After the first split, doubling down and further splitting of hands may be limited. After the first split, an ace and a ten-card may be regarded as a non-blackjack 21. After splitting aces you're generally not allowed to hit more than once.

Generally, you are allowed to hit or double down on a split hand, with the exception of if you have split two Aces, in which case the two hands are often not allowed to consist of more than two cards. In some cases, a Blackjack achieved on a split hand will not count as such, and simply be valued at 21.