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Posted By: Tom Keith
Date: Wednesday, 28 January 2015, at 1:10 a.m.

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

So if we say that we want to separate out the "luck" from the "skill," we have to be careful what we mean. Do we mean that we want to separate out all the randomness from the non-randomness?

Yes, it's what I'd like to do. But of course that's difficult.

This is why I like backgammon. In backgammon a large part of the luck can be attributed to rolls of the dice. If you focus just on that portion of luck, you can make meaningful statements about it.

Definition: The "equity" of a position is the probability that a perfect player playing a perfect opponent wins the match from that position.

Note the assumption of perfect play in this definition. This is not the same as "practical equity," which takes into consideration the players involved and how they are likely to play out the game. And it is not the same as "bot equity," which is a bot's estimate of the equity of the position.

Definition: The "luck" associated with a roll of the dice is the difference in your equity after you rolled the dice compared to your equity before you rolled the dice. If your equity went up, the roll was lucky; if your equity went down, the roll was unlucky.

This is close to what the bots calculate as "luck," but since the bots don't know the true equity of most positions, their luck calculation is really just an estimate.

Unfortunately, in setting up my example, I forgot that most people think of shooting baskets not as a "pure skill" task but as something that involves "luck," despite the absence of external randomizing elements. To avoid confusion, I should have picked some task that is commonly thought of as a "pure skill" task, such as solving chess or backgammon puzzles.

Is solving a backgammon puzzle "pure skill"? Sometimes I get a backgammon puzzle right just by a lucky guess. That's why it's good to play variations on a theme, so you can see if the features you thought were important really are, and if you were thinking about the position properly.

We have all had the experience of reviewing a game we played earlier only to discover that our choice on the second go round was different than our choice in the actual game. Suppose one choice was right and the other wrong. If we made the correct choice in the actual game, you could call that good luck because we know that there is at least some chance we could have made the wrong choice. If we made the wrong choice in the actual game, you could call that bad luck because we know there is some chance we could have made the correct choice.

Why did we make different choices for the same position? Who knows? In the actual game, maybe we were narrowing in on the correct play but, one millisecond before we were about to have a key insight, a fly landed on our arm creating enough of a distraction to take us off our train of thought. Tough luck.

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