Proving all the axioms of probability theory using game theory instead of measure theory.

A couple of years back I wrote up a short proof of the law of large numbers using game theory. http://www.marksaroufim.com/2015/02/14/probability-without-m...

All the ideas are inspired by this book by Shafer and Vovk https://www.amazon.com/Game-Theoretic-Foundations-Probabilit...