>>>You have selected door # 1 of three doors on the price is right.
>>>Monty Hall shows you door # 2. Behind door # 2 is a got chewing on an old tin can. Behind one of the two door is another got and behind the other is a new boat.
>>>
>>>Monty Hall asks you if you want to change the door you have chosen. Should you change? And why?
>>
>>Dan,
>>
>>Yes you should change. Here's why;
>>
>>Your first choice of one of three doors had a probability of 1 out of 3 to select the correct door, that is there are 2 out of 3 chances that you chose the wrong door. The probability that your first choice is wrong is double the probability that it was right.
>
>Jim Booth and Christof Lange are correct.
>You can either run Christof's prgoram or I can give you a simple example that proves it.
>
>You have three cards. One ace. Two Jacks. You are trying to get the ace. There are nine possible scenarios based on which card you pick but I will only cover three.
>
>1.
> 1 2 3
> A J J
>
>2.
> 1 2 3
> J A J
>
>3.
> 1 2 3
> J J A
>
>We will automatically switch each time.
>I will assume you take card #1 without looking at it.
>
>In the first example, I show you #2, you pick #3. You get a J and lose.
>In the second example, I show you #3, you pick #2. You get an A and win.
>In the third example, I show you #2, you pick #3. You get an A and win.
> _
>That's 2/3 or 66.6. Try it yourself with cards, if you don't believe it. I know it seems like it should be a 50/50 shot, but it really is 2/3.

Sorry, Dan, you're wrong. See my latest reply to Walter Meester. Where you guys are all falling down is in including the result of the already known door in your analysis. The analysis is of 2 doors, not 3; one contains a boat, the other a goat. You own one of the two doors. Therefore the door you already own has a 50% chance of containing the boat. There is no advantage or disadvantage to changing your choice to the other unknown door.