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, in the case that the winning card goes to the bottom of the winning player's deck before the losing card, I was able to find a way to construct a deal of an $n$-card deck that cycles, for any $n$ that is not a power of 2 or three times a power of 2.

  For example, the following deal of a 52-card deck cycles.

<pre><code>
26 46  1  7  8 27  9 28 29 47  2 10 11 30 12 31 32 48  3 13 14 33 15 34 35 49

16 36 17 37 38 50  4 18 19 39 20 40 41 51  5 21 22 42 23 43 44 52  6 24 25 45 
</code></pre>

It takes over 30,000 battles for the deck to return to this ordering.  The mathematical argument for why this deal cycles is in the paper<strike>, which has been accepted for publication by the journal *Integers* but has not appeared in print yet</strike>.  Among other things, the re-loading rules do make a difference, as other 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.

Edit: The paper has now been published on the *Integers* web site, in the games section, as [Vol. 10][2], Article G2, 2010, pp. 747-764. 


  [1]: http://math.pugetsound.edu/~mspivey/War.pdf
  [2]: http://www.integers-ejcnt.org/vol10.html