  The game of war is one of the most popular international children's card
games. In the beginning of the game, the pack is split into two parts, then on
each move the players reveal their top cards. The player having the highest
card collects both and returns them to the bottom of his hand. The player left
with no cards loses. Those who played this game in their childhood did not
always have enough patience to wait until the end of the game. A player who has
collected almost all the cards can lose all but a few cards in the next 3
minutes. That way the children essentially conduct mathematical experiments
observing chaotic dynamics. However, it is not quite so, as the rules of the
game do not prescribe the order in which the winning player will put his take
to the bottom of his hand: own card, then rival's or vice versa: rival's card,
then own. We provide an example of a cycling game with fixed rules. Assume now
that each player can seldom but regularly change the returning order. We have
managed to prove that in this case the mathematical expectation of the length
of the game is finite. In principle it is equivalent to the graph of the game,
which has got edges corresponding to all acceptable transitions, having got the
following property: from each initial configuration there is at least one path
to the end of the game.
