Problem of the Week #27: September 6


Cash game. Black owns the cube.




Part (a): Black on move. Black to play 2-2.




Part (b): White on move. White to play 4-2.

These both seem pretty staright forward. I look forward to Bill's discussion,

Position 1 : Make the 4 pt, move up with the back checker, and hit.

Position 2: Run out as every other play is very ugly.

a) Black is behind in the race, 222 to 101, so timing is not an issue in hitting white. Can black turn this from a backgame into a containment game? It doesn't hurt to try -- if he can trap a white checker, white's board will crash quickly. If he fails, it likely will be because white escapes, not because his board crashes. The best play for going forward is 6/4(2), 18/16*, 24/22, building the inner board, hitting a checker that will hopefully be contained, and getting the extra checker on the 24-pt in the best position to get into play. I considered 16/14 instead of 24/22, duplicating the 3 white may need to enter from the Bar instead of leaving a blot 5 away, but black's not too concerned about losing any timing, so getting hit is not a disaster, and he needs all his checkers in play.

b) White's goal is to get out of Dodge and back to his home. He won't accomplish that by waiting for the Marshal to gather a posse. Moving 24/18 leaves direct 5's and 3's, plus 7's and 8's, 29 rolls in all, but black misses over 19% of the time. And when black hits, he potentially leaves a blot that white can hit in turn -- a likely winning combination.

White's best alternative is 24/22, 6/2, preparing to jump out of the black's home board without completely stripping the builders from any of his prime points. Black won't point on him (except with the miracle 33), and if white get's a return shot black may be stuck on the Bar for a few rolls while white gets home. This scenario is more likely with this move. Also, if black doesn't hit white on the 22-pt, white is likely to have some indirect shots as black spreads out in an attempt to contain the white checker.

Given these two scenarios, I'd opt for 24/22, 6/2 because it's less likely to constrain my next moves. If I'm hit after 24/18, then one die of my next roll is forced without a direct shot. If I'm hit after 24/22, then 97% of the time I have a direct shot back. And if I'm not hit, I expect to have more shots next turn, and less than an 80% chance of being hit when I finally escape Dodge.

a) It looks like black is majorly screwed here.
I don't think hitting helps so much at this stage. However, I guess the only hope is to build some sort of prime, hit white and force white to eventually break the 6 point.
So black does not want to get hit in this position because it will make it much harder to block white.

So, 18/16* seems necessary. After that, 6/4 (2) and 12/10 to try and stop white from hitting the blot on the 10 point.

b) White should play 1/3 and hope to get the check out next roll. 17/21 looks like the best 4 available.

a) First question is whether or not to hit. With the gap on the 18-point and the ability to make the 4-point now, I think Black still has decent equity by hitting now, although it might be closer than many people think.

So start with 18/16* 6/4(2). Then Black wants to stay as far back as possible and maintain contact otherwise, and activate as many checkers as possible, so 24/22 to accomplish both those goals.

b) Running out is initially tempting, but nearly every roll by Black hits, while also bringing attackers/builders into play. Sometimes you just run out anyway, but I think 1/3 19/23 is better here. Keep a spare on the 17-point which is pretty important, position the runner for the chance for a real leap next move, and bury a checker that is pretty much useless anyway.

a) We have a really decent backgame with excellent timing. Of course the thing about well-timed backgames is that even if they might leave you as a favorite to win sometimes, then you're getting gammoned an awful lot. So I think we should hit and try to win this going forward. If we can jump some of those spares from the 24 and 22 point into the outfield and pick up the second white checker then white could face a decent amount of difficulties bringing it home. So I'll play 6/4 (2) 18/16* 24/22.

b) 24/18. Nothing else makes any sense.

a) 6/4(2) 18/16* 12/8

With 2 White blots, trying to win the straightforward way looks reasonable and not too commital. For the 4th deuce I prefer 10/8 slotting the expected prime.

b) 24/18

What else ? Burning 25% of the spare pips seems premature.

1) Make the 4 point before doing anything else.

Since the bar point is open, I'm inclined to try to win going forward. Hit the checker on the 16 point and play 10/8. You don't really want to make the 10 point since you've got the 4 point locked up. I don't think getting hit will increase your gammon chances all that much since you've already got 6 in the back quadrant. So it's not really a big loss if he hits coming in.

2) Just run. I don't think there's a lot of value in burying a checker. It looks like everything will hit except 64 and 66, but that's okay. By moving into the outfield, you basically force black to hit. This means that he loses control over his checkers and this stops him from consolidating anything.