In this position, with Black on roll, who is a favorite?
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This is a good problem for two reasons:
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Many players look at this position and think the answer is almost too obvious to even require a discussion. At the same time, they often can’t quite agree on what the obvious answer is.
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It’s a position which illustrates in stark terms the relationship between a racing lead and a positional edge, and as such it has some real historical significance.
Back in the period 1977-1982, the elite backgammon world was ruled by what was then known as the "pure style". The Bible of the pure style was Barclay Cooke’s Paradoxes and Probabilities, a collection of 168 checker and cube problems, which was published in 1978 and which became wildly popular among the tournament set. The essence of the pure style was that backgammon was a game of key points and primes. The race had some relevance, but not nearly as much as had been thought by the simpler players of an earlier generation. Playing for the race too early caused players to sacrifice positional assets, to their later detriment.
The theory of the pure style led naturally to a basic game plan: Grab both 5-points, slotting if you needed to, control all four quadrants, build a prime, and finally hit and trap a checker, with an easy win. If your blots got hit, just fall into a well-timed back game and turn things around later. It was a seductive plan, leading to beautiful-looking positions with powerful primes, high anchors, all checkers working, and a complete absence of stacks.
The pure style was very attractive to the new wave of former chess players who were moving into the backgammon world in large numbers. It offered a view of backgammon that made the game similar to chess: strong points, control of the center, good development of the pieces, all leading to victory in the end.
Most successful tournament players tried to play some version of this style, and the style seemed to work. The players who were winning big tournaments were (with a couple of exceptions) playing just this way. I tried to model my own game on this approach, and by 1981 I was having some success. I’d won a couple of big tournaments, as well as many smaller ones, and I was doing well in chouettes around Boston. Life was good.
Then I met Alex.
Alex was probably in his mid-70s when I met him. His location and date of birth were a little hazy, but according to his stories he’d bounced around the world a lot, spending most of his time in the Middle East and Eastern Europe. He’d played backgammon for a long time in a lot of different places. He never played for high stakes ($5 a point was his limit) and he didn’t like tournaments because they took too long. He liked to hang around the Cavendish Club in Boston and watch the $20 chouette (the big game in those days) and occasionally play heads-up for $2, $3, or $5 a point.
On Sundays the big game was a bit of a hit-or-miss affair, so sometimes I’d find myself at the club with nothing to do. Alex and I would get to chatting about his travels, and we started playing heads-up to pass the time until a chouette would start. I figured Alex played an old-fashioned game and would be pretty easy pickings for a veteran like myself, schooled in all the latest tricks.
I was right about Alex’s style. It was old-fashioned. He split his back men with most opening plays, and never ever slotted. His goal was to get into a race or a holding game as quickly as possible. He handled blitzes reasonably well, and never seemed to get into a back game. His cube action seemed a little weak – he was slow to double in positions where he had strong threats, and I thought he was too quick to drop some interesting positions.
I had faced opponents in tournaments who just tried to play a racing game, but they were beginners or intermediates who made lots and lots of obvious mistakes and were easy to beat. Alex was different; he wasn’t easy to beat. As the days passed and the count of games climbed to 200 and then 300 and then 400, I realized to my shock that I was just breaking even. As far as I could tell, I was supposed to be winning big. My cube action was clearly better, I saw Alex making technical errors in positions that I had rolled out and understood well, and to top it all he was playing this passive style that should have been cannon fodder for my state-of-the-art hyper-aggression. Had I just hit a really unlucky streak?
I doggedly pressed on over the next few weeks, and the game count mounted to 500 and 600 and 700. My luck finally changed. It got worse. Alex was now up 30 points or so in our long session. At last he quit, as he was going on a long trip to see friends and relatives. I paid up and now had plenty of time to ponder just what had happened.
I was tempted to shrug and conclude that our sessions had just been an aberration, in which I had an extended run of bad luck against a much weaker player. But that just didn’t feel right. I really didn’t believe that I had been all that terribly unlucky. As I thought about the session, I realized that the mix of our two styles had led to a lot of holding games, where I had some nice holding position like the 5-point plus an extra man back, while Alex had escaped his back checkers and led in the race, but with little or no structure. According to the theory of the time, I was supposed to be better in those positions. But now I started to wonder about that.
As an experiment, I created the position at the start of this post, which is an extreme case of the sort of situation I was remembering. Black has a racing lead but absolutely no structure, and White is beautifully placed with both 5-points and control of all quadrants. I thought White had to be a solid favorite here. If I had taken this position to a tournament and shown it to a bunch of good players, I was certain they would concur unanimously. But I got a lot of these positions against Alex, and didn’t seem to win as often as I thought I should.
I decided to roll the position out 300 times, with no cube, and see what happened. I also decided to play Black’s position just as Alex had played it, never leaving a shot unless I had to. (Conventional wisdom of the day was that Black should slot points quickly, before White’s board got too strong.) The rollout took a few days (this was 1981, remember – no bots) and when it was finished Black had won 58% cubeless.
I was startled, but also excited. I understood why I had been losing to Alex. Whatever edge I had in complex positions and cube handling had been overcome by the number of times I had taken too many chances in the opening and been swept into playable but inferior holding games. Clearly, my early game play needed some serious adjustment, and I had some hard work ahead. On the bright side, I’d stumbled on an idea that would certainly improve my game a lot, and I couldn’t wait to refine it into a real weapon.
Now suppose you were Black in this position. How would you play these rolls?
- A. 5-2
- B. 4-1
- C. 2-1
- D. 6-5
Solutions:
First note that Black is a favorite. White might get a shot and then hit it, but Black has a lot of safe rolls, and a lot of rolls that leave only a single shot. Note also that just being hit isn’t the end of the game. A cubeless Extreme Gammon rollout puts Black at 56%, close to the 58% from my manual rollout many years ago.
(A and B) The right idea for Black is not to leave a shot unless he has to. With 5-2, he should just play squat with 13/6, while 4-1 should be played 13/8 rather than hitting on the 1-point. Alex understood that Black had time to wait, while most players of that era would have tried to clarify the position quickly with 13/8 6/4 or 6/1*.
(C) If you have to leave a shot, the outfield is usually the right place, since White will have to make a concession to hit by breaking his anchor. With 2-1, play 13/10.
(D) Occasionally a roll arises which is potentially so strong that it’s right to play big. With 6-5, the right play (but only by a little bit) is 13/7 6/1.
White hits with 20 shots, but Black becomes a very solid favorite when White misses because of the slotted bar-point. Contrast that with the 4-1 play, where Black still has a ton of work to do if he plays 6/1* and White misses.
