A shuffle of a deck of cards obtained by successively exchanging the cards in position 1, 2, ..., 
with cards in randomly chosen positions. For 
, the most frequent permutation is 
, where 
if 
is even and either 
or 
if 
is odd (Goldstine and Moews 2000). Amazingly, for 
cards, the identity permutation (i.e., the original
state before the cards were shuffled) is the most likely (Goldstein and Moews 2000).
Exchange Shuffle
See also
Riffle Shuffle, ShuffleExplore with Wolfram|Alpha
References
Goldstein, D. and Moews, D. "The Identity Is the Most Likely Exchange Shuffle for Large
." 6 Oct 2000. http://arxiv.org/abs/math.CO/0010066.Robbins,
D. P. and Bolker, E. D. "The Bias of Three Pseudo-Random Shuffles."
Aeq. Math 22, 268-292, 1981.Schmidt, F. and Simion, R.
"Card Shuffling and a Transformation on 
." Aeq. Math 44, 11-34, 1992.Referenced on Wolfram|Alpha
Exchange ShuffleCite this as:
Weisstein, Eric W. "Exchange Shuffle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ExchangeShuffle.html