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Posted By: Timothy Chow
Date: Wednesday, 28 January 2015, at 12:06 a.m.

In Response To: A made-up game to illustrate some points about skill and luck (Tom Keith)

Tom Keith wrote:

The problem with free throws, as others have pointed out, is that there is luck involved in those too.

This of course depends on one's definition of luck.

If the outcome of some "game" is completely deterministic, then it is generally not considered to be a "game" but is something like a "measurement." (This is another insight I learned from Garfield and Elias.) We can make your sumo-wrestling example even more deterministic by ending the "game" after the weigh-in; whoever weighs more wins. Not really a game, is it?

If we accept this point of view then it will follow that even games of pure skill are non-deterministic. This was basically Robertie's point about chess. In common parlance, chess is a game of pure skill. Nevertheless, the outcome of a chess game is non-deterministic—certainly between closely matched players, and arguably even between highly mismatched players. One can rather successfully model the outcomes of chess games using probability theory. This is one of the assumptions behind the Elo rating system.

So if we say that we want to separate out the "luck" from the "skill," we have to be careful what we mean. Do we mean that we want to separate out all the randomness from the non-randomness? With that definition, even in chess we still are faced with the task of separating out the luck. Similarly, as already discussed in this thread, in backgammon, getting a bunch of easy decisions, or decisions that you happened to have studied the night before, would have to count as "luck" and your error rate would not be a pure measure of skill.

I prefer to take the attitude that skill is random. What distinguishes skill from luck is not that skill is deterministic and luck is non-deterministic, but that skill refers to the aspect of the game that is under the players' control in the sense that players can improve their results through training. So for me, sinking putts and making baskets and spelling randomly chosen words and solving randomly chosen chess or backgammon puzzles and running races are all skilled tasks rather than luck elements. This point of view aligns nicely with the usual partition between luck and skill in backgammon bots.

Unfortunately, in setting up my example, I forgot that most people think of shooting baskets not as a "pure skill" task but as something that involves "luck," despite the absence of external randomizing elements. To avoid confusion, I should have picked some task that is commonly thought of as a "pure skill" task, such as solving chess or backgammon puzzles. The mathematical analysis would have been identical but people would have been less likely to worry about whether my supposed task of "pure skill" had some "luck" in it.

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