re: Let's discuss the Monty Hall problem (probabilities, odds)

just go watch 21 they explain it there.

but it has to do with what i call relative probability.

ETA: Think of it this way - you pick your door for the prize. Then if someone said "i'll let you choose either to keep your door or to choose both of the other doors" which would you choose?

This is essentially what the host is doing by removing the incorrect door. While the new choice is essentially 50 / 50 - given what you know about the way the game is set up it is really 33% your door and 66% the other door since the other door has also taken on the probability of the door which the host has already revealed.

That is probably the best i can do without writing out a proof. Probability Theory and Discrete Mathematics is really fascinating - one of the courses i kept my textbook for.