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broadcast shuffle in practice

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"Cube Draft" is a format for Magic the Gathering where, before play can begin, the maybe 6-8 players must work together to shuffle a deck (the eponymous "cube") with about 400 cards in it. "Broadcast Shuffle" is a method of doing so that produces good results in a reasonable amount of time. I've linked the full writeup that introduced the method, but it suffices to say here that broadcast shuffle includes a step, the eponymous "broadcast", where everyone takes the stack of cards they are shuffling and evenly distributes it among all the shufflers, such that the stack everyone has after this step is comprised of a roughly even number of cards from every previous stack.

I introduced this shuffling method to my cube group, and we wanted to use it, but had trouble actually physically performing the broadcast step. It's not so bad if you're four shufflers sat around a table, as you're all in reach of eachother (though it does take some care to not turn piles upside-down accidentally), but four shufflers is about 100 cards to shuffle each, and that's still somewhat cumbersome with just one set of paws. Introducing more shufflers seems to turn the broadcast step into a chaotic mess where you're all getting in eachother's way, especially if you need to get up from the table to reach the other players. But, I've figured out a way to do it methodically, inspired by the actual draft step of a cube draft. After all, drafting cards from packs is a way of evenly distributing their contents across a table of players! So, here is the full method for broadcast shuffling a cube, as we actually do it in our cube group:

the method

1. Split the cube into n (approximately) equal piles, where n is the number of shufflers you have. Each shuffler gets a pile. For ease of writing, we will henceforth assume n = 8, but this method works with any reasonable number.
2. Shuffle: each shuffler shuffles their pile, briefly. There is no need to spend too much time on this step; more iterations of the process are overall more important.
3. Broadcast: each shuffler:
   1. Removes approximately 1/8th of their pile, placing it in front of them, and passes the remaining 7/8ths to the shuffler on their left.
   2. Removes 1/7th of the pile they receive (or, an amount of cards roughly equal in size to the first 1/8th), again placing it in front of them and passing the rest onwards.
   3. Repeats this process, taking 1/6th, 1/5th, and so on, until they receive their eigth pile, which they take 1/1th of (i.e, keep the pile and pass nothing on).
   4. Combines the eight piles in front of them into one new pile.
   You may find in this process that you are handed a surprisingly small pile of cards, like having to take one quarter of a pile of 10. This just seems to happen, it's fine.
4. Repeat the shuffle and broadcast steps until three or four broadcasts have been done (or everyone is ready to play).

With this process complete, the cube is now shuffled! Everyone can start dealing out packs from the pile they have (and trading cards to make it even as necessary).

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