Problem of the Week #135: Solution
Money game, center cube, Black on roll.
(a) Should Black double? If he does, should White take?
(b) Assume Black doubles and White takes. How should Black play the following rolls: 6-6, 4-4, 2-2, 6-4, 6-2, and 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.
Black is off to a good start in Problem 135. He’s neatly filled in his 3, 4, and 5-points, making a strong home board. White has only managed to escape one back checker, getting it as far as his 8-point.
What a pretty position! At first glance, Black’s edge seems overwhelming, especially to a beginner or intermediate. But let’s step back for a minute and apply Joe Sylvester’s trusty ‘Position-Race-Threats’ criteria, which serves us pretty well in these early positions.
: Big edge to Black, obviously.
: Black leads by only two pips, 149 to 151.
: None. (Of course 6-6 is crushing, but in any early position there will be a couple of doubles for which that’s true. When we talk about threats we’re really looking for ordinary non-doubles that play very well. Here Black is threatening to threaten, which is not quite enough to give him a check in the ‘threat’ column.)
With no edge in the race and no particular threats, Black’s game doesn’t look quite so overwhelming. In fact, it would appear that the take is now trivial, and it’s the double that’s in question. Rollouts back up this conclusion. The double/no double decision for money is very marginal (making this a good and easy to remember reference position) while the take is simple.
As we look a little closer into the position, we notice another feature that strengthens our opinion of White’s game: he has very few bad shots. All his doubles play well, of course. His sixes either make a point (6-1, 6-4), run to the midpoint (6-5) or run to the outfield (6-2, 6-3). Black’s open deuce-point has the curious effect of making White’s aces more playable. Now he makes a point with 3-1, and can hide on the 2-point with 5-1, 4-1, and 2-1, making those good numbers as well. He makes inner points with 5-3 and 4-2, leaving only 5-4, 5-2, 4-3, and 3-2 as awkward shots, and of those, all but 5-4 could be played safe if necessary. We’re trained to assume that positions with no structure will play poorly, but a close examination will often really more resiliency than might be expected.
Now we come to the checker plays. Before we look at individual moves, let’s note a couple of features of the position:
(1) Since Black’s board is so strong, splitting is better than usual for him. White is less inclined to hit loose, because of the obvious danger, but White also needs to leave blots in the outfield, and splitting makes that more dangerous.
(2) Black’s bar-point has assumed a larger than usual importance, so Black is also inclined to bring down builders to his outfield.
(3) Black’s good board makes hitting loose on the ace-point better than usual. For the same reason, switching points with doubles may be more attractive.
Now on to the checker plays.
: Making both bars is good, but pointing on the ace-point with 13/1*(2) is the clear winner. Both plays win about 80% of the time, but making the ace, with White still undeveloped, wins about 55% gammons, compared to about 35% gammons for the positional play.
: Best here is just the normal 24/20(2) 13/9(2). The attacking play 13/1* 13/9 wins about 5% more gammons than the quiet play, but also sacrifices about 5% winning chances, a poor trade. Switching with 5/1*(2) 13/9(2) ruins the board and costs even more wins.
: Now switching is strong, because the resulting inner board, while a little weakened, is still powerful. After 3/1*(2) and 13/11, you can choose between 13/11 and 24/22 with the last deuce. While 24/22 looks more thematic, 13/11 does almost as well on rollouts.
: These two should be considered together. Black can choose between an out-and-down play (24/18 and 13/9 or 13/11) or a slotting play (13/7 and 13/9 or 13/11). Slotting works better with 13/7 13/11 because the checker on the 11-point is better placed if White rolls a six. After 13/11, Black gets a double shot if White rolls 6-1, 6-2, or 6-3, while after 13/9 he only gets a double shot after 6-1. The plays are otherwise very close, and that consideration makes the difference. Slot and down with 6-2, split and down with 6-4.
: On the opening roll, 24/20 13/10 and 24/21 13/9 are about equivalent. Splitting to the 20-point slots a better point and guards the whole outfield, but 13/9 produces more combinations to make inner points. The result is a wash. Here there are no inner points to be made, so 13/10 is a little better than 13/9 (extra shots on White’s 6-2) while 24/20, attacking the 14-point directly, is a little better than 24/21.
Solutions: (a) Marginal double and easy take.
(b2) 24/20(2) 13/9(2)
(b3) 3/1*(2) 13/11 and either 13/11 or 24/22 with the last deuce
(b4) 24/18 13/9
(b5) 13/7 13/11
(b6) 24/20 13/10