TFA explains the trick somewhat oddly, to make the math angle more obvious. Here's a (random) video of someone doing it a more usual presentation of the effect:

https://www.youtube.com/watch?v=Xau8Ng4aQ6Y

Not the world's greatest magic trick or anything, but I don't think it's as transparently obvious to figure out as several commenters are suggesting.

Having dabbled in magic some, I can confirm that the delivery is far more important than I originally thought. Several times I have had my mind absolutely blown by a card trick, then found out it's a trick I have done myself! But they had put in so much more effort on honing the delivery, presentation, and patter to the point it became a different trick.

Work it with a mentalist angle.

Separate the cards into a face up and face down, shuffle, deal out two piles while explaining that you can read their mind. That you can pull numbers right out of their head.

Have them pick a pile. Slide it over to them and slide one under the table while telling them so you can't see what you're doing. But really it's because they can't see what you're doing.

Tell them to go through their pile and count the number of face up and face down cards. But don't tell you. Emphasize that they shouldn't tell you the numbers. Once they have the counts, stare at them, make some jokes about what they're thinking. Then shuffle the cards around under the table a bit. Make it look like you're thinking about what you're doing, mutter, "yes, yes, no, up, down" etc.

Then after a few seconds, say you got it and do the reveal.

Bonus, if they flipped their deck before counting and therefore the counts are backwards, you can go "ta-da" and flip your deck in front of their face, working the misfire as a false reveal.

For an impressive self working trick I can recommend this video https://www.youtube.com/watch?v=EW8w7uXkb1M .

The magician term is "patter", and it's just as important as the technique. Often some of the best tricks are just very good stories, and the technique is the storytelling device.

Yes - it boils down to “there are 10 cards. Pick some number of cards, give me the rest, and I’ll tell you how many you picked”. The addition of “more cards” very thinly disguises the basic fact that you are subtracting a number from 10. It’s not obvious to me how this could be done in a way that seems impressive.

Probably have to add some elaborate narration and then some sort of routine in the process of flipping your own cards so they forget how things started out.

Also, given that you're on HN, you've probably chosen a partner who is at least somewhat intellectually stimulating and thus significantly more likely to think this through than the average person.