Please see the wikipedia for the description of the Monty Hall problem .
The Russian roulette problem is: There are two bullets placed randomly in a 6 chamber revolver. Your opponent goes first and survives the first trigger pull. You are given the option whether to spin the barrel. Should you?
The conditional probability of you losing in the next round given the opponent survived the first round is 2/5. In my opinion this is an "intuitive" answer, because there are 5 chambers left and 2 bullets in them.
On the contrary, the "intuitive" answer for switching doors in the Monty Hall is 1/2, which is incorrect. I say 1/2 because conditioned on the goat being shown, there are now two doors to choose from, one of them containing the car.
My question is: what is the difference between these two problems which makes the Monty Hall problem deceptive? Is there a way to apply Bayes Theorem to the Russian roulette problem?