Most casual players split 10's when the dealer has a weak upcard like a 5 or 6 (although I have seen many players during my career split 10's no matter what the dealer shows). Their logic for splitting on the dealer's 5 or 6 goes something like this:

The dealer has a weak card and I've got a good chance to make two good hands starting with a 10 so why not split and double my winnings. Oh, really.

Let's look at your expected value or the average amount you would win per hand when you stand compared to when you split. Computer simulation tells us that when you stand on a pair of 10's against a dealer's 6 up-card you will win 85% of the time. That's not to surprising because it's tough for the dealer to beat a strong hand of 20. If you split the 10's, the computer results show that you will win only 64% of the hand. That's a significant decrease in the number of hands won simple because if you split you will often end up with less then 20 on both hands.

Of course when you split you will be doubling your bet. Therefore to compare the expected value of splitting over standing, the question we need to answer is this, Is it better to win $1 85% of the time or $2 64% of the time? Let's do the quick math and find out.

Standing

In 100 tries I expect to win one dollar 85 times and lose one dollar 15 times thus be ahead $70 ($85-$15). This is a net expectation of 70 cents per hand.

Splitting

In 100 tries I expect to win two dollars 64% of the time and lose two dollars 36% of the time thus be ahead $56 ($128-$72). This is a net expectation of 56 cents per hand.

Yes, you will make money if you split 10's when the dealer shows a 6 up-card to the tune of 56 cents per hand. However, you will make 14 cents more per hand on average if you stand (70 cents vs. 56 cents). This is why standing on a pair of 10's is the preferred play.

If you do the same analysis for 10's against a dealer 5 you'll arrive at a gain of expectation of 16 cents per hand when you stand vs. split making standing the more profitable play.

If it's more profitable to stand on 20 rather than split why do the pros sometimes split? The answer to this has to do with the composition of the undealt cards.

The above analysis was done assuming the top of the deck composition of cards. In practice the composition of the cards change from hand to hand depending upon the cards played. The pros carefully watch the card played so they have useful information on the composition of the undealt cards. So, if a pro sees a lot more small value cards being played compared to the 10's, picture cards, and aces, then he knows that the undealt cards must have a higher proportion of the latter cards. This will be the ideal time to split the 10's since the chances are greater of drawing two tens or aces for pat 20 or 21 hands. Also, the pro knows that if the dealer has a 5 or 6, he must draw a third card (unless he has an ace-6) and the probability is great that he will break when he draws from a ten rich deck.

The only way you are going to know when the undealt cards becomes rich enough in 10's and aces to make splitting 10's a more profitable play then standing is to learn a card counting system. For example, for the popular High Low counting system, the pro would split 10's against a 6, when there is an excess of 4 more high value cards per deck than normal. Although this doesn't happen too often, when it does, the pro knows that his expectation is greater when he splits compared to standing.

The bottom line for splitting tens is this if you are a casual player, never split 10's no matter what the dealer shows because in the long run that bird in the hand (20) is worth a lot more than two in the bush (i.e. taking your chances and splitting).