Why would that be illegal?

Casino licenses are contingent upon offering a fair game at stated odds. The odds are allowed to benefit the house, of course, since that's how running a casino becomes a sustainable, profitable enterprise, but the stated odds cannot be dynamically changed in the middle of the game to benefit the house.

Published blackjack odds depend on "dumb" reshuffles. If the house is "smartly" reshuffling the deck to reduce house payouts, then the published odds do not match the real odds, which is illegal.

Correct me if I'm wrong, but I think that not being allowed to count means that you should treat odds as if the cards were extracted from an infinite stack with a given statistical distribution of cards. Reshuffling when you only extracted a low number of cards from a finite stack basically approximates the infinite stack, so, the odds should be exactly as expected.

Except that the stack isn't infinite. There's a statistical difference between playing off a physical deck and playing off a random number generator, and in a physical deck, the dealing of various cards increases the relative odds that the other cards will come up later in the deck. It's the statistical foundation upon which card counting works.

Imagining that the physical deck is a virtual deck does not make it so. In an RNG-populated/virtual deck, there is a small but still real chance that, for instance, 20 aces could be dealt in a row, which is why game programmers use techniques like shuffle bags to prevent that from happening. An "infinite" physical deck, that was actually "infinite", would suffer from the same problem, and would need a physical solution, which would affect the odds which the casino is legally obligated to publish and adhere to.

> It's the statistical foundation upon which card counting works.

Exactly, so, if counting cards if forbidden (I'm not arguing if that is right or not), then having that statistical foundation isn't useful. As a different comment suggested, reshuffling at a fixed point (say, after one third of the cards have been dealt) should solve the problem in practice, also preventing the house to use counting in a meaningful way.

That would be true if the casino always reshuffled after a certain number of cards came out.

But a dishonest casino could do the same card counting that players can do, and reshuffle when the count favours the players.

I agree that having a fixed number of cards between reshuffles would be the fairest solution.

And when the dealer messes up the count you can have one hell of an exit!

Very loudly:

"Aha! You should have shuffled the cards! Messed up the count didn't you!"

Sunglasses on and just walk away.

card counting is about a few percentage points advantage wrung out over hundreds of hands, you would never get a jackpot moment like that if you are doing it correctly.