Abstract. This work is inspired by a 2013 paper from Arne Traulsen's lab at the Max Plank Institute for Evolutionary Biology. They studied the small mutation limit of evolutionary games. It has been shown that for 2 by 2 games the ranking of the strategies does not change as strength of selection is increased. The point of the 2013 paper is that when there are three or more strategies the ordering can change as selection is increased. Traulsen et al did numerical computations for fixed N. Here, we will instead let the strength of selection β = c/N and let N tend to infinity to obtain formulas for the invadability probabilities that determine the rankings. The integrals that give these probabilities are difficult to evaluate in general, but they do allow us to compute the ranking order when c is small or c is large.