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Problem of the Week #50: Solution
02-21-2010
, 02:52 PM
Problem of the Week #50: Solution
Cash game, center cube.
Black to play 4-3.
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.
We start off in Problem 50 with a basic choice: play safe or leave a blot. The only safe play is horrendously ugly; it’s 11/8 6/2, which leaves Black with a combination of stripped and stacked points. However, it’s the only play which doesn’t leave an immediate shot. There are a couple of constructive plays which volunteer a shot: 11/4 and 8/1*. Playing 11/4 starts a good point and leaves the minimum 11 shots, so Black gets hit only about 30% of the time. Playing 8/1* leaves the same number of shots but puts White on the bar. If White enters but misses the shot, he’ll have to enter on a high point, after which Black can attack the blot more easily.
Before we decide whether safer is better, let’s pick between the two plays that leave a shot. Here, hitting is better than slotting the 4-point by a wide margin. Hitting has two advantages: hitting nets a small but measurable increase in gammon chances when White dances (about 2%), and hitting forces White forward when he misses the shot, giving Black better chances to attack, as well as better chances to pass by more easily. So 8/1* dominates 11/4.
So now our choices are between volunteering a shot with 8/1* or playing safe with 11/8 6/2. Right now Black leads by 17 pips in the race, 95 to 112. After playing his 7 pips he’ll be up by 24. The general principle when bearing home is simple: don’t leave a shot unless you have to. However, there are exceptions. If White’s home board is weak and the safe play is very awkward, leaving the shot may be best. Take a look at this next position:
Position 50a: Black to play 4-3.
Black’s position is the same, but now White has an open 3-point, giving Black plenty of chances to survive after being hit. This one is a no-brainer: 8/1* is better by a lot.
In our original position, however, White’s home board is immensely strong. Against a board like that, it’s extremely rare to ever volunteer a shot. If Black gets hit, he’s basically dead unless he can immediately respond with a 6-1.
Nonetheless, rollouts show that 8/1* is still correct in this position, although by a very small margin. That in itself makes the position very interesting, as it gives us a measure of just how bad the safe play needs to be in order to volunteer a shot against a nearly-perfect home board. In this case, the position after 11/8 6/2 is just bad enough.
That insight in itself would make this a standout position, but we’re not done yet. There’s another factor working.
A couple of posters wondered why Black didn’t double before he threw his 4-3. He could have, although the double is very marginal. (The take is quite easy.) All Black’s doubles were good, as well as 6-1, 6-3, 3-1, 4-2, 4-1, and 5-1. That make 17 rolls that improve Black’s position in some way, with 19 rolls that are either neutral or cause his game to deteriorate.
Over the board, doubling would be a hard call because of the lack of obvious market-losers (sequences where Black rolls, White rolls, and now if Black doubles, White has a big pass). For instance, consider the sequence Black 4-2, played 8/4 6/4, and White 4-2, played 8/6 8/4. Black would be happy with this sequence, yet the resulting position is still an easy take. Players look for some big market losers when they think about doubling a position that’s obviously an easy take, and if they don’t see them, they tend to leave the cube in the middle.
However, the cube position has a big effect on our original position and roll! If either side owns the cube, the right play with the 4-3 is to play safe, 11/8 and 6/2. Only with the cube still in the middle is 8/1* actually correct. Here we run into the Jacoby Rule once more. No matter who has the cube, once it’s been turned gammons are activated, and Black gets gammoned about 10% of the time after hitting. With the cube in the center, White isn’t strong enough to double from the bar, but once he hits, Black will be dropping a double and the gammons never come into play. A noteworthy position.
Solution: 8/1* (with the cube still centered)
Cash game, center cube.
Black to play 4-3.
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.
We start off in Problem 50 with a basic choice: play safe or leave a blot. The only safe play is horrendously ugly; it’s 11/8 6/2, which leaves Black with a combination of stripped and stacked points. However, it’s the only play which doesn’t leave an immediate shot. There are a couple of constructive plays which volunteer a shot: 11/4 and 8/1*. Playing 11/4 starts a good point and leaves the minimum 11 shots, so Black gets hit only about 30% of the time. Playing 8/1* leaves the same number of shots but puts White on the bar. If White enters but misses the shot, he’ll have to enter on a high point, after which Black can attack the blot more easily.
