Friend and anti-hyphen crusader Robb Fynewevermuyskens wrote some pointed and excellent questions about backgammon in the comments of this entry. My response ended up being rather lengthy, so I’m putting it up here as a new entry. Here’s Robb:

My assumption is that, at a certain point, most backgammon players have roughly similar skills. That is to say, given a certain board set-up and dice roll, there’d be very few “best” choices of moves, allowing for personal choice (in aggressiveness or defensiveness). That being the case, it seems to me the games themselves are determined entirely (short of a player making a “mistake”) by chance, i.e. by the roll of the dice. Do you find this to be true?

Some background: I’ve always grouped chess and backgammon together in my mind as Cool, Old-School Games that are somehow superior to games of my generation (i.e. Clue, Monopoly, etc.). Part of this is the vastly superior pieces (though maybe Sorry!(tm) would be as cool if it had solid, weighted pieces and a hardwood, parque board. . .naa). Most of the superiority, however, comes from their simplicity of play versus their complexity of strategy. Anyone can learn to play chess and backgammon, but superior players will beat inferior players on a regular basis. Which brings me back to my question. How much more superior does one have to be at backgammon to consistently beat their opponent? Or does that not come into play once you’ve learned some basic strategy, because ultimatly the dice determine the winner? Maybe that’s an exaggeration. The dice rolls being roughly the same (which theoretically they should), should produce the more skilled player as winner most of the time. But I recall an instance at a chess tournement when, right after being mated, a player jumped out of his seat and yelled, “You got so lucky!” Well, that’s absurd. There’s no luck in chess. So I’m wondering, does your enjoyment of backgammon necessarily involve an excitement of the randomness of the dice? Does backgammon even lend itself to competition, or is it more like the buzz generated around a craps table? If it is competitive, isn’t it horribly disappointing to have a solid lead evaporate with just a few rolls of the dice?

Briefly: yes, the enjoyment of backgammon necessarily involves excitement stemming from the randomness of the dice. But it is not the case that the results become essentially random when the players all arrive at a sort of skills plateau. The reason for this is that there is no such plateau; rather, there is the constant possibility for incremental improvement in strategy and play that’s a hallmark of all great strategy games. The luck factor obscures it somewhat, but backgammon has a definite “lifetime to master” continuum of skill levels.

It is true that a rank amateur could win a game against a top-ranked player, given enough luck — something that would never happen in chess. This is not because there isn’t any subtlety to the strategy, though. Some moves are obvious or forced, but in most cases there are a hundreds of ways to play a particular roll. The thing is, the relative merits of, say, the best half-dozen moves in a given situation are often rather slight. Backgammon software will analyze a game and report its “equity,” the odds of either side winning from a given position. At the beginning of the game each player’s equity is 50%. Very often, the difference between the best possible move (according to the computer) and the second-best move is less than a percentage point of equity. So anything can happen, but over time (and even in a single game, there are dozens of rolls) making the better moves adds up significantly.

No serious backgammon player would play without the doubling cube, which increases strategy by an order of magnitude. The numbers are fairly straightforward: for reasons that my math-impaired brain takes somewhat on faith, if you feel that you have 25% equity in a game, you should accept the cube if offered, thus doubling the point-value or stakes of the game (the alternative would be to decline, which grants your opponent the win at the current point value). Of course, knowing what your equity is at any given moment is an incredibly complex and subtle operation. It’s the sort of thing that computers can do well in most cases, but sometimes can’t beause they’re not fast enough to evaluate them through brute force in a reasonable amount of time. The strategy on deciding when to offer the cube in the first place is even more complex because of issues revolving around something called volatility, which is something I still know very little about.

To make the cube make sense you either have to be playing for money, in which case the effect of doubled stakes is obvious, or be playing a match to a finite number of points. Five and seven point matches are common because you can usually finish them in under an hour. While an amateur might beat a backgammon master in a single game, it’s extremely unlikely that he’d win an entire match — the longer the match, the more clearly the superior player will become evident. Give me a smart gamer who has just learned backgammon, and I wouldn’t be willing to bet a hundred bucks that I’d beat him in one game. But I’d happily bet $900 that I’d win a nine-point match.

When you?re looking at equity numbers it’s easy to forget that different styles of play can have a big effect in countless imperceptible ways. My favorite backgammon opponents at Common Grounds are Steve and French; the three of us have played hundreds of games against each other. There is a definite pattern in those games: French beats me more than I beat him, I beat Steve more than he beats me, but Steve has a definite edge over French. The trend has been continuing far too long for it to be just coincidence, and we’re all of roughly equal ability, so clearly my style of play must, in some way I’m not even aware of, work better against Steve than it does against French.

“Does backgammon even lend itself to competition, or is it more like the buzz generated around a craps table?” The answer would be “yes” and “yes.” There is the thrill of knowing that anything can happen, but there are also tangible rewards for studying the game and playing thoughtfully. That part’s easy to forget when you’re in the middle of an inexplicable slump, at which point it’s very easy to conclude that it is just a stupid luck game. Backgammon constantly creates those situations where the winner thinks the game was decided by strategy, while the loser believes that the dice were dead-set against her. Nine times out of ten, the winner’s the one with the right idea.