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This alternative formulation from a Mathematics StackExchange answer[1] makes the decision to switch much more obvious: "There are three boxers. Two of the box
by alexhutcheson 7y ago
This alternative formulation from a Mathematics StackExchange answer[1] makes the decision to switch much more obvious:
"There are three boxers. Two of the boxers are evenly matched (i.e. 50-50, no draws!); the other boxer will beat either them, always.
You blindly guess that Boxer A is the best and let the other two fight.
Boxer B beats Boxer C.
Do you want to stick with Boxer A in a match-up with Boxer B, or do you want to switch?"
[1] https://math.stackexchange.com/questions/96826/the-monty-hall-problem/3360686#3360686 https://math.stackexchange.com/questions/96826/the-monty-hal...
- jedimastert 7y agoI'm gonna have to do a lot of thinking to make sure this matches the problem at hand, but if it does this is an incredible translation.
- bobbylarrybobby 7y agoMonty Hall: if you pick one of the bad doors, which has probability 2/3, then you should switch after shown a bad door. Otherwise (probability 1/3) you should stick with your door. Boxers: if you pick one of the bad boxers, which has probability 2/3, then you should switch after shown a bad boxer which happens when the first round fight ends. Otherwise (probability 1/3) you should stick with your boxer.
- Vadoff 7y agoIt's not quite the same being shown a bad door vs a bad boxer that you were told would always result in a draw otherwise. That means the other boxer is always the better one (or the car), it doesn't take into account that the winning boxer could be what you have.
- zaksoup 7y agoHere's the explanation I like to use every year when this makes it to HN: You pick door 1. Out of three doors you have a 1/3 chance of having a car behind your door. The chance that the car is behind one of either of the other two doors is 2/3. Let's pretend that instead of opening a door and revealing a goat, Monty instead says to you "You can switch to both of the remaining doors. If the car is behind either one of them you get to keep it." Your likelyhood of getting the car by switching is now 2/3. Instead, Monty does the statistical equivalent: He allows you to know for sure which of the other doors definitely has a goat.
- leeoniya 7y agoanother way to think of it is: monty has the car 2/3 of the time. when he has the car, he must tell you where it is (by showing you where it isn't). that last part is key. he is not making a random selection. so if you go with his remaining door, it will have the car the same 2/3 of the time.
- BrandoElFollito 7y agoThank you. At last I understood it now.