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James Propp
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probability theory for combinatorialists

More than one combinator(ial?)ist has asked me to recommend a good book to learn probability from, and I never know what to say; the probability theory that I use in my research up was mostly learned piecemeal. (The stuff I learned in grad school from reading Chung and Feller hasn't been as useful, and I didn't especially enjoy those books.) Any suggestions?