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Problem of the Week #13: Solution
06-06-2009
, 09:49 PM
Problem of the Week #13: June 2
Cash game, center cube. Black on roll.
(a) Black to play 5-3.
(b) Black to play 3-1.
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Many backgammon problems boil down to a simple question: hit, or don’t hit. In essence, backgammon is a pretty simple game. In general, you want to make points, and in general, you want to hit.
When you can hit a checker on the other side of the board, gaining both time and racing equity, you almost always want to do so. (The only exceptions occur when the alternative is to make a very strong priming or blocking point on your side.) But when the only possible hit is to hit a blot in your inner board, the choice is more difficult. Now you’re risking a significant loss of race equity if you get hit back, so the hit is rarely automatic. For a hit in your inner board to be correct, one of these two reasons usually applies:
> You’re hitting on a key blocking or priming point, which you very much need to make.
> Your opponent has so many threats that a tempo play is necessary; that is, you’re hitting to prevent your opponent from attacking with his entire roll.
Keep these ideas in mind as we look at Problem 13a.
This problem is best solved by a process of elimination. Black will enter with his three, Bar/22, and choose among four fives, none of which stands out as an excellent play. Try discarding the obviously worst choices first until you’ve narrowed the field, then see which looks most appealing between the survivors.
6/1*. Hitting loose on the ace-point in the early game is a tantalizing play. It often looks necessary, it’s almost always wrong, but on the occasions when it’s correct, it’s usually correct by a lot. The hit is a tempo play (designed to take away half of the opponent’s roll), but to be correct, the need for a tempo play must be huge. That means that your opponent needs plenty of builders ready to pounce, and you absolutely must put him on the bar. Here the play is wrong because White doesn’t have enough serious threats. True, White has some pointing numbers. But to make his 3-point, he’ll have to break his 7-point or 8-point. He’ll do that if he can, but it’s not a threat you need to guard against because of the broken points and the return shots. Meanwhile, 6/1* just dumps a checker out of play and risks losing plenty of ground in the race.
8/3*. The same idea as 6/1*, but even worse. Black strips the important spare off the 8-point, while leaving almost twice as many shots as 6/1*.
11/6. Better than the first two choices by a lot, but look at that hideous stack on the 6-point. In the absence of crushing threats, the idea in the early game is to unwind stacks, not make them worse.
13/8. Doesn’t do anything great, but doesn’t damage the position either. Here it’s the winner by default, as the other choices are all ruinous.
In Problem 13a, White’s threats weren’t all that serious, so a quiet play made sense. If White had a more dangerous collection of builders, 6/1* might have become the best play.
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Problem 13b is a little different. The only available hit, Bar/24 6/3*, is now a horrible blunder. It has all the disadvantages of the hits in 13a, but in addition it leaves Black stuck on the 24-point, just when Black needs to be taking some small risks to get an advanced anchor in White’s board.
Instead, Black needs to enter with the three, Bar/22, which gives him both an escaping number (6) and a threat to make an anchor, and then consider whether 24/23 or 22/21 is his best ace. The former is a little safer since Black avoids the point White most wants to make next (his 4-point). The latter play moves to that point and tries to get the best anchor available.
Either play might be right depending on circumstances. Here the circumstances favor moving directly to the 21-point. To see why, we’ll use a frequently handy trick in these sorts of positions. Find White’s best non-double that attacks or advances his prime, and see how that number plays on the other side of the board. The right play will often duplicate this number.
After Bar/22/21, White’s best non-double for advancing his prime is clearly 4-2, which plays 8/4* 6/4. But on the other side of the board, 4-2 is also a great shot, making the 20-point anchor. Eureka -- duplication!
Now consider Bar/22 24/23. White’s best non-double for moving his prime is 5-3, which he would play 8/3* 5/3. But on the other side of the board, 5-3 is pretty useless. Hence the 24/23 play creates a new great number for White, which isn’t the right idea. So Black should play the simple Bar/22/21.
