The mathematics of the perfect penalty shootout

When all the rivalries, the personalities and the occasion are stripped away, penalty taking is a very simple sort of game with just two players: the taker and the keeper. Fortunately there is a branch of mathematical sciences, known as Game Theory, dedicated to understanding and interrogating the dynamics of such simple competitions. To use the language of that subject, penalty taking is a zero-sum game: for the taker to score the keeper has to concede and for the keeper to triumph they must ether save the shot or rely on the taker missing. Either way, there is only one winner.

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