 More precisely, Diaconis showed that, in the Gilbert–Shannon–Reeds model of how likely it is that a riffle results in a particular riffle shuffle permutation, it takes 5 riffles before the total variation distance of a 52-card deck begins to drop significantly from the maximum value of 1.0, and 7 riffles before it drops below 0.5 very quickly (a threshold phenomenon), after which it is reduced by a factor of 2 every shuffle.When entropy is viewed as the probabilistic distance, riffle shuffling seems to take less time to mix, and the threshold phenomenon goes away (because the entropy function is subadditive).Diaconis has coauthored several more recent papers expanding on his 1992 results and relating the problem of shuffling cards to other problems in mathematics.