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Posted By: sita
Date: Tuesday, 27 January 2015, at 3:55 p.m.

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

This game is a very nice illustration what's going on in backgammon, I think. I explained this phenomenon to me always like this, spoken in the terms of the game:

Let's look at the state of the game after 20 coin flips, e.g. Let's say, the coin flipped 11 times in Rs direction, and thus 9 times in Bs direction. Since R is also more skillful, it could very well be that R has won now. R was also luckier, but only a little bit. Now look at a sequence which 11 times favors B instead. Now B has not won, the marker might even on Rs side. So, if B wants to win, she has to be way more lukier than R has to be to win.

Thus, If R wins, she might have an average luck of +2. If B wins, she might have an average luck of +4. Because at +2 she simply has not won the game yet. Since the total luck has to be 0, R ends in twice as many games luckier than B, though "less luckier per game" than B. Both win most of their games when luckier.

You could simplify the game even more, when you say that you only flip coins, but every 10th flip the more skillful person sets the marker one point in her direction.

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