My paper ["Cycles in War"][1] 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.


  [1]: http://math.pugetsound.edu/~mspivey/War.pdf