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Problem of the Week #106: Solution
06-16-2011
, 03:32 PM
Problem of the Week #106: Solution
Cash game, White owns the cube. Black on roll.
Black to play 3-3.
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.
Note that there was a mistake in the original problem, which was displayed with the cube in the middle. The position originally came from a match where Black was playing for an undoubled gammon. In a cash game with the Jacoby Rule in effect, Black would at least have doubled before this roll, if not at some earlier point in the game.
With that blunder out of the way, let’s look at the position.
After Black plays 11/5 with two of his threes, White will be stuck in a pretty bad ace-deuce back game. No matter how Black plays his last two threes, White’s looking at a position where he’ll only win about 20% of the time. The other 80% of the time, the breakdown looks like 30% singles losses, 40% gammons, and 10% backgammons. The only good news for White is that he still has some chance to make Black’s 3-point, after which he might be able to switch into a 1-3 or 2-3 back game, which offer slightly better chances because they don’t require quite as much timing.
Once Black plays 11/5, the fight shifts to Black’s 3-point. Whoever makes the point first will improve his chances somewhat. Black has to ask two questions: “How badly do I want the point?” and “What risks will I take to get it?”
For most of the time I’ve been playing backgammon, this position would have been played in one of two ways: either 11/5 13/7, bringing a new spare to aim at the 3-point, or the more flexible 11/5 13/10 24/21, moving a checker closer to the 3-point but also keeping it available to make the 9-point if necessary. The idea was to either make the 3-point naturally, or to hit loose there if White entered with a three, and cover later. Slotting the point with 6/3 was virtually never considered; it seemed counter-productive, since if White entered with a three and hit, he was very likely to make the point before Black could bring up more troops.
The modern view of these positions, however, has evolved somewhat. When you have your opponent pinned in a back game or a low-anchor game (ace-point or deuce-point game), and you have a solid grip on the position, it’s often correct to slot the last open point in your board rather than wait to cover it naturally. The slot turns out to be a play with a noticeable upside and almost no downside. If the slot works, you’ve eliminated a concern and you can put your checkers where they belong for the rest of the game. If your slot gets hit, you may lose the chance to make the point, but your opponent’s timing gets worse since you’ve lost 22 pips in the race. And, of course, you still might make the point even after being hit.
Another, even simpler way to look at the problem is to ask “What are the possible uses for my spare checker on the 6-point?” Right now, it can serve one of three functions:
(1) Help make the 3-point.
(2) Recirculate to help ruin White’s timing.
(3) Recirculate to help make the 9-point.
Notice that playing 6/3 serves all of these functions at close to zero risk.
So he best play with the third three is just 6/3. If White misses, you’ll cover with fives or tens (17 numbers). If White misses and stays on the bar with both men, you’ll also cover with fours and remake your bar-point later.
What about the last three? This one is a bit of a puzzle. Over the board, I would have had a slight preference for 13/10 over 24/21, since it adds 6-1 and 4-3 as useful cover numbers. Three-ply rollouts on both Snowie and XG, however, show a clear preference for 24/21 over 13/10 (by 0.03 in both cases). I’ll take an educated guess that 24/21 avoids some minor variations where Black either gets stuck back on White’s ace-point at an awkward moment, or gets forced to hit too many checkers on the way out. Those variations wouldn’t seem to amount to much, but perhaps they do.
Solution: 11/5 6/3 24/21
Cash game, White owns the cube. Black on roll.
Black to play 3-3.
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.
Note that there was a mistake in the original problem, which was displayed with the cube in the middle. The position originally came from a match where Black was playing for an undoubled gammon. In a cash game with the Jacoby Rule in effect, Black would at least have doubled before this roll, if not at some earlier point in the game.
With that blunder out of the way, let’s look at the position.
After Black plays 11/5 with two of his threes, White will be stuck in a pretty bad ace-deuce back game. No matter how Black plays his last two threes, White’s looking at a position where he’ll only win about 20% of the time. The other 80% of the time, the breakdown looks like 30% singles losses, 40% gammons, and 10% backgammons. The only good news for White is that he still has some chance to make Black’s 3-point, after which he might be able to switch into a 1-3 or 2-3 back game, which offer slightly better chances because they don’t require quite as much timing.
Once Black plays 11/5, the fight shifts to Black’s 3-point. Whoever makes the point first will improve his chances somewhat. Black has to ask two questions: “How badly do I want the point?” and “What risks will I take to get it?”
For most of the time I’ve been playing backgammon, this position would have been played in one of two ways: either 11/5 13/7, bringing a new spare to aim at the 3-point, or the more flexible 11/5 13/10 24/21, moving a checker closer to the 3-point but also keeping it available to make the 9-point if necessary. The idea was to either make the 3-point naturally, or to hit loose there if White entered with a three, and cover later. Slotting the point with 6/3 was virtually never considered; it seemed counter-productive, since if White entered with a three and hit, he was very likely to make the point before Black could bring up more troops.
The modern view of these positions, however, has evolved somewhat. When you have your opponent pinned in a back game or a low-anchor game (ace-point or deuce-point game), and you have a solid grip on the position, it’s often correct to slot the last open point in your board rather than wait to cover it naturally. The slot turns out to be a play with a noticeable upside and almost no downside. If the slot works, you’ve eliminated a concern and you can put your checkers where they belong for the rest of the game. If your slot gets hit, you may lose the chance to make the point, but your opponent’s timing gets worse since you’ve lost 22 pips in the race. And, of course, you still might make the point even after being hit.
Another, even simpler way to look at the problem is to ask “What are the possible uses for my spare checker on the 6-point?” Right now, it can serve one of three functions:
(1) Help make the 3-point.
(2) Recirculate to help ruin White’s timing.
(3) Recirculate to help make the 9-point.
Notice that playing 6/3 serves all of these functions at close to zero risk.
So he best play with the third three is just 6/3. If White misses, you’ll cover with fives or tens (17 numbers). If White misses and stays on the bar with both men, you’ll also cover with fours and remake your bar-point later.
What about the last three? This one is a bit of a puzzle. Over the board, I would have had a slight preference for 13/10 over 24/21, since it adds 6-1 and 4-3 as useful cover numbers. Three-ply rollouts on both Snowie and XG, however, show a clear preference for 24/21 over 13/10 (by 0.03 in both cases). I’ll take an educated guess that 24/21 avoids some minor variations where Black either gets stuck back on White’s ace-point at an awkward moment, or gets forced to hit too many checkers on the way out. Those variations wouldn’t seem to amount to much, but perhaps they do.
Solution: 11/5 6/3 24/21
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