Solutions:
a) Bar/22 13/8.
b) Bar/22/21.
Cash game, center cube. Black on roll.
(a) Black to play 5-3.
(b) Black to play 3-1.
------------------------------
Many backgammon problems boil down to a simple question: hit, or don’t hit. In essence, backgammon is a pretty simple game. In general, you want to make points, and in general, you want to hit.
When you can hit a checker on the other side of the board, gaining both time and racing equity, you almost always want to do so. (The only exceptions occur when the alternative is to make a very strong priming or blocking point on your side.) But when the only possible hit is to hit a blot in your inner board, the choice is more difficult. Now you’re risking a significant loss of race equity if you get hit back, so the hit is rarely automatic. For a hit in your inner board to be correct, one of these two reasons usually applies:
> You’re hitting on a key blocking or priming point, which you very much need to make.
> Your opponent has so many threats that a tempo play is necessary; that is, you’re hitting to prevent your opponent from attacking with his entire roll.
Keep these ideas in mind as we look at Problem 13a.
This problem is best solved by a process of elimination. Black will enter with his three, Bar/22, and choose among four fives, none of which stands out as an excellent play. Try discarding the obviously worst choices first until you’ve narrowed the field, then see which looks most appealing between the survivors.
6/1*. Hitting loose on the ace-point in the early game is a tantalizing play. It often looks necessary, it’s almost always wrong, but on the occasions when it’s correct, it’s usually correct by a lot. The hit is a tempo play (designed to take away half of the opponent’s roll), but to be correct, the need for a tempo play must be huge. That means that your opponent needs plenty of builders ready to pounce, and you absolutely must put him on the bar. Here the play is wrong because White doesn’t have enough serious threats. True, White has some pointing numbers. But to make his 3-point, he’ll have to break his 7-point or 8-point. He’ll do that if he can, but it’s not a threat you need to guard against because of the broken points and the return shots. Meanwhile, 6/1* just dumps a checker out of play and risks losing plenty of ground in the race.
8/3*. The same idea as 6/1*, but even worse. Black strips the important spare off the 8-point, while leaving almost twice as many shots as 6/1*.
11/6. Better than the first two choices by a lot, but look at that hideous stack on the 6-point. In the absence of crushing threats, the idea in the early game is to unwind stacks, not make them worse.
13/8. Doesn’t do anything great, but doesn’t damage the position either. Here it’s the winner by default, as the other choices are all ruinous.
In Problem 13a, White’s threats weren’t all that serious, so a quiet play made sense. If White had a more dangerous collection of builders, 6/1* might have become the best play.
-----------------------
Problem 13b is a little different. The only available hit, Bar/24 6/3*, is now a horrible blunder. It has all the disadvantages of the hits in 13a, but in addition it leaves Black stuck on the 24-point, just when Black needs to be taking some small risks to get an advanced anchor in White’s board.
Instead, Black needs to enter with the three, Bar/22, which gives him both an escaping number (6) and a threat to make an anchor, and then consider whether 24/23 or 22/21 is his best ace. The former is a little safer since Black avoids the point White most wants to make next (his 4-point). The latter play moves to that point and tries to get the best anchor available.
Either play might be right depending on circumstances. Here the circumstances favor moving directly to the 21-point. To see why, we’ll use a frequently handy trick in these sorts of positions. Find White’s best non-double that attacks or advances his prime, and see how that number plays on the other side of the board. The right play will often duplicate this number.
After Bar/22/21, White’s best non-double for advancing his prime is clearly 4-2, which plays 8/4* 6/4. But on the other side of the board, 4-2 is also a great shot, making the 20-point anchor. Eureka -- duplication!
Now consider Bar/22 24/23. White’s best non-double for moving his prime is 5-3, which he would play 8/3* 5/3. But on the other side of the board, 5-3 is pretty useless. Hence the 24/23 play creates a new great number for White, which isn’t the right idea. So Black should play the simple Bar/22/21.
Solutions:
a) Bar/22 13/8.
b) Bar/22/21.
