Proposition 8.13 -- the riffle shuffle mixes in $2\log_2 n+O(1)$

The riffle shuffle (Gilbert–Shannon–Reeds) of a deck of $n$ cards cuts the deck into two packets and interleaves them; it is formalized as the time reversal of the inverse riffle, in which every card independently receives a uniform bit and the cards labeled $0$ are pulled to the top, both packets keeping their relative order. (The reversal is legitimate because the stationary distribution — uniform over the $n!$ orderings — is preserved, and a walk and its reversal mix at the same speed.) The mixing time $t_{\mathrm{mix}}$ is the first time $t$ at which $\max_x\|P^t(x,\cdot)-\mathrm{unif}\|_{TV}\le\tfrac14$, with $\|\mu-\nu\|_{TV}=\max_A|\mu(A)-\nu(A)|$ the total variation distance.

The theorem (Proposition 8.13 of Levin–Peres–Wilmer) asserts: for every deck size $n\ge2$,

Order $\log_2 n$ riffle shuffles suffice — for a standard $52$-card deck this bound is in the famous "about seven shuffles" range. The proof tracks the bits accumulated by the inverse shuffles: once all $n$ bit-strings are distinct, the deck is exactly uniform.