Context:
I am a rising CS senior planning on going for a PhD. I would like to study probability theory on my own for its usefulness in machine learning and game theory. There are quite a few textbooks out there, so I would like a recommendations on books that have good coverage on stuff relevant in CS.
I was thinking of going either with Probability Theory: The Logic of Science by Jaynes or with Introduction to Probability by Bertsekas and Tsitsiklis. Both seem to be received very positively, but I don't know if I should go with these or another textbook written with applications in mind.
My probability class used the second one and it covers all the basics while getting into estimation, inference and some stochastic processes. I personally liked it and several of my friends used it to prepare for out machine learning classes.