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Mochy & Phil Prop

Posted By: Timothy Chow
Date: Tuesday, 21 April 2015, at 11:25 p.m.

In Response To: Mochy & Phil Prop (trichard)

trichard wrote:

It will be interesting to assess to what extent Mochy won on skill vs. luck. (Looked to me like mostly luck.)

This kind of question is more mathematically subtle than most people realize.

Ignoring the cube-ownership odds for a moment, the following are (almost) always true:

1. If you add up the luck of all the rolls over all games, both players will be equally lucky. In fact both players' total luck will be close to zero.

2. In each game, the player with more luck in that game wins. Another way to put it is that the player who wins more games "out-lucks" the other player in more games.

3. If enough games are played then the more skilful player will win more often.

Putting this together, we see that the way skill manifests itself is by causing the more skilful player to out-luck the other player in more games. So it's something of a false dichotomy to try to assess whether the winning player won "because of luck" or "because of skill."

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