What mutations are needed for a particular trait (e.g. wings) to arise?

I hope you will forgive me for butting in. I'm new and still learning the customs here. I recently read a book called "Lightning Strikes" about probability. The author points out that if you run a coin-flipping tournament with (I think) 1024 contestants, you are guaranteed to wind up with a winner who won ten times in row. You just wouldn't be able to predict who it would be beforehand. Perhaps this is related to the difficulty here?Edited by Woodsy, : spelling

In these discussions, we quite naturally focus on the "winners" and lose sight of the vast numbers of individuals who do not "win". The point of the coin-tossing example was that "extreme dumb luck" can happen naturally and is in no way way miraculous. We are impressed by the sequence of wins, but the chances surely reset at each cycle, so each win is just as likely as any of the others, and if there are many players, we should expect strings of wins to show up.

codegate: That's a very clear account.
skepticfaith: Are you expecting mutations in response to changes in selection pressure? As I understand it, evolution is not forward looking, or even sideways. One would expect that random mutations give rise to variations in a population that can then accommodate a new selection pressure or opportunity. When we add the antibiotic to the Petrie dish, it is the microbes who happen to be already resistant who survive. As another thought experiment, after a new tree with tough nuts grows in the neighbourhood, a bird who happens by chance to grow a stronger beak is in luck.