My dad said the house has the advantage in Blackjack because you can't play one hand against the dealer, you can only play on your own if you play two hands, and this gives them an edge.
I know their edge actually comes from playing last (as if you both bust, you don't push, the player loses), but would playing 1 or 2 hands against the house make a difference, or would their edge stay the same?
A lot depends on how the house perceives you as a customer. If you are a "regular" and have played many rounds with them in the past, they will likely deal to you alone today, even if you only play one hand.
If this is your first time, and you've been betting the minimum, that's kind of a different story. The house may then decide that it's not worth the dealer's time and effort, and may require a "two hand minimum" to run the table, either from you, or between you and another party.
If you are not card counting, the house has its edge/hand no matter what. For N hands, you just multiply the house edge by N to get the new house edge.
If you are card counting, the question gets more complicated, but one additional hand is not likely to make a difference between favoring the player and favoring the house. Any difference in player edge is going to come from the fact that more cards are dealt out between hands (card counters get most of their edge from changing their bet sizes based on the distribution of cards left in the deck).
All of this assumes that dealers reshuffle well before reaching the end of the deck/shoe, which is the case virtually everywhere these days.
By the way, the assumption that no one lets you play one hand at a table by yourself is false. I did it all the time when I lived in Washington state.
