Enigma 1473: Even odds
15 January 2013
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From New Scientist #2634, 15th December 2007
Connah Tiste runs an unusual fairground stall. It consists of 15 touching circular lights as shown.
You pay £1 and three of the lights come on, the trio being chosen completely at random. If the centres of the lit circles form the corners of an equilateral triangle, you win £10.
Recently one of the bulbs developed a fault which means it never lights up. Each punter now gets a random trio from the remaining lights. Connah has decided to do nothing about correcting the fault because it lowers the chances of him having to pay out. In fact he will now expect to pay out once in every certain whole number of goes.