Have you heard of the "Law of total tricks"? It is simple, and every aspiring bridge player should be using it to improve their results in every session. It states:

Note that the high card strength is irrelevant, as is the position of crucial cards such as missing kings etc. (A losing finesse is one trick less for you, but one more for them - the total number of tricks available is not altered.) This is the reason that on some hands both sides can make a game, even a slam; yet on others neither side can make a two level contract.

The idea was proposed by Jean Renes-Vernes in the 60's. He analysed hundreds of hands and found that this simple law is right a majority of the time - and the hands where it doesn't work can often be spotted. Ignoring these refinements, you will still gain lots of matchpoints by using the law. Here are a couple of examples where internationals went wrong when they ignored the law. Can you do better? :-

It is the 1979 Bermuda bowl. You are playing for the USA against Italy in the form of Pittala and Giorgio Belladonna. You are not vulnerable, they are.

S J93	
H Q86
D A743
C A53

USA 	Pittala		You		Belladonna

					1D
1H	1S		2H		3C
-	-		?

The Law makes it clear. It looks very much like two 8 card fits - a total fit of 16 cards, and so 16 available tricks according to the law. The table below shows what could happen if we bid 3H (as I suspect most players would).

Clearly bidding on is a losing tactic.

(In the event, both sides could make 8 tricks. Bidding on turned USA's +100 into -50)

Later on in the same match you become an Italian. You are partnered by Giorgio Belladonna. You are vulnerable, they are not.

S K9732	
H 94
D AQ10
C J82

USA 1	You	USA 2	Belladonna
				
-	-	1C	1D
2H	2S	3H	-
-	?

You have 10 points and an excellent diamond fit. Do you bid on?

In the event Belladonna's partner bid 4D. The Law tells us that this MUST be wrong. Consider the likely fits:

We have an 8 or 9 card fit; they have an 8 or 9 card fit. The total fit is probably 16 or 17 cards rather than 18. Let us assume 17. The law tells us that there are 17 tricks available between us.

	If they make 9 tricks in 3H, we score -140. In 4D we make 17-9 = 8 tricks for -200. (So bidding loses 60)
	If they can make 8 tricks in 3H (+50), then in 4D we can make 17-8 = 9 tricks for -100 rather than +50. (Bidding loses 150)
	If we can make 10 tricks for +130 in 4D, then they would have made 17-10 = 7 tricks (+100 to us) we are slightly worse off. If you think that 4D might make, the best action is to DOUBLE 3H
	If the total fit is only 16 (as is equally likely) they will be 3 down - this and all the other possibilities point even more firmly to pass (or double)

(In the event there were two 8 card fits, a total fit of 16. 4D made 9 tricks for -100. In the other room, three hearts went two down (the law working nicely) - and another 100 went to the bad guys.)

It is not really necessary to work out all these possibilities at the table. Just remember that it is usually wrong to bid beyond your fit length unless you have the surplus of points to compensate for the lack of trumps. If they bid beyond the fit level, pass (or double them).

I can, therefore, thoroughly recommend the book "To Bid or Not To Bid" by Larry Cohen. It deals with competitive auctions, expounding the "Law of Total Tricks", it helps us to decide when it is right to "bid one more", and when to avoid bidding at all costs. It is well written, being rich in examples and tests (though it does go on about some obscure American conventions which are best ignored). A 2nd book on 'the law' by Larry is also available, named "Following the Law: The Total Tricks Sequel". It is also worth checking on Mike Lawrence's riposte 'I Fought the Law'.

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