Daily Illuminator

February 6, 2024: Math Is Hard (And The Answer Is Seven)

I did a deep dive recently into the topic of shuffling, and I came up with one inescapable conclusion: statistics does not make for light reading. Seemingly every college-acquired math fact dribbled out of my brain sometime in the past few decades.

But, hey, I have a few conclusions I can share, and I think they'll make a fun few articles.

So, if you start researching the topic of card shuffling, two facts come readily to light:

• Conventional wisdom is that, for a standard 52-card deck, "seven is enough." That is, everyone seems to agree that seven standard riffle shuffles is enough adequately randomize a deck of cards.

• Everyone refers to this wisdom in the same breath as "Trailing the Dovetail Shuffle to Its Lair," an article by Dave Bayer and Persi Diaconis, from a 1992 issue of The Annals of Applied Probability.

However, if that article actually specifies that somewhere, I haven't been able to find it. I suspect that it's a logical thing one can deduce by studying the paper and being smart with math – which means I've got two strikes against me.

Still, I think I've found an analysis of the math behind it on . . . um . . . a discussion of an episode of the show Numb3rs. This article seems to do a decent level of explaining it such that my puny brain can almost wrap around it.

All of this is preamble to say that "seven is enough." I usually mentally internalize that as "eight is enough," because I find the act of shuffling a deck therapeutic so an extra shuffle won't kill me, and my brain loves remembering Dick Van Patten-related trivia.

I'll have more to say in a future installment, but I wanted to leave you with something useful for now: namely, the integer seven. You're welcome.

-- Steven Marsh

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