Quote:
Originally Posted by ME_Andy
Yep, the key to all of this (as I understand it) is that the host intentionally makes his choice in a way that doesn't give you any more info.
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Wrong. The host
always gives more info.
The chance of the host showing A goat is 100%. This is the format of the gameshow.
Once the host shows that goat, he
collapses the probabilities, making it much easier to win the game. Just because the other possibilities no longer exist, doesn't mean you shouldn't count them in assigning percentages!
Simplest way to put it:
If
Car = Your Door (1/3rd chance), host can open either door.
Changing mind = 0% wins.
If
Car =/= Your Door (2/3rd chance), host will never open the winning door. The remaining door is the Car.
Changing mind = 100% win
100% of 2/3rd is 66% chance of winning, overall.
It's that simple.
And statistical testing backs it up.
If you want long, boring tables, though:
Code:
Car You Host You Win %, Changed mind
A A xxx xxx xxx 0.00%
A A xxx xxx xxx
A A xxx xxx xxx
A A B A win
A A B xxx xxx
A A B C lose
A A C A win
A A C B lose
A A C xxx xxx
B A xxx xxx xxx 100.00%
B A xxx xxx xxx
B A xxx xxx xxx
B A xxx xxx xxx
B A xxx xxx xxx
B A xxx xxx xxx
B A C A lose
B A C B win
B A xxx xxx xxx
C A xxx xxx xxx 100.00%
C A xxx xxx xxx
C A xxx xxx xxx
C A B A lose
C A B xxx xxx
C A B C win
C A xxx xxx xxx
C A xxx xxx xxx
C A xxx xxx xxx
Chances 66%