Law of total tricks

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This article concerns contract bridge and uses terminology associated with the game. See Contract bridge glossary for an explanation of unfamiliar words or phrases.

In contract bridge, the Law of total tricks (abbreviated as LoTT) is a guideline used to help determine how high to bid in a competitive auction. It is not really a law (because counterexamples are easy to find) but a method of hand evaluation which describes a relationship that seems to exist somewhat regularly. Written by Jean-René Vernes for French players in the 1950s as a rule of thumb, it was first described in English in a 1969 magazine article. Marty Bergen and Larry Cohen popularized the approach in the 1980s in a series of comprehensive books.

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[edit] Definition

The "law" can be stated as follows:

The total number of tricks available on a deal is equal to the total number of trump cards both sides hold in their respective best suits.

Total tricks is defined as the sum of the number of tricks available to each side if they could choose trumps. As an example, if N-S between them hold 9 spades and E-W hold 8 clubs, the LoTT says that the total number of tricks available is 17 (9+8). Note the LoTT says nothing about how many tricks each side will make; this depends on the split of HCP as well as the number of trumps held - if, in the example, the side with 8 clubs held all the HCPs, they would make all 13 tricks with clubs as trumps - but if the other side could choose spades as trumps, they could well make 4 tricks (draw trumps and cross ruff) - note 13 + 4 still = 17. When the HCP are fairly evenly split between the two sides, the number of trumps held by each side is a close indicator of the tricks available to each side.

This method works on the assumption that for shapely hands, the combined length of the trump suit is more significant than points or HCP in deciding on the level of the final contract. It is of most value in competitive bidding situations where the HCP are divided roughly equally between the partnerships.

The "law" is said to be most accurate when the high card points are fairly evenly divided between the two sides and the bidding is competitive. Experts also apply adjustment factors to improve accuracy.

[edit] Total trumps principle

By combining the LoTT with the scoring table, it is argued that the following Total trumps principle is quite often a winning strategy:

Bid to a number of tricks equal to the number of trumps you and your partner hold (and no higher) in a competitive auction.

Thus, if with an eight-card fit, a pair is safe to bid to the two level but are unsafe to go to the three level. But, with a nine-card fit, the three level will be safe.

In this context, "safe" does not necessarily mean that the contract will be made. But if not, it means that it is a worthwhile sacrifice against the opponents' contract. For example, if the opponents have bid to two spades, and you have a nine-card heart fit, the "law" says you should bid three hearts. Assuming the opponents have an eight-card spade fit, there are 17 total trumps. If the opponents can take 8 tricks, the "law" says you can take 9. If the opponents can take 9 tricks, the "law" says you can take only 8. But down one (even doubled, if not vulnerable) is a less negative score for you than letting the opponents make three.

Derived from the LoTT, this principle assists players judge the level to which they should bid in a competitive situation. At its simplest a player should bid to the level of their calculation (from the bidding) of the number of trumps held by their side:

  • When the balance of HCP is unfavourable, bidding to this level will act as a useful sacrifice
  • When the balance of HCP is favourable, bidding to this level will be an achievable contract
  • When the HCP are fairly equally split between the two sides, bidding to this level avoids the danger of a misplaced sacrifice

In certain competitive situations, vulnerability can influence the optimum contract. Thus, with the HCP evenly split and facing a bid at the three level by the opposition, bidding to a level above the number of trumps held can be a useful sacrifice at favourable vulnerability.

[edit] Examples

For example, suppose that North-South have an eight-card heart fit and East-West have an eight-card spade fit. The total number of trumps is 16 so the "law" says the total number of tricks is also 16. That is, if North-South can take 8 tricks playing in hearts, then East-West can take 16 - 8 (also 8) tricks playing in spades; if North-South can take 9 tricks in hearts, the "law" says East-West can take only 7 tricks in spades.

♠ KQ853
♥ K63
♦ 7
♣ J1043
♠ 107

N

W         E

S

 ♠ J4
♥ A8765 ♥ 1092
♦ J94 ♦ KQ103
♣ KQ9 ♣ A872
♠ A962
♥ QJ
♦ A8652
♣ 65

In the diagram, N-S have 9 spades and E-W 8 hearts combined. N-S can make 4 spades (conceding two clubs and heart ace) while E-W can make only 1 heart on a good defense (which takes a trump from QJ, two spades, diamond ace and two diamond ruffs)—the law holds, as the total tricks available is 10+7=17.

Note, however, how minor card rearrangements affect the law:

  1. If the N-S diamonds were divided 4-2 instead of 5-1, with clubs consequently divided 3-3, the available total tricks would be only 8 for N-S + 8 for E-W = 16
  2. If, on the other hand, the E-W spades were divided 3-1 instead of 2-2 (with appropriate minor-suit rearrangement), they could make 2♥, while N-S could still make 4♠, giving 18 total tricks.


[edit] Consequences

There are a number of bridge conventions that take advantage of this principle. For example, Bergen raises following an opening bid of one of a major (using a 5-card major system):

  • 3 of the major = 4-card support and 0-6 HCP
  • 3C = 4-card support and 7-9 points
  • 3D = 4-card support and 10-12 HCP

In 2002, Anders Wirgren called the accuracy of the "law" into question, saying it works on only 35-40% of deals. However, Larry Cohen remains convinced it is a useful guideline, especially when adjustments are used properly. Mendelson (1998) finds that it is "accurate to within one trick on the vast majority of hands"

[edit] References

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