As a result if you initially picked a goat, and you switch, you will
definitely win the Ferrari, but if you initially picked the Ferrari and you switched, you will definitely receive a goat, but because the chance of initially picking a goat is higher (2/3 as opposed to 1/3), you will overall have a 2/3 chance of winning a Ferrari if you switch to door C, (and only a 1/3 chance if you stick with door A). If, despite my fantastic explanation you are still confused, don’t worry, one of the most influential and brilliant mathematicians of the 20 th Century, Paul Erdős, did not accept that you would have a higher chance of winning if you switched door until he was shown a computer simulation of thousands of outcomes of the game show. 7 The third and final problem is known as the Truel problem. This is one of the most fascinating game theory problems, as it again illustrates how counterintuitive decisions can lead to the best outcome. There are 3 people participating in a 3 way duel, a truel! Each person ( A, B and C) has a gun, and takes it in turns to aim and fire 1 shot of their gun, first A will shoot, then B will shoot, then C, and then A again and B and the cycle continues until there is only 1 person left alive. Each participant will die if they get hit by a single shot. However, person A is a bad shot, and only has a 1/3 (33%) chance of hitting one of the other participants if he aims at them, person B is a better shot and has a 2/3 (67%)chance, and person C is a great shot and has a 3/3 (100%) chance of hitting. Each participant knows the other participants chances of an accurate shot. If one of the participants gets killed, then of course they cannot themselves shoot. For example, if A goes first and shoots C and kills him, then it will be B’s turn, then if B misses it will be A’s turn, and so forth until only 1 participant is left alive. Imagine you are person A and you are going first, assuming that the other 2 participants are logical, should you aim at B? Should you aim at C? What should you do to maximise your chances of winning this truel? Try to come up with the answer before looking at the solution below.
Solution: What you probably thought, is that A should aim at C, because he is the more likely of the other participants to shoot accurately, and therefore he should be eliminated. It would be illogical to aim at B, because if you happened to kill B, then C would have a 100% chance of killing you, as it is their turn
7 Arbesman, S. and Pearson, G. (2014) Monty Hall, Erdos, and Our Limited Minds. Available at: http://www.wired.com/2014/11/monty-hall-erdos-limited-minds/ (Accessed: 13 May 2015)
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