Problem of the Week #16: June 21


Cash game, Black owns the cube. Black on roll.



(a) Should Black double?

(b) If doubled, should White take, drop, or beaver?

This is difficult; these positions are so rare that it's hard to have an intuition about how the game is likely to unfold. It looks like white has a take despite despite the potential gammon threat since black still has to bring home 3 men stuck behind a 5 prime, which will require him to roll 3 6's and an ace before too long. In the meantime white should be able to anchor on black's ace point (partly since black has no builders ready with which to attack) and have reasonable winning chances. There's also the possibility that black may roll very poorly and crunch his board before he has a chance to escape his back men. It looks to me like white will still have a take after most average sequences, and giving up the cube in this position could be costly, so I'm going to say no double / take. I could be grossly misevaluating this position, though.

I would wait, at this moment it seems too good to double. The only number that makes you crunch your board the very next roll is double 4. There is still some time left to escape those backcheckers with 6's and every 6 you roll gives you some more time.
Too good to double/drop.

Whether or not this is theoretically correct to double, then in praxis it's a must double. Several good scenarios can happen:

1) Your opponent passes a nodouble/take
2) You misevaluated and it is in fact double/take
3) Your opponent passes a double/take
4) It was a pass (or too good) and your opponent takes.

Only when the position is very clearly not a double and our opponent takes or it's very clearly too good and our opponent passes do we really lose anything by doubling. So there's a much larger scope the guy being doubled to make a mistake.

I do think this is a double anyway. Rolling a six would lose the market if black hasn't already. He will still have some trouble escaping the last two checkers, but he will win a gammon pretty much every time he succeeds. I'm gonna say double/pass. One of the problems for white is that even when blacks crack his board white still need to get 3 checkers in from the bar, which gives black some extra time.

Black wins a lot of gammons here, but white has a number of things in favor of his defense. Black has to roll reasonably well to get those back checkers out, and if he hits loose on the ace point to try to get a closeout, a return hit sends him back behind the 5-prime. A lot of sequences can make this very awkward for Black very quickly. So, I think it looks scary but white can still take. Black should double since almost all of his wins are gammons and the volatility is huge--an immediate 6 makes him way too good to double (that I'm certain about at least).

I think mute's comment that forcing the decision on your opponent here is right on the money. If I'm right that it's d/t, you will probably get some passes; if I'm wrong and it's TGTD, you will get some takes (from me, for one).

i think it's a no double/take, but not because it's too good to double. black only has 15 pips left before his 2 spare checkers are in his inner board and still has to roll 2 6s, a 1 and another 6 to get everyone out. i havn't done any math, but it seems like black is not favored to get all 3 out before his board starts to crumble. and once his board starts to crunch white will be able to redouble soon i think.

Here's hoping for not 0/3 on cube quizzes...

I'm pretty sure this is a no double/take. Black has too much work to do to spring those three checkers, but not nearly enough time. Black needs a 6 in the next three rolls, and then will need a six in the next three rolls after that, plus another six in the next three rolls after that (assuming that he squeezed out a 1 somewhere in the mix). 55/44 and (sometimes 33) are disaster rolls that completely destroy black's game. Once that board starts to crash, black loses all control over his checkers and is in deep trouble. If white has the cube, he can probably ship it right back and cash it without actually having to win it.

In the meantime, white could roll a couple 1s himself over the span of those 5-6 rolls and establish an anchor to make things harder for black. But even without the anchor, black might have some bearoff troubles if he isn't able to fill the gap. I think all of these problems for black add up to a take for white.

I don't play cash games, so I'm not sure about beavers, but it might be one because of white's nearly immediate cashing potential. (Edit: I take it back... the gammon possibilities might be too big here. When white cashes, he doesn't win as much as black does when he gammons.)

All of this being said, I would double against a weaker player. I think this gets dropped very often.

I had double/take originally then changed my mind to double/pass, because I figured even after black starts crunching he will still have some time before white get three checkers in from the bar. With all the take arguments presented I'm slowly changing my mind again, but I do still feel very good about doubling here as black even from a theoretical standpoint (what gammoner said about gammons and volatility).

Also from a quiz standpoint it's probably likely, that Robertie figures, that whites three checkers on the bar will get someone to incorrectly say double/pass .

I think that black may actually lose his market after a 6 and a fan from white (the gammon threat seems too strong), so I think double / take is probably right. I also agree that if it happened this position was not a technical double, it's still probably right to double against most opponents in practice because of the good chance of getting an incorrect drop.

I also wanted to point out that black has more time to extricate his back men than it appears, since when he doesn't roll a 6, the pip value of his roll will generally be well below average.

No redouble, take. Took me a while to see clearly on this one. White's three checkers on the bar are a ruse - he is not really in much worse shape than Black. Black also has three checkers behind a five-prime that will require lucky rolls to extract. Moreover, Black is in worse shape than White if he fails to extract the checkers quickly. While White will simply have to wait a while longer to roll on, he will most likely eventually anchor on the 1 and get a poor holding game. However, if Black fails to roll well, his board is going to get destroyed, which will ruin his game completely.

Edit:

I definitely agree with this. I think this is a no double by a slim enough margin that even a small chance of a drop would cause me to turn the cube. Also, my initial reaction was that this was double/drop, so I definitely think I would have dropped this OTB as White.

I agree with it that it's a double (changed my mind after thinking it over again and reading some comments) but I think white might have enough equity to take here actually. For black to escape his last three men he must roll 3 6's and an ace prior to the last 6, while maintaining his strong home board to swing 'em around. That's a lot of work with little timing. I tend to lean over to a take now, but I'm not even close to sure. White will need some time to bring in his three checkers ofcourse, even if blacks 5-prime would crumble to a 4-prime, but those 3 black checkers behind a 5 prime with little timing is pretty bad.

Awesome problem btw. Every single option has been raised already (apart from beaver).

Aaron mentioned beavering.