The movie 21 Please explain the math.

[sdduuuude]

By the way, this logic provides some insight into poker as well.

If you are playing 10-handed no-limit hold ’em, for example, and one guy bets, then 8 guys fold pre-flop, and you have a mid-quality hand, you should fold. Even though it comes down to you against him, the fact that he is likely the best of 9 hands makes it very unlikely you have a better starting hand.

However, if there are only 3 players, one guy bets and the other guy folds, you should probably stay in as your maginal hand has a much better chance against the best of 2 random starting hands as opposed to the best of 9 random starting hands.

The act of folding in this case is like the host taking away the door with the goat.

[recordsclerk]

You have three doors
One of the doors is a winner (car)
Each original door has a 33% or 1/3 chance of being the winning door.
So if you choose two doors then your chances of winning are 66% or 2/3.
If one of your doors are revealed and it’s not the winning door, in theory your odds are still the same. You still have a 66% chance of winning the car from the original circumstances. So in reverse if you choose one door you have a 33% or 1/3 chance of winning and the other two doors have a 66% or 2/3 chance of winning. By revealing one of the other doors, you still have a 66% chance of winning with the remaining door, so changing to that door gives you a probability of 66% or 2/3 chance of winning.
BTW if you have two doors, your chances are 50/50

[recordsclerk]

You have three doors
One of the doors is a winner (car)
Each original door has a 33% or 1/3 chance of being the winning door.
So if you choose two doors then your chances of winning are 66% or 2/3.
If one of your doors are revealed and it’s not the winning door, in theory your odds are still the same. You still have a 66% chance of winning the car from the original circumstances. So in reverse if you choose one door you have a 33% or 1/3 chance of winning and the other two doors have a 66% or 2/3 chance of winning. By revealing one of the other doors, you still have a 66% chance of winning with the remaining door, so changing to that door gives you a probability of 66% or 2/3 chance of winning.
BTW if you have two doors, your chances are 50/50

[recordsclerk]

You have three doors
One of the doors is a winner (car)
Each original door has a 33% or 1/3 chance of being the winning door.
So if you choose two doors then your chances of winning are 66% or 2/3.
If one of your doors are revealed and it’s not the winning door, in theory your odds are still the same. You still have a 66% chance of winning the car from the original circumstances. So in reverse if you choose one door you have a 33% or 1/3 chance of winning and the other two doors have a 66% or 2/3 chance of winning. By revealing one of the other doors, you still have a 66% chance of winning with the remaining door, so changing to that door gives you a probability of 66% or 2/3 chance of winning.
BTW if you have two doors, your chances are 50/50

[recordsclerk]

You have three doors
One of the doors is a winner (car)
Each original door has a 33% or 1/3 chance of being the winning door.
So if you choose two doors then your chances of winning are 66% or 2/3.
If one of your doors are revealed and it’s not the winning door, in theory your odds are still the same. You still have a 66% chance of winning the car from the original circumstances. So in reverse if you choose one door you have a 33% or 1/3 chance of winning and the other two doors have a 66% or 2/3 chance of winning. By revealing one of the other doors, you still have a 66% chance of winning with the remaining door, so changing to that door gives you a probability of 66% or 2/3 chance of winning.
BTW if you have two doors, your chances are 50/50

[recordsclerk]

You have three doors
One of the doors is a winner (car)
Each original door has a 33% or 1/3 chance of being the winning door.
So if you choose two doors then your chances of winning are 66% or 2/3.
If one of your doors are revealed and it’s not the winning door, in theory your odds are still the same. You still have a 66% chance of winning the car from the original circumstances. So in reverse if you choose one door you have a 33% or 1/3 chance of winning and the other two doors have a 66% or 2/3 chance of winning. By revealing one of the other doors, you still have a 66% chance of winning with the remaining door, so changing to that door gives you a probability of 66% or 2/3 chance of winning.
BTW if you have two doors, your chances are 50/50

[pepsi]

I wrote my own program and, to my surprise, 66% is the right answer. ( I thought it was 50% chance)
Then I reviewed my own program and I finanlly understand why 66% is the right answer.
The reason is at the door the host opened.
In 2/3 of chance, the door he opened is not a random pick.
In your first guess, you have 2/3 chance to guess wrong, so the door number the host must opened is limited to a certain door. (He can not opened the other door).

By doing the switch, you are saying: “the first door I chose is wrong”, which is 2/3 of chance.

And that is why you must switch !

[pepsi]

I wrote my own program and, to my surprise, 66% is the right answer. ( I thought it was 50% chance)
Then I reviewed my own program and I finanlly understand why 66% is the right answer.
The reason is at the door the host opened.
In 2/3 of chance, the door he opened is not a random pick.
In your first guess, you have 2/3 chance to guess wrong, so the door number the host must opened is limited to a certain door. (He can not opened the other door).

By doing the switch, you are saying: “the first door I chose is wrong”, which is 2/3 of chance.

And that is why you must switch !

[pepsi]

I wrote my own program and, to my surprise, 66% is the right answer. ( I thought it was 50% chance)
Then I reviewed my own program and I finanlly understand why 66% is the right answer.
The reason is at the door the host opened.
In 2/3 of chance, the door he opened is not a random pick.
In your first guess, you have 2/3 chance to guess wrong, so the door number the host must opened is limited to a certain door. (He can not opened the other door).

By doing the switch, you are saying: “the first door I chose is wrong”, which is 2/3 of chance.

And that is why you must switch !

[pepsi]

I wrote my own program and, to my surprise, 66% is the right answer. ( I thought it was 50% chance)
Then I reviewed my own program and I finanlly understand why 66% is the right answer.
The reason is at the door the host opened.
In 2/3 of chance, the door he opened is not a random pick.
In your first guess, you have 2/3 chance to guess wrong, so the door number the host must opened is limited to a certain door. (He can not opened the other door).

By doing the switch, you are saying: “the first door I chose is wrong”, which is 2/3 of chance.

And that is why you must switch !

[pepsi]

I wrote my own program and, to my surprise, 66% is the right answer. ( I thought it was 50% chance)
Then I reviewed my own program and I finanlly understand why 66% is the right answer.
The reason is at the door the host opened.
In 2/3 of chance, the door he opened is not a random pick.
In your first guess, you have 2/3 chance to guess wrong, so the door number the host must opened is limited to a certain door. (He can not opened the other door).

By doing the switch, you are saying: “the first door I chose is wrong”, which is 2/3 of chance.

And that is why you must switch !

[drunkle]

it’s much easier to think about with higher numbers. ie., 1000 doors; your odds of picking the winner is 1:1000. the odds of the car being behind any one of the remaining doors is 999:1000. eliminating all of the other incorrect doors means that the chance of the car being in the door you didn’t pick is 999:1000.

[drunkle]

it’s much easier to think about with higher numbers. ie., 1000 doors; your odds of picking the winner is 1:1000. the odds of the car being behind any one of the remaining doors is 999:1000. eliminating all of the other incorrect doors means that the chance of the car being in the door you didn’t pick is 999:1000.

[drunkle]

it’s much easier to think about with higher numbers. ie., 1000 doors; your odds of picking the winner is 1:1000. the odds of the car being behind any one of the remaining doors is 999:1000. eliminating all of the other incorrect doors means that the chance of the car being in the door you didn’t pick is 999:1000.

[drunkle]

it’s much easier to think about with higher numbers. ie., 1000 doors; your odds of picking the winner is 1:1000. the odds of the car being behind any one of the remaining doors is 999:1000. eliminating all of the other incorrect doors means that the chance of the car being in the door you didn’t pick is 999:1000.

[Author]

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