Game-Theoretic Foundations for Probability and Finance (Wiley Series in Probability and Statistics)
ISBN: 0470903058
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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...