Re:Another interesting math problem (Score 1)

While making a table of all possibilities is generally a good idea, you have to watch out that all the cases you are mapping out are equally likely. If you look at your table again, you initially pick the right door 50% of the time. That can't be quite right...

1 2 3 K S
P N N W L
P N N W L
P N N L W
P N N L W
(picking the right door 2 times out of 4?)

You are probably confused because in that case the host has two doors he can open, so he will open each of them 50% of the time. If you compensate for that by weighting these lines with a factor of 0.5, than you'll come out at the right 1/3 against 2/3 probability.

But probably the best way to get a feeling for this problem and how weird probability can be would be to find someone to play the host for you and just try it ;)