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Luck vs. Skill

Posted By: Tom Keith
Date: Saturday, 6 December 2008, at 3:52 a.m.

In Response To: Luck vs. Skill (trichard)

Still, I'm curious to what extent luck outweighs skill. To start with, let's look at a single game. Assume two players of approximately equal ability - one makes errors in the game totaling .06 and the other .03 (if these figures are unrealistic, just assume a difference of .03 at any level you choose). On average, the game will end when one player has an equity of .57. So .03 vs. .57 would mean that in this single game, luck was about 20 times more important than the difference in skill.

I'm not sure where you got the .57 from.

The more skillful player starts with an equity of 53%. (50% + 3% because he expects to make fewer errors.) The dice will have to contribute either 47% luck (if the favorite wins) or 53% luck if the underdog wins.

So there is about 17 times as much luck as skill in this particular game.

To extend to an 11-point match, you could use the backgammon Elo formula (though it is not terribly accurate for this type of comparison). A 3% advantage in one game becomes about a 10% advantage in an 11-point match. Now the ratio of luck to skill is only 5-to-1.

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