I am trying to do some research into shuffling decks of cards. Most information I come across is too basic, doesn't have an answer or doesn't give the information I am looking for. I have heard that 7 riffle shuffles will randomize a 52 card with 4 of kinds, what I am interested in, is in bigger, smaller and decks with less matching kinds. I wanted to do the math for a 40 card, 60 card and 100 card deck to see how many shuffles it takes to fully randomize. any leads would be greatly appreciated.
This paper describes how to compute that seven is about the right number. It won't vary much for different deck sizes, growing slowly. The abstract to this paper says it asymptotically takes about $\frac 32 \log_2 n$ shuffles to get a reasonable mix. I don't have access to the paper. For a $52$ card deck this is $8.5$