Mastering Backgammon

Playing the Slot-or-Split Rolls
by Bill Robertie
This article originally appeared on, September 25, 2006.

The last group of opening rolls is in many respects the most interesting one.

The starting position.

This group consists of the rolls where Black's choice, after bringing down a builder, is to either slot his 5-point with an ace or split his back men. Since 3-1 and 6-1 make a good point on the opening roll, only three rolls fit this category: 2-1, 4-1, and 5-1. Let's take a look at the resulting position for the two possible plays with an opening 2-1.

Diagram 1.
Black has played 2-1 by
slotting his 5-point.

Diagram 2.
Black has played 2-1 by
splitting his back men.

The idea behind the split play is pretty clear: it's a safe, reasonably constructive way to play a nondescript roll. Splitting gains a little (better outfield coverage, a few more combinations to make a blocking point) while risking very little. It's a very reasonable play that makes small improvements in Black's game.

The idea behind the slotting play is equally clear: Black wants to make his 5-point and he wants to unstack, and this play does both. If slotting didn't have a downside, it would be the overwhelmingly correct play. Unfortunately, it has a definite downside: if White now rolls a four, he hits on the 5-point, and Black loses 20 pips in the race.

So what's right? Does the gain from slotting outweigh the risk, or is the safe play the best choice? The answer in a second, but first a little history lesson.

For at least a century and a half prior to the 1970s, the accepted play with 2-1 was the safe 13/11, 24/23. Slotting was obviously risky, and since players of that period had no tools to evaluate risk, they reasonably opted for the safe and sane alternative.

In the 1960s and 1970s, backgammon was struck by the games-playing equivalent of a perfect storm. The game exploded in popularity, caused largely by the unique promotional skills of Prince Alexis Obolensky, a charismatic backgammon fanatic who may or may not have been an exiled Russian prince. The rise in popularity attracted a whole new breed of players, among them many chess masters and experts. The chess players saw a lot of profit potential in backgammon, but they also saw a game that could be visualized in a new way; not just a simple racing game, but a game where a strategic, structural approach with an emphasis on complex maneuvers, prime-building, and back games could overwhelm the old racing style. This new approach was born in the New York games clubs like the Mayfair, formerly a bridge club but now the epicenter of the new backgammon scene. The new way soon had a name: pure style, where purity referred to the desire to put pieces where they belonged to facilitate the construction of quick, decisive primes.

With the pure approach, rolls like 2-1, 4-1, and 5-1 were easy to play: just slot the 5-point with the ace and don't ask any questions. The 5-point was key to building an early prime, and no risk was too great.

Was the pure style better than the old racing style? The answer seemed to lie in the results. Advocates of the pure style became the dominant stars of the new era. The old racers were swept away. Everyone wanted to play complex backgammon. By the end of the 1970s, it was literally possible to play in a tournament and never see an opening 2-1, 4-1, or 5-1 played with the split.

The status quo was maintained through the 1980s and into the 1990s. Then some contradictory data appeared. The early neural nets, TD-Gammon and then Jellyfish, didn't slot with the opening aces. Instead, they played 24/23 with the ace. Many players switched to splitting right away, figuring that if a computer said it was right, it must be right. Some of the top players, however, weren't yet convinced. Slotting led to more back games. The computers still played back games horribly. Could that account for the difference? The argument was plausible, but no one really knew.

As later generations of the bots became available, the answer became clear. As the bots' skill in back games increased, the slotting plays all rose in value. However, 2-1 was the only roll where the slot actually became the preferred play. With 4-1, the slot was clearly wrong, and by a substantial margin. With 5-1, splitting maintained a slight edge, but the slot was a reasonable alternative.

A careful analysis of the results led to some surprising insights. Backgammon, it seems, was even more complex than the purists had imagined. The slotting versus splitting question hinged, not on the value of the 5-point, but on exactly where the other building checker was placed. Move a checker from the midpoint to the 11-point, and the slot was right. Move it to the 9-point instead and the slot was wrong. Stack it on the 8-point and the choice was a tossup.

Why did the location of the building checker make such a difference? Look at the problem this way. Forget about the play of the ace for a second, and just consider the change in the position caused by moving a builder from the midpoint to Black's outer board. Now ask yourself the question: "How much work does this checker do from its new location?" On the 11-point or the 8-point, the answer is "Not much." A checker on the 11-point adds just a couple of new building numbers (4-1 to make the bar-point and 6-3 to make the 5-point) while a fourth checker on the 8-point does almost no new work. (Well, perhaps just a little; 1-1 now makes a 4-prime.) A checker on the 9-point, however, is a real powerhouse. After 13/9, the only rolls that don't make a good new blocking point next turn are 6-4, 5-1, and 3-2. The other 30 (!) rolls all make good points.

From this analysis, a good rule emerges:

The more upcoming rolls that improve your position naturally,
the less you want to take risks.

The time to take risks is when your position is awkward and unlikely to improve on its own. The time to play safe is when your position rates to just keep getting better. This idea is an outgrowth of a key general principle of backgammon called Efficiency. You want your checkers working hard, but if they're already working hard, it's inefficient to take risks to make them work a little harder.

So the right plays with these rolls are:

  • With 2-1: play 13/11, 6/5, slotting the 5-point.

  • With 4-1: play 13/9, 24/23, splitting the back men.

  • With 5-1: either play is all right, but 13/8, 24/23 is probably slightly stronger.

Next time:  Does your bot cheat?.

See:  More articles by Bill Robertie

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