A cycle C={v1,v2,.,v1} in a tournament T is said to be even, if when walking along C, an even number of edges point in the wrong direction, that is, they are directed from vi+1 to vi. In this short article, we show that for every fixed even integer k≥4, if close to half of the k-cycles in a tournament T are even, then T must be quasirandom.This resolves an open question raised in 1991 by Chung and Graham 1991. © 2012 Wiley Periodicals, Inc.