Martingales and Betting Strategies Does anyone know of a good introduction to the theory of martingales and betting strategies from the point of view of statistics and/or probability theory?  I'm looking for something basic, with lots of examples. Thanks.
 A: I haven't read it, but I saw Glenn Shafer give a talk on his and Vladimir Vovk's game theoretical approach to probability.  It could be an interesting/more intuitive approach than the usual measure theoretic approaches.  They discuss martingales in several chapters of their book and I'm certain there's lots of applications/examples especially from finance.  Might be worth a look:
http://www.probabilityandfinance.com/chapters/toc.html
A: no doubt that Probability with Martingales is excellent, but I am not sure that this is a very satisfying book for someone interested in "the point of view of statistics". 
A: I don't know about statistics per se but the best introduction to martingales period is Williams' Probability with Martingales:
http://www.amazon.com/Probability-Martingales-Cambridge-Mathematical-Textbooks/dp/0521406056
A: Shiryaev's "Probability" is an excellent source.
A: Have a look at "The Doctrine of Chances: Probabilistic Aspects of Gambling"
by Stewart Ethier
http://www.springer.com/mathematics/probability/book/978-3-540-78782-2
Lots of examples related to just about every casino game you've ever heard of, and a few you have not.
