If you play your two aces as one hand, you’ll start with a value of 12 (one is played as an 11 and the other as a one). Only a nine will give you 21. A 10 or face card will force you to play the second ace with a value of one, bringing you back to 12. On the other hand, if you split, you have four ways to get a 21 in either hand (being dealt a 10, J, Q, or K).
Playing your two eights as one hand starts you at 16 (a very weak hand). Hitting at this point is a risky proposition. Anything above a 5 will cause you to bust, so you have about a 60% chance of losing the hand from the get-go. On the other hand, if you split, it’s impossible to bust out on your first hit, so you at least have a chance of getting a more favorable hand.
Note that this requires you to triple your original bet (splitting the first time requires you to double it). House rules may vary here. Most Blackjack games will allow you to split a maximum of three times (to play a total of four hands).
If you play a pair of 10s, your hand has a value of 20, which is quite good. If you split 10s, you need to get an ace to improve your stance — anything else will give you a hand that has an equal or lesser value. Statistically speaking, splitting tens is most likely to give you two hands worse than the first one. Some card-counting experts suggest splitting 10s in very specific situations. For example: if you’re counting cards and know that there are lots of 10s left in the shoe, it can make sense to split 10s against a dealer showing 5 or 6 (which suggest a weak hand). This way, you stand a reasonable chance of getting at least one 20, while the dealer will have to get lucky to match or beat you. [1] X Research source
When you hit on a pair of fours, it’s impossible to bust out — the highest you can go is 19 if you get an ace, which is a pretty decent hand. If you split your fours, you’re likely to get left with a less-valuable hand (if you get a two or three) or a hand that is possible to bust out on if you hit (if you get an eight or higher). You need to get a five, six, or seven to be better off than you were originally.
Splitting a pair of fives is like splitting fours, only worse — you give up a strong starting hand for a very slim chance at getting something better. With a pair of fives, you can’t bust out and you have a chance of getting 21 on the first hit. If you split, you’ll be left with a weaker hand (if you get a two, three, or four) and/or a hand that it’s possible to bust out on if you hit (if you get a six or above). There’s really no way to come out ahead by splitting on fives.
Some resources recommend splitting twos and threes (but not sevens) when the dealer shows an eight.
