Cash game. Center cube. White to play 3-2.
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.
This position is taken from a game which began with a lot of hitting, but not much point-making. Both sides have now secured good anchors; White also has the 22-point, so he has the making of a strong holding game. Each side has managed to add one outside point along the way. White has his bar-point, while Black has his 9-point. For good measure, Black has built a 53-pip lead in the race.
What are the game plans going forward? Black’s is pretty simple. He probably won’t be able to build an effective prime, so he needs to capitalize on his racing lead by scrambling his back checkers home, and the sooner the better. He’ll want to start with the checker on his 24-point, and then follow with the checkers on his 20-point. He’s not averse to building the low points in his board; the spares on his 6, 8, and 9-points don’t really have anywhere else to go, and a strong board might help him if he can hit a lucky shot
White is losing the race, but he’s the one with the priming chances. His job is to get his back checkers out and try to extend his little prime. His first goal is to make his 9-point or his 10-point, which starts putting real pressure on Black’s rear checkers. For now, he’s not interested in making home board points. Every checker that makes a home board point is another checker that can’t help build the prime.
With White on roll, who’s a favorite? Actually, it’s Black, but only by a small amount (about 53-47, cubeless). White’s positional advantages almost compensate for Black’s huge racing lead, but not quite.
Now we get to the real question: How should White play a 3-2? One play is very obvious, namely 14/11 13/11. It makes a good point and leaves no blots. But as a number of posters commented, if a play’s that obvious, how can it be a problem? The answer must be something more subtle, like 20/15.
Over the board, it would be very hard not to go on automatic pilot and make the 11-point. But now we have plenty of time and we’ve been warned this is a problem, so let’s list the relative merits and demerits of the two plays.
Play A: 14/11 13/11
The strength of making the 11-point are pretty clear: White makes a blocking point and cleans up two blots. The weaknesses of the play are a little more subtle, but become apparent on a second look.
(1) After making the 11-point, White’s position is a little fragile. He has only two spares, both on the 20-point; a roll that won’t allow him to move one of these checkers will force him to break a point somewhere else on the board. That point will almost certainly be the 11-point, since his other points are all more valuable right now.
(2) The 11-point doesn’t actually do much. It blocks Black’s 20-point, but Black doesn’t want to move those checkers for a while. Right now he’d like to get the checker on the 24-point moving, and if that’s not possible, he wouldn’t mind making his 2-point. The checkers on the 20-point are quite happy to stay where they are.
(3) White’s position has become hard to improve anytime soon. The points he most wants to make are his 9-point and 10-point, to extend his prime. But unless he rolls 1-1 or 2-2, which allow him to shift his 11-point forward, those points will be hard to come by for some time.
Play B: 20/15
Play B is the opposite of Play A: the weaknesses are apparent, the strengths more subtle. The weaknesses are that the play doesn’t make an available point, and it leaves three blots instead! Now let’s look for the strengths.
(1) White’s position is less dangerous than might appear. Black has only 12 hits: 6-2, 5-3, 4-4, 6-3, 5-4, 6-4, and 5-5. The hits with 5-5 and 4-4 don’t swing much because those are great shots anyway. The other hits leave White with a ton of return shots. After 6-3, for instance, played 20/11*, White has 22 return shots: all 2s plus 1-1, 5-1, 3-1, 6-5, 6-3, and 6-1. The hits with eights or tens are a little better for Black but still far from crushing.
(2) White’s position is much more flexible than after making the 11-point. He’s in no danger of cracking anything vital, and he’s got a bunch of combinations to make the 9-point or 10-point. If Black doesn’t hit, White will be able to play pretty easily for the next few rolls.
(3) Hopping out lets White control the outfield. Black has lost his grip on the outfield, and his army’s getting disconnected. The checkers on his 20-point are 11 pips away from his checkers on the 9-point. With 20/15 White stakes a claim to the outfield, Black’s most vulnerable area. Games with multiple men back on both sides are frequently decided by outfield control, because both sides need a link between their back checkers and their front position, and the player who loses that link can become an underdog quickly.
Do the advantages of 20/15 outweigh the value of a solid point? Rollouts show that they do, although it’s a hard judgment to make over the board. Making the 11-point is so inviting that most players would grab it in a shot and pick up their dice. (I did – the position is from one of my games.) The value of this problem is to show that massive outfield control, coupled with your opponent’s toothless inner board, can outweigh plays that are solid but inflexible.
Solution: 20/15
