:::: Ok, now I understand your way to look at the situation but I still dont't find this makes things clear about the "paradox". The problem is that we *have proved* that for any possible n if my envelop contains  then the best thing to do is to change the envelope. We can say exactly what is the expected gain I recive: it is  (another way to express 2^(n−2)q(1 − 2q)/R ). It is a well defined positive number for any possible n. So now let's leave the probability theory and use pure logic: if for any possible sum that I could find in the envelop the best thing is to change, WHY should I waste time looking at it? Let's change immediatly! *This* sounds paradoxical, and this is not explained by the argument about ∞ − ∞!!