Quote:
Right. But when you hear it in those words, you don't believe it because it's so counterintuitive. What Furtive was looking for was a way to explain it to nonbelievers so that they would understand.


Believe me, I can relate!
The first time I ran across this conundrum (almost exactly 10 years ago, when Marilyn vos Idiot ran it in her column) I didn't grok it and had to blow half an hour writing, running, and playing with a simulator in C in order to convince myself. (Hey, I figured a few hundred thousand trials would make it clear to me.) And what do you know, I won 66.66% of the time when I switched and 33.33% of the time when I didn't.

Of course, just the process of writing the code kind of clarified my thinking. Only then did I remember this little thing called "conditional probability" from a class in "Random Variables." D'oh.

However, now the solution has seemed so obvious to me for so long that I can't understand why it ever seemed counterintuitive. So, weirdly, I'm having a hard time wrapping my mind around exactly what little *aha* push someone else might find useful.

My point in my previous post was just that ninti's explanation seemed to clarify everything very succinctly and provide a good understanding to mlord's "double your odds" comment.