On the other hand, consider the chance that the car may be picked out by host and the participant may permanently lose the car. If calculated that way, the overall probability of the participant to win the car is always 1/10.
Intuitively, if a game never helps the participant gain any extra advantage, the overall probability is always 1/10, no matter how complicated the game rules are.
The above statement is important. People design complicated rules in the hope to increase the probability, but all end up the same way. This is applicable not only to stock investing, but also to gambling in Las Vegas.
The original problem in this post is different, because in that problem the host has extra knowledge of which door is car and which is donkey. This extra knowledge is utilized by the participant and results in extra winning probability, 2/3.
