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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.

This is pretty wordy, so I think it's best to jump into some examples...


Examples

            North           
AQT32
KQ3
WestT9East
54AT3976
AT985J72
AK63South87
J8SKJ8KQ976
H64
DQJ542
C542


West    
1H
Pass
North    
1S
Pass
East    
2H
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 2H and 2S. Playing 2H, West would make exactly 8 tricks after losing 2 spades, 2 hearts and a club. In 2S, 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           
AQT32
K3
WestT93East
54T83976
AQT985J72
AK6South87
AJSKJ8KQ976
H64
DQJ542
C542


West    
1H
4H
North    
1S
Pass
East    
2H
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 4H, West will win 11 tricks against best defense, losing only 2 spades. If North were allowed to play 2S, he would only win 6 tricks; East-West would score 2 diamonds, a diamond ruff, 3 clubs and a heart. 11 tricks + 6 tricks = 17, which is equal to the total number of spades and hearts in the deal.

The bidding in the above examples was clear-cut, 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:

S 973
H KQ32
DJ2
CQT72

The auction begins:


Partner    
1H (1)
Pass
Opp 1    
Pass
2S
You    
2H
?
Opp 2    
Pass

  1. 5-card major.

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

Opp 1
AQT6
987
PartnerQ985You
54A9973
AJ654KQ32
AT76Opp 2J2
K6SKJ82QT72
HT
DK43
CJ8543

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 2S (8 tricks), then your side can make 3H (9 tricks). That is the case in this deal.

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


Bid your number of trumps

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 2H 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. 1S - 3S) 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 3S over 3H in the above auction. However, this is much more attractive if North-South are not vulnerable. If vulnerable, 3S doubled is -200 which is obviously a worse score than defending 3H.

  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
    WestT93East
    54T839
    AQT985J742
    AK6South872
    AJSKJ876KQ976
    H6
    DQJ54
    C542

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


    Origins

    The Law of Total Tricks was created and popularized by American experts Marty Bergen and Larry Cohen. Cohen has written a popular and comprehensive book on the subject, To Bid or Not to Bid. As you can probably imagine, a 240-page book by the Law's expert inventor is a bit more informative than what I've written here.


    External Articles