The following riddle has stumped the math departments of some of the nation’s top Universities. In the end, they came up with the answer “Yes, you should switch.” I disagree and say it doesn’t matter. What say you?
You are on the TV Show LET’S MAKE A DEAL. Monty Hall allows you to pick 1 of 3 doors. Behind 2 doors are a goat, behind the third door is a car. You choose door number 1. He shows that behind door number 2 is a goat. Monty then gives to you the option of keeping your original door, or switching to door number 3.
After #2 has been eliminated, by switching to #3 your odds are now 1 in 2.
Sounds screwy, but it’s stats. It supposed to be screwy. And the fact that it seems so counterintuitive to most is why people so frequently make shitty decisions.
What separates professional gamblers who make money (sometimes fortunes) from gambling addicts is that the pros are very good at continuously calculating odds and only make/increase bets when the odds are in their favor, the gambling addict relies on luck and “hunch.” What your “gut” is most likely telling you is that your body is exhibiting the signs of anxiety and not which door actually has the car.
Maybe I’m a shitty decision maker:D, but how would your odds not still be 1 in 2 if you were to leave pick at #1. Correct me if I’m wrong but wouldn’t you still have a 50/50 shot at getting the car regardless of whether you pick #1 or #3?
You can flip a coin 99 times and have it come up heads every time. What are the odds it’ll be heads on the 100th flip? Fifty/fifty.
Google the Monty Hall Problem or Paradox and you can probably find a much better explanation than I can provide. It’s just probabilities. When you picked #1, that door had a 33% chance of being the winner. When you change to #3, that door has a 50% chance of winning. The fact that #1 was in the mix both times doesn’t change the probabilities. Would you want to stand on a 1 in 3 shot when you could improve your odds to a 1 in 2?
To know which door the has the goat, first I must discern what sort of man Monty is.
If Monty is honest and truthful, he will tell me to pick Door #3 because he knows the goat is behind Door #1. I can clearly not choose Door #1
But if Monty is a liar, he will tell me to choose Door #3 because the car is behind Door #1. I can clearly not choose Door #3
But if Monty is a clever liar, he will know that I must be smart to make it far enough to have a chance at the car and that I would know he is lying, so I can clearly not choose Door #1.
However, Monty has made one of two classic military blunders. The first is to never engage in a major land war in Asia. The second, only slightly less well known, is never go against a Sicilian when goats are on the line!
I do not want Door #1 nor do I want Door #3. I stay with Door #2 knowing there is nothing more satisfying than to be on national TV with some smarmy gameshow host when I finally get his goat
I don’t buy that explanation. When door 2 was opened to reveal a goat, and he asks you if you still pick door 1, if you pick door one you have essentially chosen again. At that point in problem door one has a 50/50 chance of winning, same with door 3. It is most definately not a case of door one still having a 33% chance and door 3 having a 50% chance against door ones 33%. Infact door 3 also had a 33% chance of winning the first time around aswell, changing your choice does not magically make it have a 50% chance and door one only a 33% chance. When monty opened door 2 both door 1 and 3 both had their odds upped to 50%
They both have a 50% chance at that point. You are no better or worse by changing your pick at that point.
