The Law of Total Levels

by Aimin Yang, Shaanxi, China

The Law of Total Tricks uses the two sides' total number of trumps as an estimate of the total number of tricks available to the sides. Here, I suggest a more effective format: The Law of Total Levels (LTL). LTL uses this vocabulary for counting winners:
high winners: the ace, the king, the queen in every suit;
ruffing winners: the expected winners generated by ruffing in the short trump hand [for example, with a five-three or a four-four fit, 2-3 if the short trump hand has a void, 1-2 if it has a singleton, 0-1 if it has a doubleton, or 0; similar range estimates apply to other fits];
long-suit winners: the number of cards over three in the trump suit.

When convenient, the sum of ruffing winners and long-suit winners is called extra winners.

Since a winner represents a trick, each side's bidding level is the sum of its winners minus six. Thus, sum of the two side's bidding levels is the sum of all winners minus 12. All the winners is the sum of all the high-card winners and all the extra winners; as there are always 12 high-card winners:

The Law of Total Levels: The sum of the two sides' bidding levels equals the sum of all extra winners.

The key to using this law effectively is being able to estimate the number of the extra winners, a problem with difficulty that varies with circumstances.

Suppose, for example, that both sides have a five-three fit. The Law of Total Tricks estimates 16 total tricks, with each side's security level the two-level. For a side with no ruffing tricks likely to be available, The Law of Total Levels suggests a security level of the two-level (two length winners), but when a ruffing trick is likely to be available, the security level is the three-level (two length winners, one ruffing winner, hence three extrs winners).

What if both sides have a five-four fit? The Law of Total Tricks estimates 18 total tricks, with a security level for each side of the three-level. The Law of Total Levels finds each side with two length winners; in most cases, there will be one or two ruffing winners, so the suggested security level for each side is the three-level or the four-level.

In any given deal, a player using either The Law of Total Tricks or The Law of Total Levels will make adjustments--for example, based on significant length in a second suit. or on the types and locations of honor strength, or on the opponents' tactics. The Law of Total Levels offers more scope for applying bridge judgment, making it a more practical tool.

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