It has been proven previously that for a deck of $52$ cards, $7$ randomized riffle shuffles are enough to randomize the deck to the point that any further riffle shuffles will not meaningfully get the deck closer to an uniform distribution of the $52!$ arrangements.
Does anyone familiar with the proof know how to generalize these results for other numbers? From the Mathematica page on riffle shuffling, I see:
"Aldous (1983) showed that $\frac{3}{2}log_2n$ (correcting a typo) shuffles are sufficient to randomize a large n-card deck, yielding eight to nine shuffles for a deck of 52 cards. When combined with results of Aldous and Diaconis (1986), this analysis suggests that seven riffle shuffles are needed to get close to random (Aldous and Diaconis 1986, Bayer and Diaconis 1992)."
So it seems like the $\frac{3}{2}log_2n$ number is an upper bound at least but the details are omitted. Particularly interested in $40$ and $60$ cards cases.