I'll play your game and assume for the sake of argument that the average occurs at set intervals - it doesn't at all, just because the guy gets an average successful guess of once per minute it in no way means that he was "going" to get it in ten seconds just because 50 had already elapsed - but even if it did, if it's just a guess anyways why would it be any less valid for the next card? He wasn't homing in on the correct number, his guesses are random. It is just as likely he will get a guess on the next card in those next ten second if we assume average=interval (which it does not).