The “Law of Total Tricks” and Some Bridge Probabilities

Aug 23, 2026

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A bridge-focused explanation of the “Law of Total Tricks” and how it supports bidding decisions in competitive and even non-competitive auctions. The document reviews related bidding concepts such as counting HCPs, adjusting for suit length and shortness, and estimating sure winners or quick tricks. It then applies the law to guidance on safe contract level bids based on total trump holdings, followed by detailed discussion of a specific board through early play.

LanguageEnglish

CategoryTechnology

FormatPDF

Pages10

Reading Time25 min

AccessFree to download

Concepts

Law of Total Tricks

Board #15

Bidding

Play

c: \bridge\tot_trick.docx 11/7/20 11/8/20 The “Law of Total Tricks” and Some Bridge Probabilities Bruce Thompson To return to the “Esther Bridge Lessons,” CLICK: [https://esther-bridge.com/index.html](https://esther-bridge.com/index.html) Concepts 1. There is a lot of science in bridge, including a lot of statistical science. But there is also a lot of art in bridge. Certainly being a successful Declarer requires both science and art. One of the best books on being Declarer is Louis Watson’s classic book, The Play of the Hand. 2. There are a lot of ways to decide what to bid, including counting High Card Points (HCPs), making point adjustments for length in trump (only after the suit is determined), and making point adjustments for shortness of non-trump suits. Other strategies that can and should be used in conjunction with point strategies involve counting “sure winners” or “quick tricks,” and especially: invoking the very important “Law of Total Tricks.” Law of Total Tricks The “Law of Total Tricks” was first proposed by Jean-Ren é Vernes in a 1966 book in French titled, Bridge Moderne de la Defense . Since this book was written by Vernes numerous books both pro and con also have been written about this Law . But in general the Law is taken quite seriously by serious bridge players (Sharks) . A fabulous short summary of the “Law of Total Tricks” is available at [www.bridgebum.com](www.bridgebum.com:)[:](www.bridgebum.com:) “The Law of Total Tricks .” For our purposes, it may be enough to know that the “Law of Total Tricks” is most useful in deciding how high you can safely bid in a competitive auction (i.e., both pairs are bidding) . For example, N/S may be bidding Spades, while E/W may be bidding Hearts . A “competitive auction” implies that both sides have points, but neither side holds the vast preponderance of the points. However, the “Law of Total Tricks” also should be considered even in a non-competitive auction. © Copyright, Bruce Thompson, 2022. All rights reserved. The “Law of Total Tricks”1 says you are pretty safe (something like 75% to 85% sure) that you will make your contract if you bid to the level that equals the total number of trump cards that your partnership holds. So, if your partnership holds 9 trump cards, you can probably safely bid a 9-6 = 3-level bid, even if you are somewhat short on HCPs . This does not mean that you can never make a 4-level contract holding only 9 trump cards! This does not mean that you can never make a 4-level bid holding only 8 trump cards! For example, certainly holding 9 trump cards along with a singleton or void may make it perfectly reasonable to bid a 4-level contract. But the Law gives you some idea about approximately how high you can safely bid in a competitive auction, and how close you may be to a danger zone. Board \#15 SDBC 2 99er Game Thursday P .M . 11/5/20 Dealer: SOUTH Vul: N/S NORTH (12) S : A Q 4 3 2 H : D : A Q 5 4 C : T 7 4 3 WEST (13) EAST (9) S : K J 7 S : 8 6 H : J 5 2 H : A Q T 9 8 7 4 D : J 3 D : 8 6 C : A Q J 9 8 C : K 2 SOUTH (6) S : T 9 5 H : K 6 3 D : K T 9 7 2 C : 6 5 1 For further discussion of the importance of the “Law of Total Tricks” see the “Esther Takes Bruce to the Woodshed for Not Believing In and Bidding Using the ‘Law’” section in “Esther Bridge ‘Pop’ Quiz \#87“: [https://esther-bridge.com/quiz/q0087_q.pdf](https://esther-bridge.com/quiz/q0087_q.pdf) For discussion of some empirical bridge research about how well the “Law of Total Tricks” works see: [https://esther-bridge.com/pdf/LOTT_bad.pdf](https://esther-bridge.com/pdf/LOTT_bad.pdf) Bidding SOUTH: PASS SOUTH: PASS SOUTH: PASS WEST: 1C WEST: 4H NORTH: 1S NORTH: PASS EAST: 3H EAST: PASS Play Lead. Because E/W may slough Spades, and then trump E/W’s Spade winners, unless Spade winners are taken early (especially since EAST’s jump in Hearts promises long Hearts, and thus shortness in the other su

FAQs

What is the “Law of Total Tricks” used for in bridge auctions?

It helps estimate how high a partnership can safely bid, especially in competitive auctions where both sides have points but neither dominates. It can also inform bidding in non-competitive auctions.

How does the law relate safe bidding to trump holdings?

The law suggests you are roughly 75% to 85% sure to make your contract if you bid to a level equal to your partnership’s total number of trump cards. For example, 9 trumps supports a 3-level bid (9 minus 6).

Does having only a small number of trumps make higher contracts impossible?

No. The law provides an approximate safe bidding zone, but higher-level contracts can still succeed with fewer trumps if distribution and card structure (such as a singleton or void) support them.

Aug 23, 2026

Upload by Patrick