The stats shown after you play here make it very clear:
Here is a summary of how previous contestants have fared. # of Players Winners Percent Winners Switched 2570 1746 67.9 Didn't Switch 2415 814 33.7
In effect he has not.
You had three choices each 1/3 of a chance of winning.
You had one, the host had two.
So he had 2/3 of a chance of having the winner. You had 1/3.
Now the host removes one of his which was a loser.
So now you have yours at 1/3 chance of winning and his remaining one at
2/3 chance of winning.You know this, the new contestant doesn't know this.
No there are still three doors. You now know that it isn't behind one of the hosts doors. But it is still 2/3 chance that it is behind one of his doors.
that you still have a 50% chance of winning.
You are correct it doesn't change the odds.
At the start the host has 2/3 chance of having the car and you have 1/3.
So if he said you could have his two doors would you swap?
Now he throws away one of his doors by opening it and showing it to be a loser. Would you swap now knowing that he still has 2/3 of a chance of winning vs. your 1/3?
It's harry.
It very much *does* mean that it is true.
If something has been proven mathematically, then it is the end point of a chain of *irrefutable* logic that stretches back to the axioms upon which you start - these are, essentially, the things that are so self-evidently true that they are unprovable, e.g. 1 + 1 = 2.
So if you reject the truth of a mathematical proof that you find inconvenient, you are rejecting the truth of 1 + 1 = 2.
NB to pedants - tried to keep it simple, 'kay?
Commit suicide. It is more preferable than appearing on a TV game show.
That worries me!
What, that Harry doesn't get it yet or that you don't?
Tim
He's not always wrong. (would be useful if he was!)
But this time he is.
Andy
Progress at last :-)
MBQ
That's probably the best answer yet!
No, that if Harry agrees with me, that greatly increases the probability that I'm wrong!
Roger Mills put finger to keyboard:
You've *still* not got it? ;-)
You choose one of the three boxes, yes?
Assuming you always switch:
If you initially choose the box with the car - a one in three chance - you will lose because you've switched to a box without a car.
If you initially choose either of the boxes without the car - a two in three chance - you'll always win because you've picked one of the non-car boxes and the host has opened the other non-car box.
2/3 of the time?
Lol
I did, come on baby light my fire ......
Maths is discovered, not constructed.
I'm getting there!
What you have written makes perfect sense - and certainly stacks up with an Excel simulation which I have done, in which the ratio of swapping wins to non-swapping wins is approximately 2:1
But I'm still somewhat conflicted because I can't see anything wrong with the logic which concludes that the odds are 50:50
Clearly they can't *both* be right! I still have a bit of work to do.
Now that's interesting.
Not the result, but that roughly half the people decide to stick.
Ignoring the maths, there's a psychological pressure not to switch. People hate losing something they did have, but don't mind not winning something they never did.
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