 2 and make the advanced anchor.

At the cost of introducing two more shots, you make it very scary for white to move up (since he knows he will be attacked, and being stuck on the bar increases his gammon chances immensely). And now he might prefer to just sit with three anchors on the ace point and essentially concede the 3 point to you.

I looked at the position again. If white succeeds in hitting the blot and then covering, that will be a bit of problem. However, it is not likely at all. First of all, as you stated, the hitting chances are about 1/3. So, even assuming white is able to hit right away, he will only roll another 2 about 1/3 times. Furthermore, white has a blot on his home board which will require a 2 or a 5 to cover. So, the only rolls that are really good for white are 2/2 and 5/2.

If white doesn't get one of these rolls, black can potentially hit the blots on the 22 or 17 point and really make life difficult for white.

However, playing 5/4 from the 13 point and saving some checkers to hit white if he tries to move up definitely has some merit. So, maybe that's the better play.

If he sticks you on the bar, you're not going to be able to attack that blot for at least a couple rolls (unless you roll 44). So he may get a few chances to make that point.

Hitting a blot isn't an automatic win for you. A fourth checker back means that he can make two anchors. If he makes a second anchor, he has the beginnings of a backgame. His timing looks bad right now, but it can get better (for example, if you hit go for the 5th checker and he spends a couple rolls on the bar, or if you roll big doubles).

Just in general, I think slotting without having a direct shot to follow-up on the very next roll is too risky. Your opponent will miss twice in a row only 4/9 of the time, meaning that he's a favorite to hit if he gets two shots at you.