Monge's shuffle is a shuffle in which cards from the top of the deck in the left hand are alternatively moved to the bottom and
top of the deck in the right hand. If the deck is shuffled 
times, the final position 
and initial position 
of a card are related by
![2^(m+1)x_m=(4p+1)[2^(m-1)+(-1)^(m-1)(2^(m-2)+...+2+1)]
+(-1)^(m-1)2x_0+2^m+(-1)^(m-1)](/images/equations/MongesShuffle/NumberedEquation1.svg) |
for a deck of 
cards (Kraitchik 1942).
