Problem of the Week #86: Solution


Cash Game. Black owns the cube. Black on roll.




(a) Should Black double? If he doubles, should White take, drop, or beaver?


(b) Assume Black doubles and White takes. How should Black play
(1) 6-2?
(2) 6-3?
(3) 4-3?
(4) 5-4?


Note: All ‘cash game’ problems assume the Jacoby Rule is in effect. No gammons can be scored unless the cube has been turned.


Position 86 is a derivative from Position 85. Black played 2-1 by moving 5/3*/2*, and White then danced. Now Black finds himself still with a checker behind a 5-prime, but with two White checkers on the bar and a 5-prime of his own. In addition, Black has two loose blots in his board, and both sides have a blot in the outfield.

One of the many fascinations of backgammon is that positions are subject to sudden ‘phase shifts’. In the position we’re considering, Black and White have been playing a prime versus prime game. However, White’s sudden failure to enter has transformed the game completely. Black now has the option of abandoning his priming plan and simply treating the position as a late-game blitz.

In general, all else being equal, we prefer blitzing to priming. A good prime will win the game just as well as a good blitz, but a blitz will win lots of gammons, while a prime will not. Seen as a blitz, Black’s game has suddenly become overwhelmingly strong: 40% of his rolls will cover both blots next turn and create a 5-point board – all aces plus 6-5, 6-6, and 3-3. His fives can cover the 2-point, strengthening the blitz while retaining the prime as a defensive option. Sixes can either escape or cover the 1-point. Even 4-4, usually a bad roll in priming games, here becomes a min-perfecta, hitting in the outfield and covering the 2-point.

White has a huge pass in this position, and technically Black is too good to double by a small margin. “Too good to double” positions are a little tricky, however, because even if you’re sure that you’re too good, as a practical matter you’ll want to double anyway. Even something like a 10% chance that your opponent will incorrectly take is usually enough to make doubling the profitable choice. When in doubt, look to see if your opponent has any ostensible counterplay. If he does, then there’s some chance that your opponent can blunder and take, and you should double. Here White’s 5-prime and Black’s blots will give some players the idea that they’re still in the game, so double.

For part (b), we’re going to assume that we doubled and Black took. Let’s see how best to play these four non-trivial shots.

(1) Black to play 6-2. This roll offers several appealing choices. We could escape from behind the prime with 24/18 7/5, or cover the one-point with 7/1 18/16. Both have merit. The best play, however, is a twofer: 18/10*. The hit sends a third checker behind the 5-prime and at the same time wipes out all White’s outside timing. If White now starts to enter, his position rates to crack when his third checker finally enters. If he doesn’t hit a blot, however, Black can switch back to blitz mode, this time with an extra checker to close out.

(2) Black to play 6-3. Here the choices are 24/18 7/4 and 7/1 18/15. In a pure priming game, escaping would be the best play, and even here it’s the best play to win the game. The overall best play, however, is the blitz-prime hybrid 7/1 18/15. Black covers one blot while keeping his 5-prime and getting a direct shot on White’s outfield checker. The hybrid wins only a little less than the escaping play, while picking up many more gammons.

(3) Black to play 4-3. A poor shot. Black can’t escape, he can’t hit in the outfield, and he can’t cover his blots in a clean way. Now the best play is to switch, 5/1 and 5/2, creating a pure blitzing position. While not pretty, the play wins more games than 8/1 (because White can’t enter and hit) and more gammons than 18/11 (because Black has a stronger board.)

(4) Black to play 5-4. Here the switch (6/1 6/2) is possible but not necessary. The hybrid play, 7/2 18/14, covers a blot and keeps the 5-prime intact, making it a stronger choice. Another possibility with this roll is the rolling prime play, 8/3 7/3. This looks pure, but it’s actually a big blunder because it allows White to both hit and get to the edge of the prime when he rolls a deuce.

The overall lesson here is instructive but not immediately obvious. In late-game positions which can still go in either a priming or a blitzing direction depending on circumstances, the best plays are often those which are hybrids of priming ideas and blitzing ideas. These can be hard plays to find because our instinct is to pick a plan, then look for the plays which follow that plan purely. In these amorphous positions, however, pragmatism is a better approach.


Solutions:

(a) Technically too good and pass; in practice, double.

(b1) 18/10*

(b2) 7/1 18/15

(b3) 5/1 5/2

(b4) 7/2 18/14

Against a very good player, is it right or wrong to double?

Even very good players can, in the heat of battle, look at a position incorrectly and make a mistake. I would still double.

I think this is the kind of position one can make huge mistakes because in all fairness, who likes to drop anything?

Thanks. That is what i do. On the other side i think: if a position is only a double, and you think too good to double, you don't miss a double in.