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Vandaag is het 18 January 2018

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Rat race - math puzzle

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On the yearly fair you can play as often as you like the game "rat race". In this game a rat is freed at the beginning of a circuit. The rat will then run to hole A, B or C, every hole with equal chance. Before the rat is freed, you can bet any amount you like on the hole the rat will run into. If you choose the right hole, you'll get back twice the amount you've put a stake. If you're wrong you loose your money.

Suppose you carry an infinite amount of money. Will you in that case always loose money playing this game, or does there exist a strategy to win money. Does this strategy also work in the more realistic situation when you carry a limited amount of money or if there is a maximum limit on the bet?
rat race

Answer

If there is no upper limit and you have an infinite amount of money, there is a way to always win money. However, be aware that in the realistic case, when there is an upper limit or that you have a limited amount of money this strategy does not work.