Very interesting! This has to be a score effect, of course.

A couple of years ago I began using no-Jacoby for my “unlimited game” practice sessions and rollouts. I turned it off so that these money games would better approximate a match with the tied score many points away from victory. Evidently, that’s enough to swing the choice of plays here, and not by a small amount.

Three rollouts follow, all made using the same seed. To shorten rollout times, I included only the slotting play and the building play. The first is for no-Jacoby. The second is for a match tied at 11-away. The third is a cash game using the Jacoby Rule. Slotting loses in the first two rollouts, but wins when Jacoby is enforced.

The key is gammon losses. You can find them among the psuedo-cubeless win percentages of the rollouts. Those are found in the second line of data given for each play. They begin with 6 numbers followed by the letters CL (and then some more numbers).

The first three numbers are estimated win percentages for Blue. The first is for games where Blue wins at least a single game, so without Jacoby (as in the first rollout), the building play 15/10 13/11 is winning about 70% percent of the time. This total includes all single wins, gammon wins, and backgammon wins. The second number is the percentage of games where Blue wins either a gammon or backgammon. Putting it another way, it is the percentage of games where Blue wins at least a gammon. The third number gives the percentage of games where Blue wins a backgammon. Of course, since White has already borne off two checkers, Blue can win neither a gammon nor backgammon, so both percentages are 0%.

Following the data for Blue is a hyphen followed by the same three numbers for his opponent White. Looking again at the no-Jacoby rollout, you can see that when Blue makes the building play, White will win at least a single game about 30% of the time. After Blue makes the slotting play, White wins just a tad more often, around 31%. The big difference is gammons. The slotting plays loses 4% more gammons than the building play, 11% versus 7%.

When there is a cube turn, the Jacoby Rule does not matter either way. Blue must pay for his gammon losses after a take. The key is what happens after a no-double. One of the things I observed when I played this position out (about 25 times) was that White usually cannot double after he is lucky enough to jump into the outfied on his first try. Even when Blue misses the shot in the outfield, White must roll, and the game often swings when he does.

If White can jump past most of Blue’s stragglers on his second roll, and survives until his third roll, often he will have lost his market. In the no-Jacoby variation, he should play on, and collect his 7% gammons. In the games where Blue slotted, that will be 11%. With Jacoby in effect, however, White should not play on. He must double, and collect just a single point when Blue passes.

What that means is that Blue can afford to slot when the Jacoby Rule is present. When it doesn’t work out for him, he won’t be paying for his gammon losses. He will simply be passing. It is these gammons that explain the big difference in equity when Jacoby is enforced. In the Jaboby rollout at the bottom, that was just enough to allow the slotting play to nose ahead of the building play.

Mike

    1. Rollout          15/10 13/11                  Eq.:  +0.62
       0.70 0.00 0.00 - 0.30 0.07 0.00 CL  +0.32 CF  +0.62
      [0.00 0.00 0.00 - 0.00 0.00 0.00 CL   0.00 CF   0.00]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 760432305 and quasi-random dice
        Play: supremo 2-ply cubeful prune [world class]
        keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
        Skip pruning for 1-ply moves.
        Cube: 2-ply cubeful prune [world class]
    2. Rollout          12/5                         Eq.:  +0.57 ( -0.05)
       0.69 0.00 0.00 - 0.31 0.11 0.00 CL  +0.28 CF  +0.57
      [0.00 0.00 0.00 - 0.00 0.00 0.00 CL   0.00 CF   0.00]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 760432305 and quasi-random dice
        Play: supremo 2-ply cubeful prune [world class]
        keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
        Skip pruning for 1-ply moves.
        Cube: 2-ply cubeful prune [world class]

    1. Rollout          15/10 13/11                  Eq.:  +0.64
       0.70 0.00 0.00 - 0.30 0.07 0.00 CL  +0.32 CF  +0.64
      [0.00 0.00 0.00 - 0.00 0.00 0.00 CL   0.00 CF   0.00]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 760432305 and quasi-random dice
        Play: supremo 2-ply cubeful prune [world class]
        keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
        Skip pruning for 1-ply moves.
        Cube: 2-ply cubeful prune [world class]
    2. Rollout          12/5                         Eq.:  +0.57 ( -0.07)
       0.69 0.00 0.00 - 0.31 0.11 0.00 CL  +0.27 CF  +0.57
      [0.00 0.00 0.00 - 0.00 0.00 0.00 CL   0.00 CF   0.00]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 760432305 and quasi-random dice
        Play: supremo 2-ply cubeful prune [world class]
        keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
        Skip pruning for 1-ply moves.
        Cube: 2-ply cubeful prune [world class]

    1. Rollout          12/5                         Eq.:  +0.59
       0.69 0.00 0.00 - 0.31 0.11 0.00 CL  +0.28 CF  +0.59
      [0.00 0.00 0.00 - 0.00 0.00 0.00 CL   0.00 CF   0.00]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 760432305 and quasi-random dice
        Play: supremo 2-ply cubeful prune [world class]
        keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
        Skip pruning for 1-ply moves.
        Cube: 2-ply cubeful prune [world class]
    2. Rollout          15/10 13/11                  Eq.:  +0.59 ( -0.00)
       0.69 0.00 0.00 - 0.31 0.07 0.00 CL  +0.31 CF  +0.59
      [0.00 0.00 0.00 - 0.00 0.00 0.00 CL   0.00 CF   0.00]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 760432305 and quasi-random dice
        Play: supremo 2-ply cubeful prune [world class]
        keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
        Skip pruning for 1-ply moves.
        Cube: 2-ply cubeful prune [world class]

The best reason to practice against a bot using the Jacoby Rule is because you play in a lot of chouettes where it is used.

The best reason to turn it off is so you get practice making the "too-good-to-double" decision (on a 1-cube). With Jacoby turned on, you can never be too good on a 1-cube.

Unlimited (money) games without Jacoby is also a good way to remove the score effects that distort play in a match. When there is no Jacoby Rule, unlimited games is the same thing as a match tied at infinity-away. That's why a lot of match players like to practice with it turned off.

BTW, whatever Aaron says is pretty much gospel with me. Back when Robertie was still doing the Problem of the Week, he had one of the best right/wrong records of any of the posters then active. His was much better than mine.

Mike

Right, except that slotting is not the best play. At normal match scores and in money games without the Jacoby Rule, it is distinctly better to position builders on this turn, and slot on the next. Only when you have the protection against gammon losses that Jacoby gives, does it pay to slot "prematurely."

Given that information, can you figure out what play is best at DMP? What about gammon-go, where you trail 2-away, 1-away in the Crawford game of a match?

Mike