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Subject: Another Interesting Dice Video rss

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Carl Frodge
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Russ Williams
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Nontransitive dice are fun. I liked his remark that you don't need to calculate the exact probabilities; you only need to show that one die beats the other more than half the time, which is often easier than calculating the exact probabilities.


But the drug example didn't really make sense if we're considering the usual sort of situation where some people take one drug and other people independently take another drug; if A cures more people than B, and B cures more people than C (e.g. A cures 50% of the people, B cures 40% of the people, C cures 30% of the people), then of course A cures more people than B.

I think he could have chosen a better "real world" example. E.g. (since this is a boardgame site), if Alfred wins more than half the time vs Bert in some 2-player game, and Bert wins more than half the time vs Charles in the same game, that does not imply that Alfred will win more than half the time vs Charles. (Often in such situations, Alfred will indeed win more often, but not necessarily, if the 3 players' preferred strategies happen to interact surprisingly.)
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