Before we decide whether safer is better, let’s pick between the two plays that leave a shot. Here, hitting is better than slotting the 4-point by a wide margin. Hitting has two advantages: hitting nets a small but measurable increase in gammon chances when White dances (about 2%), and hitting forces White forward when he misses the shot, giving Black better chances to attack, as well as better chances to pass by more easily. So 8/1* dominates 11/4.
So now our choices are between volunteering a shot with 8/1* or playing safe with 11/8 6/2. Right now Black leads by 17 pips in the race, 95 to 112. After playing his 7 pips he’ll be up by 24. The general principle when bearing home is simple: don’t leave a shot unless you have to. However, there are exceptions. If White’s home board is weak and the safe play is very awkward, leaving the shot may be best. Take a look at this next position:
Position 50a: Black to play 4-3.
Black’s position is the same, but now White has an open 3-point, giving Black plenty of chances to survive after being hit. This one is a no-brainer: 8/1* is better by a lot.
In our original position, however, White’s home board is immensely strong. Against a board like that, it’s extremely rare to ever volunteer a shot. If Black gets hit, he’s basically dead unless he can immediately respond with a 6-1.
Nonetheless, rollouts show that 8/1* is still correct in this position, although by a very small margin. That in itself makes the position very interesting, as it gives us a measure of just how bad the safe play needs to be in order to volunteer a shot against a nearly-perfect home board. In this case, the position after 11/8 6/2 is just bad enough.
That insight in itself would make this a standout position, but we’re not done yet. There’s another factor working.
A couple of posters wondered why Black didn’t double before he threw his 4-3. He could have, although the double is very marginal. (The take is quite easy.) All Black’s doubles were good, as well as 6-1, 6-3, 3-1, 4-2, 4-1, and 5-1. That make 17 rolls that improve Black’s position in some way, with 19 rolls that are either neutral or cause his game to deteriorate.
Over the board, doubling would be a hard call because of the lack of obvious market-losers (sequences where Black rolls, White rolls, and now if Black doubles, White has a big pass). For instance, consider the sequence Black 4-2, played 8/4 6/4, and White 4-2, played 8/6 8/4. Black would be happy with this sequence, yet the resulting position is still an easy take. Players look for some big market losers when they think about doubling a position that’s obviously an easy take, and if they don’t see them, they tend to leave the cube in the middle.
However, the cube position has a big effect on our original position and roll! If either side owns the cube, the right play with the 4-3 is to play safe, 11/8 and 6/2. Only with the cube still in the middle is 8/1* actually correct. Here we run into the Jacoby Rule once more. No matter who has the cube, once it’s been turned gammons are activated, and Black gets gammoned about 10% of the time after hitting. With the cube in the center, White isn’t strong enough to double from the bar, but once he hits, Black will be dropping a double and the gammons never come into play. A noteworthy position.
Solution: 8/1* (with the cube still centered)
02-23-2010
, 04:26 AM
With GNU-BG Checker Play Analysis set to "Supremo," and with "Use Jacoby rule" checked on the Cube Options tab, I created an new "Cash" game, and edited the board to setup Problem 50. Here's what the rollouts show:
Last edited by Taper_Mike; 02-23-2010 at 04:34 AM.
02-26-2010
, 02:56 PM
Quote:
Problem of the Week #50: Solution
Cash game, center cube.
Black to play 4-3.
Nonetheless, rollouts show that 8/1* is still correct in this position, although by a very small margin. That in itself makes the position very interesting, as it gives us a measure of just how bad the safe play needs to be in order to volunteer a shot against a nearly-perfect home board. In this case, the position after 11/8 6/2 is just bad enough.
Solution: 8/1* (with the cube still centered)
Cash game, center cube.
Black to play 4-3.
Nonetheless, rollouts show that 8/1* is still correct in this position, although by a very small margin. That in itself makes the position very interesting, as it gives us a measure of just how bad the safe play needs to be in order to volunteer a shot against a nearly-perfect home board. In this case, the position after 11/8 6/2 is just bad enough.
Solution: 8/1* (with the cube still centered)
My Snowie 4 3-ply Precise rollout 1296 trials has the ugly safe play correct by 0.054.
02-28-2010
, 08:42 PM
03-03-2010
, 11:41 PM