No, not the idea that
this time you'll win. :). The
fallacy of confusing random mutation with lotteries. A lot has been written about Evolution - often with unecessarily technical words - but this is often preaching to the converted (if you'll excuse the metaphor). Somehow, there are some basic concepts somewhere which have been lost. The effects of random
mutations may be one of them.
Firstly consider the idea of a lottery. A big group of people randomly pick numbers; only one number wins. Of course, everyone hopes they'll win, but only one does. So long as the sequence of numbers is short enough - AND the number of players large enough - someone's quite likely to win.
If life was a lottery you could work out the probabilities of evolution. How likely is a 100 residue peptide? How probable is an Ur-cell? The usual answers seem conclusive : Life is impossible. After all, if the lottery required a particular 100 letter sequence to win, it would need an awful lot of players (or a very long series of rollover weeks)...
These calculations may be as precise as you like, but they will never be accurate. The conceptual mistake is powerfully simple ~ and so very easy to make. It is to assume that the end product was the only possible winner. That things could not have turned out differently; that you lost, not someone else won.
Applying this back to mutation: just because a particular sequence is a winner (functional) doesn't mean it was inevitable. Saying that all mutation was bad - that is, disrupts a certain function - ignores the fact that what's bad for some things is good for others. It is as if life plays many lotteries at once, so that if it loses in one it may win in one of the others.