> the odds of which are 4/13

Actually slightly lower, 15/49. (The difference is like 0.15%.)

(I mainly mention this because I used to think my odds of drawing to a flush in poker were 1/4 per draw. It took me embarassingly long to realise that I needed to remove the cards I could see from the deck.)

While you're right that 4/13 is simplistic, 15/49 complicates it without actually making it more accurate. Even if there are no other players, there will always be more than one deck in the shoe (4-8 depending on casino), plus the three cards will never be the first cards out of the shoe - so unless you're counting cards you can't work out the exact odds.

> Even if there are no other players, there will always be more than one deck in the shoe

I hadn't realised this, thanks.

> the three cards will never be the first cards out of the shoe

Does this matter? I'm using a model of "the dealer's other card is equally likely to be any of the cards except the two I have and his face-up one", and it doesn't matter where those three were originally. The model can be improved by counting cards, but it's still strictly (albiet very slightly) more accurate than the model of "the dealer's other card is equally likely to be any of the cards in the deck/shoe".

But perhaps there's something else about Blackjack that I'm not aware of?

Let's imagine using just one deck. Your odds of 15/49 could easily be 12/45, or 15/20, depending on what cards have come before it.

Well, yes. But if you're not keeping track of that, then always using 15/49 will give you marginally better results, on average, than always using 4/13. Perhaps there will be times where, if you had kept track of the cards, you would give odds of 4/13; but you didn't, so you don't know that's the case, and you should give 15/49.

You're correct about your other objections, and 15/49 is indeed harder to work with - but "without actually making it more accurate" is false under the one-deck assumption. It is not wholly accurate, but it is more accurate.