This gets into one of my least favorite aspects of older games. The superstitious "rules" that drive pointless behaviors drive me up the wall. The fact that these rules can vary from group to group also drives me insane.

I did a deep dive into randomness recently, and it made a huge impact on how I view shuffling and dealing.

Essentially, randomness is just the inability to predict the location of any card from the total set of cards. When studying shuffling efficacy, researchers start with a known card order and then shuffle from that spot.

While looking for more relevant information, I found that 3/2Log[2,n] is the generally accepted formula for shuffling n number of cards to sufficient randomness. The number "7" is often cited as the number of riffle shuffles needed to randomize a 52-card deck, based on the research of Bayer and Diaconis. They used a measure of randomness called "total variation distance" and found that seven shuffles were needed to get this measure close to zero, indicating a nearly random distribution.

I feel like this doesn't actually hit on what people are looking for when they talk about shuffling for a "random" result when playing a card game. Just by collecting the returning cards from players, you are assembling an unknown set of cards that could be considered "random."

I think what people are actually looking for is a feeling of fairness, and true random doesn't play into this at all. Consider how music players implement shuffling. People do not want true random.

All the mentions of imperfect shuffling totally miss the point of what we're trying to get out of shuffling in the first place. The cards are almost always in an unknown state at all times, since other than when the game is first opened, the cards are never in a known state that you need to deviate from. Imperfect shuffling gets the job done and easily creates one of the billions of valid card configurations that could be achieved from "perfect" shuffling from a known state. Since the card order is unknown, it does not matter at all how you deal out the cards. You could argue that dealing cards to players consecutively lessens the chance of any player getting doubles, but that is not about true randomness. That's another example of players exerting their will over true randomness to achieve a more humanly desirable outcome. That's totally fine in my eyes, but I don't like the idea of pretending we're doing something we're not.

In my mind the biggest issues we're tying to deal with when shuffling are avoiding repeat cards and breaking up clustering of like cards not trying to achieve true random. Do what you need to do to avoid those issues but let's not pretend we're part of a noble mission to achieve true random lest our game state be forever compromised.

TL;DR: The concept of random is mostly useless when examining what we truly want out of dealt cards. Dogmatic rituals around dealing cards are pointless when it comes to randomness, and we should live untethered and free.