Thanks for the link. I was thinking of doing my own Monte Carlo, but as this article suggests a sample of 100 trials may not be enough to ascertain the right result.

For the moment, I shall be content that the experts--theoretical or Monte Carlo--have come to the right conclusion. If I am selected to be on the price is right, I will take their advice--even if my intution says it doesn't matter.

But the odds are very small I will be able to say "Switch the doors."