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Problem of the Week #152: Solution
10-04-2012
, 02:16 PM
Problem of the Week #152: Solution
(a) Cash game, center cube.
Black to play 6-1.
(b) Cash game, center cube.
Black to play 6-1.
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.
Slotting in the Middle Game
Slotting is an easy idea to understand in the opening. When we slot the 5-point with an opening 2-1, we threaten to make a very strong point while unstacking a big stack. Since our opponent has no board, getting hit is just a minor inconvenience. Although it’s not a hugely correct play (splitting our back men is almost as good), it’s not a hard play to make because the downside seems pretty small.
Slotting in the middle game or the endgame is very different. Now your opponent almost certainly has a reasonable home board, so the cost from being hit is much greater. It’s also unlikely that you still have a stacked position at this point, so unstacking probably isn’t a big goal.
With a hit being more expensive and unstacking not so important, we’ve knocked out two of the three pillars supporting an early slot, and we’re reduced to just one: the value of the point itself. When we slot in the middle game, the point needs to be really important, and the chance of making it cleanly without slotting not so good. There is, however, a new factor affecting a middle game slot: the cube. A slot followed by a miss from your opponent may give you a good double, which in some cases is enough to tip the play in favor of slotting.
With those ideas in mind, let’s look at problem 152a.
The six is clear: 13/7. With the ace Black has a choice of two safe plays, 8/7 and 13/12, and the slotting play, 6/5. Of the safe plays, 8/7 dominates since it gives more ways to make the 5-point cleanly if White steps up with a three, and the checker in the outfield will have a few more hitting numbers from the 13-point if White escapes with 5-3 or 6-3. So now our choice is between 13/7 8/7 and 13/7 6/5.
What’s right? With White having just one checker back, and Black not having a lot of numbers to make the 5-point naturally, the right play is to slot with 6/5. Black’s problem here is that if he doesn’t slot, he runs out of time fairly quickly. He doesn’t want to move his back checkers yet, and that leaves him only the checker on the 13-point that can move cleanly. White, meanwhile, only needs to roll one good number to escape his back checker and turn the game around, and his spare checkers give him time to wait for that number.
Does the cube affect the decision? Not in this case. It’s true that if Black slots and White misses with some neutral roll (say 5-2: 11/4) then Black has a huge double and White barely has a take, while after 13/7 8/7 followed by a neutral roll, it’s no double/take. However, slotting is also the double match point play, so we can’t really say that the potential cube turn makes slotting correct. The potential 6-prime is such a big swing against one checker back that the slot is worth the risk.
Now look at 152b. Here White has two checkers on his 23-point, rather than just one, as well as one fewer checker in his outfield. These changes make a big difference. Black has less need to make his 5-point, since White will require many more moves to escape. In addition, coming up to Black’s 5-point is more dangerous for White than before, since it now leaves two checkers exposed, subject to a possible blitz. The absence of the spare on White’s 11-point also has an effect, since any six by White except 6-3 will now leave a blot out there.
The effect of all these changes is that Black has no need to slot the 5-point, but can just play the safe 13/7 8/7 and wait. After a neutral roll for White like 5-2, played 6/1/ 6/4, Black can already double, and White will have a clear take.
The general lesson to take away from these two positions is that middle game slotting is more effective and necessary against one checker back. If your opponent has two checkers back, slotting is probably an overplay, unless it also lets you unstack an awkward position.
Solution: (a) 13/7 6/5
(b) 13/7 8/7
(a) Cash game, center cube.
Black to play 6-1.
(b) Cash game, center cube.
Black to play 6-1.
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.
Slotting in the Middle Game
Slotting is an easy idea to understand in the opening. When we slot the 5-point with an opening 2-1, we threaten to make a very strong point while unstacking a big stack. Since our opponent has no board, getting hit is just a minor inconvenience. Although it’s not a hugely correct play (splitting our back men is almost as good), it’s not a hard play to make because the downside seems pretty small.
Slotting in the middle game or the endgame is very different. Now your opponent almost certainly has a reasonable home board, so the cost from being hit is much greater. It’s also unlikely that you still have a stacked position at this point, so unstacking probably isn’t a big goal.
With a hit being more expensive and unstacking not so important, we’ve knocked out two of the three pillars supporting an early slot, and we’re reduced to just one: the value of the point itself. When we slot in the middle game, the point needs to be really important, and the chance of making it cleanly without slotting not so good. There is, however, a new factor affecting a middle game slot: the cube. A slot followed by a miss from your opponent may give you a good double, which in some cases is enough to tip the play in favor of slotting.
With those ideas in mind, let’s look at problem 152a.
The six is clear: 13/7. With the ace Black has a choice of two safe plays, 8/7 and 13/12, and the slotting play, 6/5. Of the safe plays, 8/7 dominates since it gives more ways to make the 5-point cleanly if White steps up with a three, and the checker in the outfield will have a few more hitting numbers from the 13-point if White escapes with 5-3 or 6-3. So now our choice is between 13/7 8/7 and 13/7 6/5.
What’s right? With White having just one checker back, and Black not having a lot of numbers to make the 5-point naturally, the right play is to slot with 6/5. Black’s problem here is that if he doesn’t slot, he runs out of time fairly quickly. He doesn’t want to move his back checkers yet, and that leaves him only the checker on the 13-point that can move cleanly. White, meanwhile, only needs to roll one good number to escape his back checker and turn the game around, and his spare checkers give him time to wait for that number.
Does the cube affect the decision? Not in this case. It’s true that if Black slots and White misses with some neutral roll (say 5-2: 11/4) then Black has a huge double and White barely has a take, while after 13/7 8/7 followed by a neutral roll, it’s no double/take. However, slotting is also the double match point play, so we can’t really say that the potential cube turn makes slotting correct. The potential 6-prime is such a big swing against one checker back that the slot is worth the risk.
Now look at 152b. Here White has two checkers on his 23-point, rather than just one, as well as one fewer checker in his outfield. These changes make a big difference. Black has less need to make his 5-point, since White will require many more moves to escape. In addition, coming up to Black’s 5-point is more dangerous for White than before, since it now leaves two checkers exposed, subject to a possible blitz. The absence of the spare on White’s 11-point also has an effect, since any six by White except 6-3 will now leave a blot out there.
The effect of all these changes is that Black has no need to slot the 5-point, but can just play the safe 13/7 8/7 and wait. After a neutral roll for White like 5-2, played 6/1/ 6/4, Black can already double, and White will have a clear take.
The general lesson to take away from these two positions is that middle game slotting is more effective and necessary against one checker back. If your opponent has two checkers back, slotting is probably an overplay, unless it also lets you unstack an awkward position.
Solution: (a) 13/7 6/5
(b) 13/7 8/7
