The fact that switching gives you 66% chance of getting a prize, compared to not-switching giving you a 33% chance isn't up for discussion. It does. This is not up for debate any more than 1 + 1 = 2.
If you would like to see this for yourself, go here, play with the simulator until you you have a statistically significant amount of samples (30+) or just have it run a couple hundred automatically for you:
The Monty Hall problem
We can have a discussion about WHY you get a better chance if you switch. We cannot have a discussion about IF you get a better chance if you switch.
---------- Post added at 11:05 AM ---------- Previous post was at 11:04 AM ----------
Quote:
Originally Posted by Strange Famous
To look at this is real terms, lets say we played the game three times, and the results happened to go by the numbers
Each time I stick
Game 1 - I guess 1, the prize is in 1. Monty opens 3, offers me a swap, I say no - I win
Game 2 - I guess 1, the prize is in 2. Monty opens 3, offers me a swap, I say no - I lose
Game 3 - I guess 1, the prize is in 3. Monty opens 2, offers me a swap, I say no - I lose
If I stick each time, I win 1/3 of the time
If I twist each time
Game 1 - I guess 1, the prize is in 1. Monty opens 3, offers me a swap, I say no - I lose
Game 2 - I guess 1, the prize is in 2. Monty opens 3, offers me a swap, I say yes - I win
Game 3 - I guess 1, the prize is in 3. Monty opens 2, offers me a swap, I say yes - I win
...
I just typed that and it makes absolutely no fucking sense.
There is a 1/3 chance it is in any of the boxes! How can it possibly be so that whether I stick of twist can effect in anyway what is in the box???
Will the sky fall in now???
|
Look at your own examples. You have a 1/3rd chance of winning (win/lose/lose) if you don't switch and a 2/3rd chance of winning (lose/win/win) if you do. Each of your three options are statistically equally likely! This is probably one of the best demonstrations I've seen as to why you get a better chance if you switch--I'm not sure how you could type such a perfect explanation and yet still not understand it!