Markov chains and skill and luck

Markov chains are a hundred years and four days old, which brings to mind Using Markov chains to analyze Candy Land. As you may know, you can’t even lose in Candy Land on purpose! The results are entirely determined by the initial shuffle. Since it’s a game for children, this is a shame; I think that at least if you have really little kids, you want to be able to lose on purpose, or at least tilt the odds in their favor. Michael Mauboussin has argued that this is a sign that Candy Land is entirely a game of luck. Okay, Mauboussin didn’t talk about Candy Land specifically, but he argues in Untangling Skill and Luck that

There’s a simple and elegant test of whether there is skill in an activity: ask whether you can lose on purpose. If you can’t lose on purpose, or if it’s really hard, luck likely dominates that activity. If it’s easy to lose on purpose, skill is more important.

As far as I can tell, you can only lose in Candy Land by stacking the deck, which doesn’t really count – if I’m going to play games with my future children and I’m going to let them win, I don’t want to have to resort to stacking the deck. This is mostly because I’m not Persi Diaconis and so any stacking I did would be ruined by my shuffle.

Mauboussin has also argued (following Tom Tango, sabermetrician) that although a shortened season is good enough for the cream to rise to the top in the NBA (like last year), the same isn’t true in the NHL (like this year).

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