I'm not sure, but I bet Michael Larson could have figured it out.
Perhaps he could have. Michael Larson does not appear to have had any special mathematical talent. But perhaps it is possible to figure out the odds by watching a few dozen episodes of the show and simply tallying the success rates of people who changed their choices versus those of people who stick.
In any event, the solution to the problem is well known by now, and this is at least the second time we have discussed the Monty Hall problem in these forums.
Dr. Adequate's explanation using the 100 doors is the clearest, most succinct one I've ever read.
Under a government which imprisons any unjustly, the true place for a just man is also in prison. Thoreau: Civil Disobedience (1846)
I have never met a man so ignorant that I couldn't learn something from him. Galileo Galilei
If there is no struggle, there is no progress. Those who profess to favor freedom, and deprecate agitation, are men who want crops without plowing up the ground, they want rain without thunder and lightning. Frederick Douglass
™ Version 4.2