You don't have to be bad at math to be bad at probability and rational choice. (Plus, rational choice sometimes tells us to do stupid things, as in the St. Petersburg paradox.)
Rational choice emphatically does not imply anything stupid in St. Petersburg paradox. Rational choice has nothing to do w/ evaluating monetary lotteries at their expected monetary value. In fact, as a professor who teaches rational choice I can tell you the following: if you answer like this on an exam you'll fail 
And you would fail as a rational choice professor, because you would not be able to explain why the St. Petersburg paradox doesn't apply when the item(s) to be won are utiles rather than monetary units.
Not only I'd be able to explain it - I do exactly that every semester, sometimes twice
Of course, not, really, that it doesn't apply, but rather that there isn't a real paradox.
Ok. What's St. Petersburg paradox? It's an example of a lottery of infinite expected monetary value that few people would care to purchase even for peanuts. It is used, primarily, to illustrate the point that expected monetary value of lotteries have little to do with individual preferences over it. Bernoulli himself (the one who coined the "paradoxical" example) suggested that it could be easily explained if one assumed "decreasing marginal utility of money". To avoid the problems with the notion of "preference intensity" (in rational choice we don't like it
), modern utility theory gives a more nuanced explanation (which I would need about half a lecture to set up), but the basic intuition of Bernoulli is there as well. At the very least, attempting to value monetary lotteries using their expected value is viewed as big and ugly mistake: if you do this in an exam, you fail.
Now, your point about "utiles" is even worse: "utiles" don't exist. There isn't a "standard unit of happiness" not even in a vault in Paris, like a kilo. We can talk about utillity (even expected utility) representation of preferences, but that's something alltogether different.
But even if they did exist, there would be no problem. Preferences (and, hence, utilities) are subjective, not in any sense "intrinsic" or "objective". The fact that nobody chooses to sell their house for the St. Petersburg lottery is evidence of common preferences in that regard. Now, there is nothing "(ir)rational" about any given price for a lottery. When economists/rational choice theorists talk about an individual's "rationality" all they mean is that his/her preferences satisfy a couple of basic consistency conditions (completeness and transitivity) - no more, no less. Any price for any given lottery, from negative to positive infinity, could be consistent with rationality. Not to mention the point, that even to meaningfully take expectations over the utilities you need to assume something (independence) far above and beyond rationality itself.
Please, take a good microecon/decision theory course - it's worth it, it's lots of fun
(and you'd clear up all the misunderstandings you are having right now). Perhaps, I should give a tutorial
PS I suggest moving this thread to the Economics board.
