Problem of the Week #10: May 11




Cash game, center cube. Black on roll.

(a) Should Black double?

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

I'm quite a backgammon beginner, but I see no reason for Black to double here.

The position looks really close. Pip counts are 126 White to 123 Black. Both have pretty strong home boards with White very close to making his 4-point (21) with a number of rolls next turn. Black isn't quite so close to making a prime as it looks at first and missing the 5-point hurts. I'm not sure how to put it but the game feels closer than it looks at first, when one would be inclined to think Black is winning comfortably.

If doubled, White should take.

Some more insight on how to evaluate these positions as a beginner would be appreciated.

Assuming even gammon changes, white would need 9 rolls to take. Black fans on 9 rolls.
But,
Position: Black has better prime, white has slightly better board.
Race: Black has better race, 3 pips , plus roll, plus fact that they have better prime.
Threats Black has 15 numbers to hit. (and also 1-1)

If black fans, it iss still not too bad for black, because white is not in the zone of close out.

In addition, white might pass or take wrongly.

My vote a) Double b) Drop

A) Double. Black has 16 combinations which hit a white blot without being reckless (4-x, 3-5, 3-1, 1-1), and nine combinations which don't re-enter (6-6, 6-5, 6-2, 5-5, 5-2, 2-2). If black gets one of the good rolls the chances for gammon should go way up, provided the cube has been offered and accepted. With one of the bad rolls, white still has to make the four point and escape with the back checker before there is any re-doubling. Black should generally offer the cube if it appears like a difficult choice for white, and this situation seems to qualify. In addition, there is added equity if white makes an incorrect take/drop decision in such a complicated position. This is by no means a comfortable cube offer as I'm always reluctant to be doing so with a checker on the bar, but the window of opportunity for white to accept may soon be gone.

B) Take. Black is only a 3:1 favorite to re-enter from the bar this roll, and misses hitting with several of those combinations. There is certainly some work to be done if black doesn't hit, but only 6-6, 6-5, 5-5, and 5-3 (which would be useful anyway) fail to do something about the blot on the four point. This is not such an easy take with the back checker nearly trapped, but the game is far from decided.

I think it is easier for me to play the white side and take black's cube offer, than it is to decide if the cube should be offered at all. This is certainly the most difficult Problem of the Week so far.

No double, take.

Black becomes too good to double when he rolls 44 or when he hits on a non-44 (15 rolls) and white dances (9 rolls). This is 171/1296 two roll sequences. There's no way that's enough market losers to make this a double. Not to mention that black will wish that he had not doubled when he dances 25% of the time (which is more likely to occur than the market-losing sequences).

Do you think white still has a take after a hit and 16, 26? I'm not sure, but they look pretty ugly (which are another 60 combos). The swing is pretty big after a hit, and we're hardly crushed even if we miss and white covers, so I'm leaning toward D/T.

I think he definitely can take after he makes his anchor (26). Looking at 16, I think it's questionable whether he can take. But if it's questionable, that means it's close, so you don't have a gigantic market loser anyway.

When things go "average" for you (you enter with a non-hitter), you still haven't lost your market. This means that you need your market losers to be huge swings in order for doubling now to be correct. I just don't think there are enough of them or that they are large enough swings to make it worth it.

Another factor to consider is that when you double, you give white full control of the cube. His ability to recube you when things go his way or to sit on the cube when things go your way means that he has added equity (or to put it another way, you lose some equity).

Perhaps the one thing that is making me wait is that white has no problem taking this cube. If white's take were questionable, then a cube here must be right. But if white's take is obvious, then turning the cube might be the mistake.

I also think you might be overvaluing your position if you dance and white covers. White only has one checker that needs to wiggle through your prime, and he's got plenty of time to do it. He also has better outfield control and your blot is a definite liability. As soon as white makes that fourth point, you're definitely in a scramble mode even if you're not "crushed."

