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Problem of the Week #151: Solution
09-12-2012
, 05:49 PM
Problem of the Week #151: Solution
Cash game, Black owns the cube.
Black to play 5-1.
Note: All ‘cash game’ problems assume the Jacoby Rule is in effect. That is, you can’t win a gammon unless the cube has been turned.
Root Numbers
In backgammon, a root number is just a dice throw that damages or destroys your position. We mostly encounter these by accident, when we throw an awkward shot that can’t be played except by wrecking our inner board or leaving a bunch of blots somewhere.
Root numbers don’t always happen by accident, however. Sometimes the only way of saving a hopeless position is to notice that by making a certain play, you can create a few root numbers for your opponent which wouldn’t exist otherwise.
Problem 151 is a good example. Black is in a pretty bad way, with three checkers trapped behind a 5-prime, none at the edge, and a front position which is collapsing. Black owns the cube, and most players would be thinking about simply avoiding the gammon. With that in mind, Black has a few obvious choices:
(1) 6/1 6/5. Since Black has to play the five on his side, this is the only play that doesn’t expose another blot. Should be good for saving the gammon.
(2) 8/3 24/23. This keeps a strong inner board, and Black will save more gammons from having the 23-point anchor than if he’s back on the 24-point.
(3) 8/3 23/22. This tries to get to the edge of the prime, but White has too much leeway. Sixes now hit and jump, while twos, threes, and fives attack on White’s 3-point.
If these were the only plays you considered, you’d probably choose play (2). Making the 23-point saves a few gammons and offers slightly better winning chances than remaining back on the 24-point. Leaving a shot is too bad, but breaking your board to avoid a shot will cost you some gammons down the road anyway.
The best play, however, hasn’t appeared on our radar screen yet. Take a look at
(4) 6/1 24/23!
Black makes the better anchor on the 23-point, but leaves a shot on his 6-point rather than his 8-point. At first glance this seems nonsensical. Why break an inner-board point instead of an outer-board point? But on a second glance the reason becomes clear. By making the 23-point and keeping the 8-point, Black blocks sixes from White’s 23-point and 8-point, leaving White totally free to play sixes only from his 7-point. Although White can run with 6-4 and 6-5 and play 8/1* with a 6-1, rolls of 6-2, 6-3, and 6-6 force him to break his 7-point. Black’s play has created five root numbers, and while those numbers don’t lose for White, they do give Black some real chances in the game. After the sequence Black 5-1: 6/1 24/23 and White 6-2: 7/1* 7/5, Black’s winning chances are in the 36% range with a few gammons, much better than the 14% to 15% chances he has after other plays of the 5-1.
A root number can ruin a good position, but finding plays to create root numbers for your opponent is difficult. Look for them in positions where both players have strong blocks and each side has some men back, and then look to see how your opponent’s big numbers play. Almost any position can handle small numbers; it’s the big numbers that can cause a problem. Above all, don’t give up on a position just because you’re losing. Stay alert, and you’ll see that these kind of plays can occur more often than you think.
Solution: 6/1 24/23
Cash game, Black owns the cube.
Black to play 5-1.
Note: All ‘cash game’ problems assume the Jacoby Rule is in effect. That is, you can’t win a gammon unless the cube has been turned.
Root Numbers
In backgammon, a root number is just a dice throw that damages or destroys your position. We mostly encounter these by accident, when we throw an awkward shot that can’t be played except by wrecking our inner board or leaving a bunch of blots somewhere.
Root numbers don’t always happen by accident, however. Sometimes the only way of saving a hopeless position is to notice that by making a certain play, you can create a few root numbers for your opponent which wouldn’t exist otherwise.
Problem 151 is a good example. Black is in a pretty bad way, with three checkers trapped behind a 5-prime, none at the edge, and a front position which is collapsing. Black owns the cube, and most players would be thinking about simply avoiding the gammon. With that in mind, Black has a few obvious choices:
(1) 6/1 6/5. Since Black has to play the five on his side, this is the only play that doesn’t expose another blot. Should be good for saving the gammon.
(2) 8/3 24/23. This keeps a strong inner board, and Black will save more gammons from having the 23-point anchor than if he’s back on the 24-point.
(3) 8/3 23/22. This tries to get to the edge of the prime, but White has too much leeway. Sixes now hit and jump, while twos, threes, and fives attack on White’s 3-point.
If these were the only plays you considered, you’d probably choose play (2). Making the 23-point saves a few gammons and offers slightly better winning chances than remaining back on the 24-point. Leaving a shot is too bad, but breaking your board to avoid a shot will cost you some gammons down the road anyway.
The best play, however, hasn’t appeared on our radar screen yet. Take a look at
(4) 6/1 24/23!
Black makes the better anchor on the 23-point, but leaves a shot on his 6-point rather than his 8-point. At first glance this seems nonsensical. Why break an inner-board point instead of an outer-board point? But on a second glance the reason becomes clear. By making the 23-point and keeping the 8-point, Black blocks sixes from White’s 23-point and 8-point, leaving White totally free to play sixes only from his 7-point. Although White can run with 6-4 and 6-5 and play 8/1* with a 6-1, rolls of 6-2, 6-3, and 6-6 force him to break his 7-point. Black’s play has created five root numbers, and while those numbers don’t lose for White, they do give Black some real chances in the game. After the sequence Black 5-1: 6/1 24/23 and White 6-2: 7/1* 7/5, Black’s winning chances are in the 36% range with a few gammons, much better than the 14% to 15% chances he has after other plays of the 5-1.
A root number can ruin a good position, but finding plays to create root numbers for your opponent is difficult. Look for them in positions where both players have strong blocks and each side has some men back, and then look to see how your opponent’s big numbers play. Almost any position can handle small numbers; it’s the big numbers that can cause a problem. Above all, don’t give up on a position just because you’re losing. Stay alert, and you’ll see that these kind of plays can occur more often than you think.
Solution: 6/1 24/23
