The Chess Paradox

At first sight, it looks like the game of chess is all about skill. After all, there is no randomness in the board setup or the interaction between the pieces. The game is fully deterministic.

Yet, chess also contains a luck component.

We know it does because if chess were solely about skill, we would expect the stronger opponent to win all games. Instead, when players are of similar ability, the stronger one only wins a small fraction of games. For example, in the latest Chess World Championships, held in 2023 in Astana, Kazakhstan, the winner only won 4 out of 18 games against the other finalist (and lost three; the rest were draws).

Imperfect Information

One reason we believe chess is a game of pure skill is that we assume perfect information. If we knew which tactics our adversary prepared against, given enough skill, we could know what the best next move is. But if we do not know which tactics our adversary studied last night, we can only guess what the best move is. The most we can do is to assign a probability, such as “I think there is only a 20% chance that my adversary studied how to defend this move, so there is an 80% chance that this is the best move.” And if the best we can do is to assign a probability to what the best move is, of course, whether we are right depends on luck – luck and skill, obviously, but not purely skill.

(If you are not convinced yet, think about the children’s game of “rock, paper, scissors.” It is a fully deterministic game, yet it’s almost all luck-based – especially if played in its “closed envelop version” that prevents using fast reflexes to “cheat.”)

It’s important to remember this. Underestimating the importance of luck is a common reason for bad decisions. Use strategies that work even if you have bad luck.

Imperfect Execution

That said, even if chess players had perfect information, there would still be a luck element.

People do not always perform at their best. Even the strongest chess player might fall sick or make a blunder, and the eventuality of that happening is at least partially due to luck.

Consider the following example, in which the strongest chess player plays two chess games against the second-strongest player. Both players play one game in full health and one game while sick. If they fall sick on the same day, the strongest player is likely to win both games, whereas if they fall sick on different days, the weakest player has a chance of winning the game on the day he is healthy, and his adversary is sick.