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Freakonomics: Why Isn’t Backgammon More Popular?

Posted By: Daniel Murphy
Date: Wednesday, 15 December 2010, at 8:28 p.m.

In Response To: Freakonomics: Why Isn’t Backgammon More Popular? (Klaus Evers)

Dubner writes:

But the fact is that the choice set of moves is in fact quite small. That is, for many rolls, there’s clearly one optimal move, or perhaps two that are nearly equal. So once you know those moves, the game is limited, and you need some stakes to make it interesting. Unlike, say, chess, where the options and strategies are far more diverse.

I suspect Dubner overestimates how often there is "clearly one optimal move" (although how many is "many" is a question, which he tries to address), and underestimates the skill needed to learn to play all those moves and, most probably, also underestimates the skill needed to play all the nonobvious moves well.

Dubner goes on to pose the question to his friend Altucher:

"... in what percent of backgammon turns would there seem to be clearly one optimal move — versus, for comparison, chess?

Altucher opines: in 5% of chess turns and 10% of backgammon there is only one optimal move, defined (for chess) where the best move has a "value greater than 'one pawn’s worth.'"

Two observations:

(1) It's not clear, although he does also mention playing experience and discussions with programmers, that Altucher's opinion is much more than a guess along this line: backgammon is easier than chess, 5% of chess plays are "optimal," therefore in backgammon twice as many backgammon plays are similarly "optimal."

(2) What is one pawn up worth? Some quick research surfing reveals that's it's asserted that a one pawn advantage is (generally) a forced draw. It's also asserted that a one pawn advantage (or equivalent) is often a win for a grandmaster, while average players frequently fail to win with a two pawn advantage.

I also learned that for the purpose of computer evaluation of chess positions, there's such a thing as a "centipawn" where 100 centipawns equal a 1 pawn advantage. A centipawn advantage can be equated to both win percentage and ELO rating difference, although the relation is not linear, and of course the value of centipawns varies greatly depending on the position. Exactly what 1 centipawn equals in ELO is unclear. One source suggest that 1 centipawn equals 3 ELO points, while another suggests that a 100 centipawn (or 1 pawn) advantage is equal to a rating difference of 100. An ELO difference of 100 is equated to a 64% match win percentage, factoring in draws. Backgammon ELO systems agree, for match length 25.

Whatever it may be exactly, it seems clear that "one pawn's worth" in chess is a pretty sizable advantage, or error, or difference between the "optimal" move and the next best. I'm at a loss to define what a similar type of move would be in backgammon. Counting moves, for instance, where second best play loses 14% match equity, doesn't appear to be the right idea. It does not seem to me that this approach is a very useful metric for comparing the complexity and difficulty of backgammon and chess. It doesn't appear to tell us anything at all about the difficulty of choosing a best move from two or more alternates. Although it's true that even very good players can improve by maximizing their success in finding the "obvious" play where all others are blunders, I suspect that Dubner, having mastered that part of the game (if he has), would not think the game so "limited" if he were aware of how much equity is to be had by consistently finding the best play in all the moves where relatively little equity is at stake, whether or not the best choice is obvious.

I can't help but be curious how XG, GNU BG or Snowie would rate Dubner and his friend Altucher in their 101-point friendly matches. And I wouldn't disagree strongly with Altucher's tentative conclusion that "to be a backgammon master probably requires almost as much study [as to be a chess master], but not quite."

By the way, this isn't the first time backgammon's come up in the Freakonomics blog. See http://freakonomics.blogs.nytimes.com/2006/07/02/is-backgammon-the-next-big-thing/ , from 2006.

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