I get a lot of Emails and forum posts about this problem. Based on feedback given, I've changed my "solution" to this problem numerous times. Suffice it to say, I've never been entirely satisfied with my explanation of why there isn't a 25% expected gain in switching. My readers have never been satisfied with my explanations either.
As of this writing, I feel comfortable that I understand the answer, but I don't know the proper way to explain it. I think there are two ways you can attack the 25% argument but I think one of them is a red herring and there needs be only one.
Suffice it to say, that I recently took down my latest explanation because it was getting too much negative feedback. So, come back later and maybe I'll have another solution to present.Michael Shackleford, A.S.A.