Source: The Law of Total Tricks is currently the most widely used guideline in competitive bidding situations. Although only fragmentary statistical evidence in support of the law was available when the original Bridge World article, excerpted below, was published, recent research, spurred by the availability of cheap computing power, has shown that the law is remarkably accurate. Details of its precision (how much the estimate it provides varies from deal to deal) are also available, and most current experimentation in this field deals with guidelines for recognizing situations in which deviations from the global total-trick average are likely to occur.

The Law of Total Tricks by Jean-Rene Vernes

As we all realize, the aim of point-count valuation is to determine the precise level to which we can afford to bid. However, a more exacting analysis indicates that we can find ourselves in two entirely different bidding situations:
WEST NORTH EAST SOUTH
1 1 Pass 4
South’s bid means simply, “Partner, my hand is such that, even if you are minimum for your overcall, we can probably make four spades.” To come to this conclusion, South has only to apply the classical methods of hand evaluation. But suppose that the bidding went this way:
WEST NORTH EAST SOUTH
1 1 4 4
Here, the significance of South’s bid may be quite different. Perhaps he expects to make four spades. But it could equally be that he is expecting to take a one- or two-trick set, even doubled, thinking that East-West will make four hearts. We are in the domain of competitive bidding. Now, in this extremely common position the classical rules are helpless to solve our problems. Certainly it is easy to figure out that with good vulnerability it will pay to go down two, doubled, to stop an enemy game; and that it is sometimes advantageous to go down one to stop a part-score. Point-count valuation will easily let us work out how many tricks we expect to make if partner is minimum for his bid. But we have no precise way to determine whether or not the opponents will make their contract. And nothing is more costly than to take a sacrifice against a contract that would have gone down. How, in fact, do good players determine, in these positions, whether to pass, or double, or bid on? We know, from long experience, that the prime factor is distribution: the more unbalanced it is, the more cards each side has in its trump suit, the higher is competition justified. Beginners learn that the more high cards they have, the greater is their chance to make game. The discovery of an exact scale, fixing the relative value of the various honors, was a great step forward. But we do not have, today, a scale to tell us how high we can bid by virtue of our distribution. Could it be that there is no such scale, that in this area we must pride ourselves on our intuition? No–my aim is to show that competitive decisions are subject to a precise law, and a particularly simple one what’s more. And just as it is impossible to talk of constructive bidding without reference to accurate hand valuation, it is impossible to investigate competitive bidding without at least indirect consideration of this law. The Law of Total Tricks Examine the following deal, Number 93 of the 1958 World Championship.

North dealer Both sides vulnerable

 NORTH  A 6  9 7  K 9 6 4  A Q 9 3 2 WEST  Q J 10 9 2  10 8 5 4  A Q  10 4 EAST  K 8 7  A J 6 2  J 10 8 5 2  6 SOUTH  5 4 3  K Q 3 7 3  K J 8 7 5