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I watched Persi give a talk where he demonstrated this trick, as part of a lecture on ways to use finite field theory to find de Bruijn sequences.

I hadn't seen Persi in a while; we'd written the "seven shuffles" paper together. Catching up, I asked him privately afterwards why he didn't use a sequence where two bits encoded the suit, then three bits encoded the card. He grinned wildly, then pulled out a spare deck to establish this was indeed what he had actually done. The spare deck was wrong. He joked how he dodged a bullet not using that deck.

That evening I burst out laughing in a solemn moment of an earnest modern dance performance. This was embarrassing, to say the least. I had recalled that Persi had shuffled the deck once as part of his demonstration of the trick. He's a legendary magician one rarely sees performing. Perfect shuffles were easy for him.




Diaconis is a real character. He gave a guest lecture to my statistics class at university ... um, several decades ago. His then-current research was around the effects of unfair dice. He was going to get his grad students to roll unfair dice thousands of times and see what effects loading and shaving would have on the outcomes.

To get some unfair dice, Diaconis went to a loaded dice shop somewhere in Los Angeles to see about ordering a set of custom dice. (This was before you could order unfair dice over the internet.) Since an unfair die is intended to have one face come up more frequently than the others, he wanted each die to have a pip only on that side, with the rest blank. This would make it easier to record the results.

The proprietor of the shop looked and him strangely and said, "What kind of game are you running, buddy?"

Diaconis said, "Oh I'm not running a game. See, I'm a university professor, and I'm doing some research into the effects of unfair dice."

Proprietor: "Yeah. Sure."


If anyone else wants to know what a "perfect shuffle" is, apparently it's this: <https://en.wikipedia.org/wiki/Faro_shuffle>


Last time this came up in HN, this YouTube video of a guy performing eight consequtive Faro shuffles came up (8 perfect shuffles restores the deck):

https://youtu.be/rEoYwyHddLc




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