The Monty Hall Problem: Deal or Switch

If you’ve ever been unfortunate enough to sit through the Gameshow “Deal or No Deal”, you might have concluded as Charlie Brooker put it, that the entire show is  “actually a massively pointless exercise in utter bloody guesswork“. If you did, you’d be right. There is however an utterly counterintuitive rule of probability that appears if we have a little play around with the rules of the game.

Imagine you are in a game show and you are presented with three boxes. In one of the boxes is a sports car, in each of the other boxes is a goat. Imagine now that you can select any one of the boxes. After you have made your pick, the presenter (Monty Hall) opens one of the other boxes to reveal a goat. The question now posed to you is do you stick to your guns or choose the remaining box? Stop and think.

If you answered, that you’d stick with the same box you’d end up with only a 33% chance of winning the car, whilst if you switched your box, your odds double. If that made your brain explode, check out this quick explanation from ASAPScience:

If you still don’t believe me, watch this demonstration of the game from the BBC and if you’d like a fuller explanation head over to the Khan Academy. It just goes to show that we can’t always trust our gut feelings.

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Image Credit: Shutterstock/Mirexon;Dvarg