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A made-up game to illustrate some points about skill and luck

Posted By: Timothy Chow
Date: Tuesday, 27 January 2015, at 12:21 a.m.

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

Phil wrote:

So given the true way luck is computed, good players will roll, in the long run, just as well as bad players.

This is correct if you mean that good and bad players will have the same average luck in the long run (namely, zero luck).

However, the somewhat surprising fact is that if you examine a long series of matches, and ask, who was luckier, the better players will be luckier in more matches.

These two facts aren't contradictory, because the amount by which the better players are luckier in those matches is smaller than the amount by which they are unluckier in the remaining matches. A lot of small positive numbers averaged together with a small number of large negative numbers can (and in the long run in backgammon, will) average out to zero.

Note that everything I have said here pertains to the true way that luck is computed, and not to the informal notion that a "good roll" is one that gives you a good position in absolute terms. So the apples/oranges objection does not apply.

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