the monty hall paradox
if you're given 3 doors, one has a prize, two don't
you pick a door, the host opens one of the other two doors and shows that it doesn't have a prize in it, and asks if you want to switch.
The logic is, you now have a 50/50 chance, but that's not the case.. As long as the host is being legit, when you choose a door, you are assigning that door a 1/3 chance to be a car, logically the combined probability of one of the two remaining doors to have a prize is 2/3. When the host opens a different door and show it to have no prize, they are assigning that door with a 0/3 probability of having a prize, and giving the remaining unchosen door a 2/3 probability of having a prize.
If the game is being played legitimately, you are ALWAYS better off switching. Of course, there are lots of ways that the game can be rigged to remove that. They can take away the ability to switch unless certain criteria, such as choosing a door with the prize or without it are met. If they always only ask about a switch when you've chosen the prize with your initial guess, switching will always lose.
It's basically Bertrand's box paradox
if you're given 3 doors, one has a prize, two don't
you pick a door, the host opens one of the other two doors and shows that it doesn't have a prize in it, and asks if you want to switch.
The logic is, you now have a 50/50 chance, but that's not the case.. As long as the host is being legit, when you choose a door, you are assigning that door a 1/3 chance to be a car, logically the combined probability of one of the two remaining doors to have a prize is 2/3. When the host opens a different door and show it to have no prize, they are assigning that door with a 0/3 probability of having a prize, and giving the remaining unchosen door a 2/3 probability of having a prize.
If the game is being played legitimately, you are ALWAYS better off switching. Of course, there are lots of ways that the game can be rigged to remove that. They can take away the ability to switch unless certain criteria, such as choosing a door with the prize or without it are met. If they always only ask about a switch when you've chosen the prize with your initial guess, switching will always lose.
It's basically Bertrand's box paradox