The best thing to do in a given situation depends not only on the value of the player's hand, but also on the dealer's. As a guide, you can keep in mind that the probabilities of improving a hand by requesting an additional card are the following:

TABLE I
PROBABILITY OF IMPROVING A HAND BY REQUESTING ONE ADDITIONAL CARD

So, looking at the above table it seems wise to hit with 14 or less and stand with 15 or more. But considering that the dealer has the same chances of improving or worsen her hand, and the fact that she must play according to fixed rules, the combination of probabilities of player and dealer leads to more complex decision rules. The following table summarizes what are the decisions with the best odds, those which maximizes the probability of winning:

TABLE II
BLACKJACK OPTIMAL DECISIONS

Here H means Hit and S means Stand. In the case the player has less than 12, he or she should always request an additional card (hit)  because the hand can only improve, bust being impossible. With a hand value of 18, 19 or 20, it is always advisable to stand, regardless of what the dealer's face-up card may be.

In the preparation of the above table only plain probabilities have been considered and very important decisions such as doubling or splitting are not included. Doubling and splitting offer additional advantages to a skilled player by rising the bet in favorable situations. Considering doubling down in a game with two decks when the player's hand contains no aces, the optimal decisions are the following:

TABLE III
BLACKJACK OPTIMAL DECISIONS INCLUDING DOUBLING DOWN
PLAYER'S HAND CONTAINS NO ACES

Key to table: H=Hit; S=Stand; D=Double

In the above table it is assumed that doubling is permitted on the first two cards, regardless of the value of the hand. This is not always the case in all casinos, but it is the rule at 4 Jacks Casino. With hands of value 8 or less, the player should always hit, not double, while with hands of 18 or more the best move is to stand always.

If the hand contains an ace (a "soft" hand), requesting an additional card may improve or worsen the odds, but will never bust. This makes a difference. In this case the optimal moves are the following:

TABLE IV
BLACKJACK OPTIMAL DECISIONS INCLUDING DOUBLING DOWN
PLAYER'S HAND CONTAINS ONE ACE

  Key to table: H=Hit; S=Stand; D=Double

Splitting is possible only when the first two cards are of the same value. As this option make two different hands playing against the same dealer's hand, it should be taken only when the split hands will have favorable odds. Computer simulations result in that the best decisions in these cases are those in Table V below:

TABLE V
BLACKJACK OPTIMAL DECISIONS INCLUDING DOUBLING AND SPLITTING

  Key to table: H=Hit; S=Stand; D=Double; L=Split

There is much more in blackjack strategy. As blackjack gained widespread popularity and given the possibility of beating the house, many different winning methods with or without card counting have been developed. Several of them can be found in books on blackjack strategy. You can find many at Amazon.com.