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My paper "Cycles in War" addresses this question, too. I was interested in characterizing the kinds of cycles that can occur. In other words, what does the structure of a cycle in War actually look like? I simplified the problem by assuming that wars are not possible (i.e., the cards have a strict ranking from 1 to n, where n is the number of cards in the deck). Even in this simpler version I found it difficult to characterize all of the cycles. However, I did find some interesting cycle structures, including one that works for 52-card decks. The details are in the paper, which has been accepted for publication by the journal Integers but has not appeared in print yet. Among other things, the re-loading rules do make a difference, as several people have already noted here. Also, given that characterizing cycle structures when wars are not possible turns out to be difficult (or, at least, I found it so), one should expect that characterizing cycles in the standard version of the game in which wars are possible would be even more difficult.