Are there really no two roll sequences where black re-enters without hitting and white rolls badly enough? For example, black 3-2 with white 6-5 looks particularly nasty. There are also some questionable moves which got excluded from the hit/dance combinations such as a black 3-3 played bar/22, 10/7, 8/2*. I think 171/1296 is too conservative here.

Even if 171 is conservative, you still have a long, long way to go before you're going to start worrying about losing your market. Don't forget that you're also balancing against the 324 dances which put you as an underdog. It doesn't seem all that close to me.

You would have to do something to weaken white's position a little more, like maybe move the 2 point to the 1 point or put a second checker back and I think you would want to double.

I'm not sure black is an underdog after a white 6-6, but I get your point.

Black will however get at least another roll to re-enter and improve if the first roll dances. I believe white has to do something about the blot on the four point, and escape with the back checker before reaching a re-double position with black still on the bar. So black is not crushed by failing to come in right away.

I would not want to be white with two checkers back even holding the cube here, unless this involved an anchor on black's five point. Having the two point is going to save gammon, but white will need a hit before black bears five off and the timing to have saved something of an inner board to cube black out of the game.

I agree with you that it's an easier decision for white to take the cube, than it is for black to decide to offer. I don't think that white hasn't any problems arriving at such a decision however.

If I thought white would have any chance of dropping this, I would ship the cube without hesitation. But I feel it's really more of a "bluff" cube to induce opponent to make a mistake, and not really a decision about the position itself.

I would be very surprised if this position turns out to be a drop. Or even if it's close to a drop.

I don't think there is a convincing argument that white should drop, but I haven't the skills to determine how close it may be. I tried to look at whether I would prefer to be playing the white side holding the cube or black, and decided I would rather be the underdog with the cube in this spot.

It's possible that Bill found a specific example of a position where there is so negligible a difference in EV between offering the cube or not, that it doesn't really matter which decision is made. I have to offer though, if I think there's maybe even a 10% chance over the board that white will drop.

A good general rule is that there will be no photo-finish problems in these little quizzes. I'm looking for positions that pretty clearly illustrate some point (whatever it might be).

Why are the boards you use rotated differently (24 top left)? Is this standard? It's tripping me out.

pretty sure dbling is wrong. u are probably not going to win more than 60perc here.

the equity of this turn will change more drastically than in most turns of bg, so wait until u see the result.

definitely take the cube if dbled.

Differently from what? All the Gammon Press titles and all the Cardoza titles, plus every issue of Inside BG, plus Magriel's book, plus BG Boot Camp, plus Classic BG Revisited, plus ... (you get the idea) all use the format of the lower player (Black in this case) bearing off to the lower left.

Exactly what 'standard' are you referring to?

This can often be an argument for doubling now.

Absolutly no way should you double while on the bar (generally speaking), way to many bad things can happen.Dance once and white is a big favorite to complete a four point board, dance again and white is one good roll away from doubling back and black would have to pass.

This is a clear take for white.

So then this is the most common way ("standard"). That answers my question. Thanks. I just play on the computer and my 24 is on the top right. The one book I've read diagrams it that way too. Hopefully I'll spend more time here and with your books and get used to it. Thanks again.

I'm going to go with no double, take, following Aaron's explanation. Double, take wouldn't surprise me; anything else would.

At first my thoughts were no double, take because a flunk or a non-hitting entry number is a realistic possibility. However, after some consideration as to why possibly double, it occurred to me that there are some good reasons to do so. First of all, you're a favourite to enter with a decent chance of hitting. If black flunks, white has 2's, 4's, 7's and 9's to cover the 4 point and so is a healthy favourite to do so. However, that would not change the winning chances of black too drastically, because he is ahead in the race and has a white checker behind his strong defensive board. Blacks chances to win are intact, even after flunking and white covering the 4-point. On the other hand, if black hits, there is a great and very realistic gammon possibility (and perhaps more with the crushing double 4). This leads me to thinking it is a double. As for white, I would take it without too much thought (perhaps wrongly so?).

Edit: the gap on blacks 5-point makes it a take, i think