Luck in Chess
Bill Robertie, 2013

[An excerpt from an interview Richard Munchkin did with Bill Robertie in 2013.]

Chess is also a probabilistic game but there is no obvious source of randomness so people don’t notice that it is a probabilistic game. In fact, it is as probabilistic as backgammon but in a different way.

Let’s suppose Gary Kasparov, a 2800 player, goes up against a Grand Master who is a 2600 player. If they play a number of games over a period of time, Kasparov is going to win 3 out of 4 of the decisive games pretty reliably. He’s not going to win them all even though he’s clearly the better player. And if Kasparov plays somebody who he’s 400 points better than, he’ll win 90-odd percent of the time, but the other guy will win a few.

Why is this happening? It looks the same as if you put two backgammon players, playing 25-point matches, against each other. You’d see the same distribution. You’d see the better player winning a higher percentage, and it would be a pretty steady percentage over time, as long as their skill remained constant.

If you stuck these players in black boxes, and all you knew from the outside is over here in Box #1 the results go W-L-W-W-W-L-W-L and over here in Box #2 the results go W-W-L-W-W-W-L, which box has the two chess players and which box has the two backgammon players? You can’t tell the difference. You just get these strings of results and somebody is winning most of them but not all. It’s obvious why this is happening in backgammon because you have the dice going on. But why is it happening in chess?

Chess is like this: Imagine it is dark and you have two people with flashlights. One guy has a big flashlight with a wide beam and the other guy has a little flashlight with a narrow beam. It’s dark and out in front of them is a forest, and in the forest is some treasure. You say to each player, “Okay, you guys go out in the forest and first one to find the treasure wins.” Well, the guy with the big flashlight is the favorite to find the treasure first, but it’s no guarantee, because the other guy could luck his way and find it instead.

And a game of chess is like that. You look at this position, and there are all these variations that string out in front of you. You know, “I could do this, or I could do that. And I’ve only got time to analyze three of these . . . .” You’re searching a tree of possibilities. Depending on how fast you think and how much you know about the game, your tree search is more efficient but it’s not guaranteed to get you to the best answer.

The other guy, who’s maybe clumsy and he doesn’t think as fast as you and doesn’t know as much about the game, could still walk into the main variation almost by chance. That’s where the chance in chess comes from. It’s entirely invisible. In fact you might feel a little uncomfortable even referring to it as “chance.” But that’s really what’s going on, two people basically searching a tree at different speeds. They are still trying to find the main line, the line that describes correct play on both sides. The better player usually searches it better, but not always.

That makes chess a probabilistic game, and that means it’s got a lot in common with these other games, such as backgammon and poker.