The Law of Total Tricks

In bridge, the Law of Total Tricks (or simply "The Law") is a hand evaluation method for competitive auctions. Technically stated, the total number of cards in each partnership's longest suit is equal to the number of "total tricks" that either side can win in a suit contract.

The Law was originally proposed by French bridge theoretician Jean-René Vernes in his 1966 book "Bridge Moderne de la Défense." He subsequently wrote a synopsis of the Law in a Bridge World article circa June 1969. It has since gained widespread popularity when American expert Larry Cohen introduced it in his books "To Bid or Not to Bid" (1992) and "Following the Law" (1994). Today, the Law of Total Tricks is widely accepted, both by experts and casual players, as a valuable guideline for bidding.

Let's jump into some examples...

		North
		AQT32
		KQ3
West		T9		East
54		AT3		976
AT985				J72
AK63		South		87
J8		KJ8		KQ976
		64
		QJ542
		542

West     1 Pass

North     1 Pass

East     2 Pass

South     2

This is a typical Law deal. East-West have 8 hearts and North-South have 8 spades. 8 hearts + 8 spades = 16 total trumps. That number happens to be the combined number of tricks that can be made in 2 and 2. Playing 2, West would make exactly 8 tricks after losing 2 spades, 2 hearts and a club. In 2, North would also win 8 tricks against best defense, losing a heart, 2 diamonds and 2 clubs. 8 heart tricks + 8 spade tricks = 16 "total tricks".

The principle is the same if we move some cards around:

		North
		AJT32
		Q3
West		A93		East
54		T83		976
AKT985				J72
KQ6		South		87
AJ		KQ8		KQ976
		64
		JT542
		542

West     1 4

North     1 Pass

East     2 Pass

South     2 Pass

North-South still own an 8-card spade fit, but East-West now enjoy a 9-card heart fit. 8 spades + 9 hearts = 17. Playing 4, West will win 10 tricks against best defense, losing 2 spades and a diamond. If North were allowed to play 2, he would only win 7 tricks; East-West would score 3 clubs, 2 hearts, and 1 diamond. 10 tricks + 7 tricks = 17, which is equal to the total number of spades and hearts in the deal.

The bidding in the above examples was fairly realistic, with or without the Law. So let's look at a hand in which the Law may actually influence the bidding. Sitting East, you hold:

973 KQ32 J2 QT72

The auction begins:

Partner     1 (1) Pass

Opp 1     Pass 2

You     2 ?

Opp 2     Pass

1. 5-card major.

Playing a natural 5-card major system, you have already described your hand with 2, and it may seem obvious to pass. But the Law would actually suggest bidding 3. The full deal:

		Opp 1
		AQT6
		987
Partner		JT85		You
54		K9		973
AJ654				KQ32
A976		Opp 2		Q2
A6		KJ82		QT72
		T
		K43
		J8543

The opponents hold 8 spades, while your side holds 9 hearts. 8 + 9 = 17, so the Law says there should be 17 total tricks available.

Therefore, if the opponents can make 2 (8 tricks), then your side should theoretically make 3 (9 tricks). That is the case in this deal.

This leads to the most important application of the Law...

In my experience, this is most common and critical at the 2- and 3-levels. If you and your partner have an 8-card fit, then you are usually safe to compete to the 2-level in that suit. And if you own a 9-card fit, then you're usually safe to compete to the 3-level. The contract will either make, or be a good sacrifice against whatever the opponents can make.

1. Corollary: Get to the right level quickly. In the above auction, East bid 2 first, which allowed the opponents to compete in spades. Playing Bergen raises, a bidding convention based on the Law, East could have shown 4-card support immediately. Moreover, Bergen raises allow a major-suit jump raise (i.e. 1 - 3) with 0 points, because of the Law's premise of a 9-card fit. This is something that standard bidding methods would never allow.

2. Corollary: Do not compete above your trump fit unless you have extra shape, points, or vulnerability in your favor. For example, South could bid 3 over 3 in the above auction. However, this is much more attractive if North-South are not vulnerable. If vulnerable, 3 doubled is -200 which is obviously a worse score than defending 3.

3. Corollary: There are "adjustments" to the Law to consider when bidding. I am not a big fan of this, and consider it to be the major weakness of the Law. Depending on the distribution of the cards, sometimes the number of total trumps does NOT equal the number of total tricks. The Law is sometimes incorrect depending on how strong each side's trump holding are, and how many total trumps exist. Once a deal gets above 18 total trumps, the Law can be a little erratic. For example:

   		North
   		AQT32
   		K3
   West		T93		East
   54		T83		9
   AQT985				J742
   AK6		South		872
   AJ		KJ876		KQ976
   		6
   		QJ54
   		542

   
   20 total trumps in hearts and spades but only 18 total tricks. 4 is cold for East-West, but North-South can only make 2. Depending on the vulnerability, it may be correct for North-South to sacrifice in 4 - the 10 combined trumps recommends it. But clearly, something is amiss with the Law here.

   
   

   Arguments Against the Law

   Mike Lawrence and Andres Wirgren wrote the book "I Fought The Law Of Total Tricks", which makes compelling arguments about the shortcomings of the Law.

   A key reason behind the Law's popularity, Lawrence and Wirgren claim, is its simplicity. It provides a straightforward framework for evaluating a bridge hand. Simplicity is certainly a virtue, but it does not necessarily equate to accuracy.

   One of their key arguments was that Jean-René Vernes relied on average values, not absolutes. To quote Vernes' 1969 Bridge World article, "Can it be possible to predict, on average, the number of total tricks?" The original Law did not claim that total tricks and total trumps are equal on every single deal. They are only roughly equal (around 60% tricks to 40% trumps) when the average is calculated across many deals. This distinction is important.

   Matthew Ginsberg, a mathematician and computer programmer, conducted a precise study and reported the results in The Bridge World (May 1996). Using his bridge software program "Goren in a Box" (GIB), Ginsberg ran a double-dummy analysis of nearly 450,000 deals to test the Law. Per his Bridge World article, total tricks only equalled total trumps on 40% of the deals.

   Thus it is reasonable to argue that the Law incorrectly assumes a direct connection between tricks and trumps, which, in reality, doesn't exist. When total trumps and total tricks happen to align on a given deal, it might be a coincidental correlation rather than a causative relationship.