Rock-paper-scissors among tennis players

Question

Three tennis players have a curious record against each other: Ann beats Bea 60% of the time, Bea beats Cyd 60% of the time, and Cyd beats Ann 60% of the time. You make a friendly bet where you must name your champion first, and then your opponent names theirs, trying to beat your pick. You name Ann.

Whom will your opponent pick, and what is their winning probability?

Accepted Answer

Look at who beats Ann. From the records, Cyd beats Ann 60% of the time. So your opponent will name Cyd, and they win with probability 60\%. This is not bad luck about Ann in particular. The three players form a cycle: Ann beats Bea, Bea beats Cyd, Cyd beats Ann, each with a 60% edge. Whichever champion you commit to first, your opponent can name the player who beats yours 60% of the time. - If you pick Ann, they pick Cyd. - If you pick Bea, they pick Ann. - If you pick Cyd, they pick Bea. Naming your champion first is the disadvantage; there is no safe choice. Takeaway. With a cyclic dominanc…

Rock-paper-scissors among tennis players

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