alternate serve directions too often, and consequently do not achieve the proper probability distribution. Professionals, on the other hand, do approach the ideal distribution more nearly, suggesting that game theory does indeed capture something about optimal behavior, and that humans do have the capability of learning how to play games with game-theoretic rationality.
And that, in turn, makes a point that I think is relevant to the prospects of game theory as a mathematical method of quantifying human behavior. In many situations, over time, people do learn how to play games in a way so that the results coincide with Nash equilibrium. There are lots of nuances and complications to cope with, but at least there’s hope.
Of course, real-life situations, the rise of civilization, and the evolution of culture and society are much more complicated than flipping coins and playing tennis. But that is also true of the inanimate world. In most realms of physics and chemistry, the phenomena in need of explanation are rarely split between two equally likely outcomes, so computing probability distributions is much more complicated than the simple 50-50 version you can use with pennies. Maxwell, and then Boltzmann, and then the American physicist J. Willard Gibbs consequently expended enormous intellectual effort in devising the more elaborate formulas that today are known as statistical mechanics, or sometimes simply statistical physics. The uses of statistical mechanics extend far beyond gases, encompassing all the various states of matter and its behavior in all possible circumstances, describing electric and magnetic interactions, chemical reactions, phase transitions (such as melting, boiling, freezing), and all other manner of exchanges of matter and energy.
The success of statistical mechanics in physics has driven the belief among many physicists that it could be applied with similar success to society. Nowadays, using statistical physics to study human social interactions has become a favorite pastime of a whole