This might be an ill-posed question, but it came up when I was playing a game that requires shuffling a very large ($n \gg 52$) deck of cards.
I can't comfortably shuffle more than 60-70 cards at a time, so to mix all the cards evenly I ended up doing the following:
- Divide the deck up into $\lceil n/m \rceil$ piles
- Riffle shuffle each pile twice
- Swap half of each once-shuffled pile with half of another pile
- Re-shuffle each pile twice
- Put the entire deck of $n$ cards back together
But I got the feeling that this can't possibly be the most efficient way to do this.
Question: Assuming we are only able to simultaneously shuffle (riffle or otherwise) $m$ cards where $m \ll n$, what's the most efficient way to shuffle the entire deck? Is there any existing literature on this?