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about those doubles

Posted By: Timothy Chow
Date: Thursday, 30 April 2015, at 10:48 p.m.

In Response To: about those doubles (Casper Van der Tak)

Yes. After I came up with my made-up game the whole situation became clear to me. It's a pretty subtle business though, so it's not surprising that it continues to cause confusion.

What's difficult to grasp intuitively is that the luckier player can win 90% of the matches and simultaneously the more skilful player can win 70% of the matches.

Most people's intuition runs something like this: The outcome of a match is determined either by luck or by skill. Both players are equally likely to be luckier. If 90% of the games are won by the luckier player—equivalently, if 90% of the matches are determined by luck—then the more skilful player will win at most 55% of the matches—namely, the 45% that are won by luck, and at most 10% of the matches that are determined by skill.

Every step of this reasoning sounds plausible, but every step is actually invalid if luck and skill are defined the way the bots define them.

From a shark's point of view, it's a really good thing that the subject is so confusing, because his livelihood depends (in part) on people not understanding the role of luck in backgammon.

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