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Problem of the Week #137: Solution
02-14-2012
, 03:18 PM
Problem of the Week #137: Solution
Money game, center cube, Black on roll.
Black to play 5-5.
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.
Problem 137 shows a pretty normal-looking mutual holding game. Black was two pips down in the race (114-112) prior to rolling. But he fired a great shot, double-fives, which moved him to an 18-pip lead. What should he do?
The normal rule with a solid lead in a holding game is to disengage from the back. That would suggest 20/10 and 16/11 with the first three fives, and then either 11/6 or 10/5 with the last five. Of those two choices, 11/6 would dominate because it leaves fewer shots (14 instead of 15) and the blot on the 10-point is a little more useful as a landing spot when clearing the 13-point.
“Clearing from the back” is a reliable general principle and I think most players would play 16/6 20/10 quickly. Nonetheless, it’s a huge blunder! Let’s see why.
Poker players are accustomed to seeing their hand from different points of view. Their first point of view is “What do I have?” The next point of view is “Based on what I’ve seen so far, what do I think my opponent has?” And a further point of view is “Based on what I’ve done so far, what does my opponent think I have?” As poker players acquire experience, they move gradually from a view that only looks at their own hand to one that incorporates all the information they have so far about their hand and their opponent’s. Failing to think on levels beyond a simple “What do I have?” gets very expensive very quickly.
Backgammon players face a variation on this same problem. Even though your opponent’s position is in full view, many players don’t really look at the unique features of their opponent’s structure when considering a checker play. Instead, they imagine they’re facing a sort of generic structure, one with no unusual weaknesses, and decide on the best play against that structure. Often, however, your opponent’s position has some exploitable features, like inner-board blots, dead checkers, or stripped points, all of which can combine to make some choices better than others.
Instead of just deciding to “move from the back, because I’m ahead in the race”, let’s look at White’s position a little more closely and see if anything prods us to do something different. The first feature we notice is that White’s outside points are all stripped, and his only inner-board spare is on the 4-point, giving him a 3 to play. That means that unless White can roll a double or hit something next turn, a lot of his rolls containing a 4, 5, or 6 must be pretty bad for him. Since we have to leave a shot anyway, that insight leads us directly to the best play: 16/1 6/1! Instead of leaving a shot but allowing White to move freely when he misses, we stay back and keep up the pressure, giving White some good rolls but lots of bad rolls as well.
Solution: 16/1 6/1
Money game, center cube, Black on roll.
Black to play 5-5.
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.
Problem 137 shows a pretty normal-looking mutual holding game. Black was two pips down in the race (114-112) prior to rolling. But he fired a great shot, double-fives, which moved him to an 18-pip lead. What should he do?
The normal rule with a solid lead in a holding game is to disengage from the back. That would suggest 20/10 and 16/11 with the first three fives, and then either 11/6 or 10/5 with the last five. Of those two choices, 11/6 would dominate because it leaves fewer shots (14 instead of 15) and the blot on the 10-point is a little more useful as a landing spot when clearing the 13-point.
“Clearing from the back” is a reliable general principle and I think most players would play 16/6 20/10 quickly. Nonetheless, it’s a huge blunder! Let’s see why.
Poker players are accustomed to seeing their hand from different points of view. Their first point of view is “What do I have?” The next point of view is “Based on what I’ve seen so far, what do I think my opponent has?” And a further point of view is “Based on what I’ve done so far, what does my opponent think I have?” As poker players acquire experience, they move gradually from a view that only looks at their own hand to one that incorporates all the information they have so far about their hand and their opponent’s. Failing to think on levels beyond a simple “What do I have?” gets very expensive very quickly.
Backgammon players face a variation on this same problem. Even though your opponent’s position is in full view, many players don’t really look at the unique features of their opponent’s structure when considering a checker play. Instead, they imagine they’re facing a sort of generic structure, one with no unusual weaknesses, and decide on the best play against that structure. Often, however, your opponent’s position has some exploitable features, like inner-board blots, dead checkers, or stripped points, all of which can combine to make some choices better than others.
Instead of just deciding to “move from the back, because I’m ahead in the race”, let’s look at White’s position a little more closely and see if anything prods us to do something different. The first feature we notice is that White’s outside points are all stripped, and his only inner-board spare is on the 4-point, giving him a 3 to play. That means that unless White can roll a double or hit something next turn, a lot of his rolls containing a 4, 5, or 6 must be pretty bad for him. Since we have to leave a shot anyway, that insight leads us directly to the best play: 16/1 6/1! Instead of leaving a shot but allowing White to move freely when he misses, we stay back and keep up the pressure, giving White some good rolls but lots of bad rolls as well.
Solution: 16/1 6/1
