# Luck of the Draw

As far as Skinny's wagers go, this one is pretty fair. But it's not 50-50, and if played enough times, Skinny can manage to come out ahead.

Skinny deliberately selected a collection of cards that allow him to exploit an aspect of probability sometimes refereed to as the voting paradox or the Arrow Paradox. The voting paradox is based on the fact the probability is not always a transitive property. Consider this:

The clubs hand consists of 3, 5, and 10

The spades hand consists of 4, 6, and 8.

The hearts hand consists of 2, 7, and 9.

If the two piles picked from are clubs and spades, spades wins 5 times out of 9. If the two piles are spades and hearts, hearts wins 5 times out of 9. But even though spades will probably beat clubs, and hearts will probably beat spades, hearts isn't a safe bet. Because clubs beats hearts 5 times out of 9.

So no matter which pile you pick, there's another pile that will probably beat it.

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