(as opposed to 10 years if you stay silent). As a result, both prisoners will benefit more from betraying, regardless of what the other prisoner chose. As a result, the outcome if the prisoners are both logical will be something which is not in either prisoner’s interests – they both betray and get 5 years in prison. The next problem is not strictly game theory, but demonstrates well how a counterintuitive choice may be the right one, It is known as the Monty Hall problem. 6 You are on a game show, and there are 3 doors (A, B and C), you know that behind one of the doors is a brand new Ferrari, and there are goats behind the other 2. You of course do not know which door (A, B or C) has a Ferrari behind it, and which doors have goats behind them. Your aim is to win the Ferrari (I hope). You pick a door, say A for example. The game show host, who does know what is behind each door, opens another door (say B for the sake of argument) to reveal one of the two goats. There is now only 1 goat and the Ferrari left in either door A or C. You are then given a choice, do you want to open door A, and receive what is behind it, or do you want to switch to door C? Try to decide which door would be best to pick, before looking at the solution. Solution: On the face of it, it seems like it shouldn’t matter, there are 2 doors left, 1 has a goat, and 1 has a Ferrari. Therefore whichever door you choose gives you a 50% probability of winning the car, right? Wrong! In fact, you will have a higher probability of winning the Ferrari if you switch to door C, this is why:
Initially, on the first pick clearly you have a 2/3 chance of picking a
goat. Let’s imagine have picked a goat.
If you do pick one of the goats, and another goat is revealed, then if
you switch to door C, you will have 100% chance of picking the Ferrari (given that you picked a goat first [a 2/3 chance]).
This is because there is 1 goat behind the door the host opened, and
there is 1 goat behind the door you initially picked, therefore behind the other door must be the Ferrari.
On the other hand, lets imagine you picked the Ferrari initially (1/3
chance), if you switch, after 1 goat is revealed, you will have 100% chance of getting a goat (given that you picked the Ferrari first [a 1/3 chance]).
6 BBC (2013) Monty Hall problem: The probability puzzle that makes your head melt. Available at: http://www.bbc.co.uk/news/magazine-24045598 (Accessed: 13 May 2015)
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