Yes I understand it perfectly. You can too by solving a larger problem of 100 doors all of which are opened except your pick and one other. Conversely you could play the game with someone a few dozen times and you would see the result tending to 2/3 wins if you switch.

I didn't understand it until the Mythbusters ran a double blind test where one set was always to switch choices the other was to stand pat over 100 choices.

the results were very impressive.

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In a rich man's house there is no place to spit but his face.
Diogenes Of Sinope

The thing to realize is that the box (or door) that gets opened is not chosen at random. It is always one that is *not* the prize, so the choice provides you with information.

1/3 of the time you will have chosen the prize door. So switching will give you a fail.

2/3 of the time you will not have chosen the prize door. In this case switching will *always* give you the prize.

So if you switch, 2/3 of the time you will get the prize.

When you chose one box you had a one third chance of picking the winner.
Conversely, two thirds of a chance of being wrong. Remove one of the known
remaining box's that is a looser and you then switch your choice over to that
other remaining box means now you have a two thirds chance of picking the
winning box. Sticking on your first choice means you had initially a 1 in 3
chance of picking the winner and still now only have that 1 in 3 chance.
The catch in this exercise is caused by exposing one of the empty box's after
you have made your choice, you think you now have a chance of being 50% right
with your initial choice of box you made. Nope, so switch for the other box
has a 2 in 3 chance of being the winner.

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The Kite Fliers

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Kite fliers: An imaginary club of solo members, those who don't yet
belong to a formal team so "fly their own kites" - as the saying goes.

And then you have Murphy's Law that says you'd probably choose the wrong door...;)

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rOZZ
Music
Pictures

And then you have Murphy's Law that says you'd probably choose the wrong door...;)

Yes, but only once in three though of choosing the wrong one. If you carried out
this box exercise in a slightly different way then you'd see why you should
always change your initial choice of selected box.

Choose a box, then your given the choice now of opening that box or opening
the other two remaining box's in stead. Clearly you would take the offer of
switching to the remaining two box's cos' you can clearly see the odds of 2 in 3
in your favour of having the winning box.

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The Kite Fliers

--------------------
Kite fliers: An imaginary club of solo members, those who don't yet
belong to a formal team so "fly their own kites" - as the saying goes.

Here's a site that has a game that lets you try out the two strategies, see for yourself:

http://betterexplained.com/articles/understanding-the-monty-hall-problem/

Here's a site that has a game that lets you try out the two strategies, see for yourself:

http://betterexplained.com/articles/understanding-the-monty-hall-problem/

That is a great site. i played the game and was convinced that it pays big time to switch doors.

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[/quote]

Old James