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Insightful comment about luck versus skill

Posted By: Fabrice Liardet
Date: Sunday, 15 August 2010, at 9:25 a.m.

In Response To: Insightful comment about luck versus skill (Timothy Chow)

Isn't it possible to compute something like the following ?

Take the whole game tree, with random events (dice rolls) depicted as moves from the player "Nature". Compare the order-1 variance over Nature's decisions with the order-1 variance over the players' decisions. If correctly weighted by the probability of the nodes, it seems to me one would come with a sound measure in % of "luck vs skill".

Not that I think that it would be an especially good fit to what people actually think of as luck and skill, e.g. :

- If at early player decisions you add a lot of legal moves that lead to immediate loss, you would boost the skill factor without adding much "real skill" to the game.

- As Xavier noted, there is luck involved in chess too. An other example of that would be playing the right move for the wrong reasons. It's just a different kind of luck : not coming from Nature's moves, but from the fact that no player can get perfect information about the whole game tree.

But the measures based on "how often does the better player win ?" suffer from the fact that the only definition of "better player" that I can think of is based on winning percentages.

Does anyone know where the %s that seem to be used in silly laws about games of chance come from ?

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