All That Luck

In Skill and Luck in Backgammon, I described the process by which I settled on the parameters tourneygeek should use to simulate backgammon tournaments. The result was that the luck factor should be set to three, which implies that backgammon is 75% luck, and only 25% skill.

This does not mean, however, that backgammon is an easy game – a game in which a few small, easily learned heuristics will allow you to play at a high level. Open any of the many more advanced monographs on backgammon strategy and tactics, and you’ll soon see that there’s an enormous body of knowledge that expert players have and others do not. There’s plenty of skill in backgammon, it’s just that this skill is regularly overwhelmed because there’s even more luck.

Is there really that much luck in backgammon? How do players cope with it?

Here’s another way to think about the skill/luck balance in backgammon. These days, backgammon skill is measured by a statistic called performance rating (PR), which is essentially the number of milipoints (thousandth of a point) difference between the player’s average move, and the move deemed best by a computer program called Extreme Gammon. (This is not quite a complete account of PR, but I’m not sure I know all the gory details, and suspect most readers would be happier without them.)

The best players in the world have a PR of about 3. That means, roughly, that for each move, the player would lose, on average, 0.003 points to the computer. Using this as the standard assumes, of course, that the computer knows how to play flawless backgammon (which is also not quite true, but it’s close enough to being true that most people respect the accuracy of the PR statistic).

On a good day, my PR is about 8. This means that, if I were playing a world-class opponent, I’d be giving up about 0.005 points in equity with every move. It’s not a steady drip – my errors come in clumps. Most of the time, the computer, the world champion, and I all play a move in exactly the same way. But over time, I’ll make enough errors to give away that average 0.005 points, which means that in an game that lasts, say, 20 moves, which is pretty typical, the expert is going to be, on average, one-tenth of a point to the good. That’s not much.

At the beginning of the game, the standard deviation of the result of the first dice throw is about 91 milipoints. And the opening position is not a particularly volatile one – there are no open shots, and doubles, which are often the best (and sometimes the worst) rolls are not allowed. The luck factor swamps skill even on the opening roll, and it often overwhelms it later in the game.

Here’s what that means as a practical matter. I play three or four times a year at events on the American Backgammon Tour. I play in the highest division, and don’t usually embarrass myself. But I’m not so conspicuously good that I’d be refused entry into a second-tier event if that’s what I wanted to play. And, while it’s unlikely that I’m going to win any of the top-tier events I enter, it’s not beyond the realm of possibility. My chance for winning a handsome sum in prize money is small, but it’s not zero.

There’s a world of difference between me and the experts in terms of skill, knowledge, and experience. If I went to an elite chess tournament with a similar skill deficit, I’d be cannon fodder. I’ve got a real chance at an elite backgammon tournament, and that’s one of the main reason I play them.

Most elite players have made their peace with the game. They study, and practice, and study some more, and they still pretty regularly drop matches – not just to respectable journeymen like myself, but sometimes to raw beginners. It goes with the territory.

But some elite players, you can tell, find their vulnerability to lesser players galling. One of the ways this shows up, from time to time, is in suggestions to change the rules of the game, a little, to reduce the influence of luck.

Nack Ballard invented a variant called nackgammon, which replaces the tame opening position with one that’s considerably more difficult to play. Phil Simborg has proposed a Simborg rule, which reduces the advantage of winning the opening roll by disallowing the best option for some of the luckier opening rolls. Other innovations have included alternating the right to roll first, and even deciding the outcome of a match, in whole or part, by calculating the PR.

The next post in this backgammon series will discuss how the skill/luck balance in backgammon affects how people learn the game. And later in the series, there will be a discussion of how computers have affected play, and why it is that so many people think that backgammon-playing computers have been programmed to cheat.

9 thoughts on “All That Luck”

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  2. Interesting article!

    “in an game that lasts, say, 20 moves, which is pretty typical, the expert is going to be, on average, one-tenth of a point to the good. That’s not much.”

    Agreed. The 0.1ppg advantage to the expert doesn’t sound that high. I myself am surprised how often I lose to the CPU 🙂

    May I ask, what % match win-rate do you have against XG?


    1. (Sorry to have overlooked your comment earlier.)

      I lose to it most of the time, too, though I don’t keep track of exactly how often. Perhaps the reason I don’t is that I usually play worse than I do against humans – I have a regrettable fondness for back games that I rarely resist when playing against a computer, and I take a lot of cubes that I should drop because I want to see how the game plays out.


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