M J Bridge
The law of total tricks
This bit of theory lies behind much good practice relating to how high to bid in the competitive auction.
However, because every auction is potentially contested there is much to be said for gaining information about how high you might choose to compete even before those pesky opponents get started.
The ‘Law of total tricks’ is an excellent aid in making such decisions.
It is not important that you understand every detail of how ‘the law of total tricks’ works -
Of course, this is not a law in either the legal or the scientific sense. It is basically just an observation that seems to work on a great number of occasions.
Stated, more or less as simply as possible, it says that:-
The total number of tricks available on a hand is equal to the total combined trump holding of the two sides.
Don’t worry if you don’t understand that sentence immediately, nor if you cannot see how this could possibly be of any help.
First of all an example to show what the statement means.
What this means
Suppose that you and your partner have a nine-
That is -
The law of total tricks states that there are a total of seventeen tricks available on the hand:-
Perhaps you can make ten tricks in your trump suit. If so the opponents can make seven in theirs;
if you can make nine then they can make eight;
if you can make eight then they can make nine.
On the next page you will find a brief explanation of why it works, but for the moment the priority is to see how this law might affect your bidding tactics.
Sixteen total tricks
Suppose that you have identified an eight-
The odds very much favour the possibility that your opponents also have an eight-
Given that there are two eight-
According to the law of total tricks there will therefore be sixteen total tricks.
The first corollary is that, in a competitive part-
That is, with an eight-
Let’s face it, if you aren’t making eight tricks then the opponents are making nine -
And if you are making only six then they have game if in a major. The sums will again depend on the vulnerabilities and on whether or not you are likely to be doubled for penalties at this level, but in general you will gain from bidding to the level of the fit.
There is a second corollary which is less frequently cited.
Not only should you compete to the level of your fit, but you should also not allow your opponents to win the contract at the level of their fit.
If yours is the higher-
If yours is the lower-
If you are making nine tricks then bidding to the three-
If you are making eight tricks then one down will pay off as they also make eight, unless doubled and vulnerable, and if you are making only seven tricks then two down will score well against the opponents’ game except when you are vulnerable against not and doubled.
Seventeen total tricks
This time suppose that you have identified a nine-
Your opponents will inevitably have at least one eight-
You have to compete to the three-
You might make nine tricks when they can make eight, and if you are making less than this then they are making at least nine.
Indeed, if they bid to the three-
Eighteen or more total tricks
As soon as the combined holding reaches eighteen or more (9-
But the principles of bidding to the level of the fit and not allowing them to play in theirs still apply. The only real difference is that you are far more likely to be doubled at these levels, and so some care is needed if vulnerable -
Are you making game?
Note that I prefaced the above by referencing ‘a competitive part-
Do not allow the principle of ‘bidding to the level of the fit’ deter you from bidding a game or slam which has a good chance of making.
The theory above is not about how many tricks you expect to make -
Bouncing your opponents
Note also that if you stick slavishly to any bit of bidding method then your opponents will also have a clear picture of your hand and will therefore be able to judge their own actions with some accuracy.
For this reason it is a common ploy to ‘bid one more’ in the hope that you will ‘bounce’ your opponents one higher into a non-
It will score well when they do and badly when they don’t.
Exactly how frequently you should deviate from the theoretically correct action, and against which opponents, is of course a matter of judgement. Don’t count on getting it right every time.
How do you know the level of the fit?
Well, of course, you don’t.
But there are frequently some strong clues.
If you opened at the one-
All you then have to do is add your own length to partner’s assumed length.
The opponents’ bidding may give similar clues, but also don’t overlook the two observations given above that if you can identify an eight-
Weak opening bids
This theory also lies behind weak opening bids and the weak jump overcalls.
If you have a six-
(It should perhaps be acknowledged that this practice predates the exposition of the theory by a considerable period of time.)
Exceptions to the law
It has been observed since the law was originally formulated that certain specific circumstances lead to the inevitable exceptions.
The most important of these situations is when a partnership has a substantial combined holding in a second suit in addition to the fit in the prospective trump suit.
That second suit will generate more tricks than you might anticipate from a simple point-
Furthermore, if one partnership has substantial holdings in two suits then the other partnership will inevitably have substantial holdings in the other two suits increasing their trick-
This situation will clearly lead to a greater number of tricks being available on the deal.
For example if each partnership has a nine-
However if each partnership also has a substantial holding in a second suit then this total might easily reach twenty or even more.
There are two ways in which this second suit holding might appear.
The first is when one member of the partnership holds length in the second suit
Note that the quality of the suits is important -
A Q T 5 4
A K Q J 8 4
K J 3 2
7 5 4
T 7 5 4
A K 9 8 6
T 6 5 3
Q J 3 2
A Q J 9 3 2
On an unadjusted count, N/S have twenty combined points and a nine-
E/W also have twenty points together with a nine-
N/S would expect to make eleven tricks in spades, losing just a heart and a club.
E/W would expect to make ten tricks in hearts losing two spades and a diamond.
Total trumps 9 + 9 = 18
Total tricks 11 + 10 = 21
Additional tricks are available on this hand, and it is not difficult to see where they come from -
The second way in which this can happen is when the holding in the second suit is split between the two hands.
Clearly this should affect your tactics.
Suppose that each partnership has a nine-
Without the second-
Now add a second-
If either member of the partnership holds a quality side-
If the second suit is split between the two hands then it will not be so immediately obvious.
For this reason a whole new category of bid has been devised -
This is a tool which I shall try to incorporate as I look at other parts of the system.
These bids reappears in a number of different contexts.
For a full analytic treatment of ‘the law of total tricks’ follow this link.
N/S have a nine-
N/S can make eleven tricks;
E/W can make nine tricks.
Total trumps 19;
Total tricks 20.
Change the E/W diamond and spade holdings to 1-
The reason lies in the double-
This time the holding in the second suit is divided between the two hands.
N/S have an excellent second suit fit in diamonds, as do E/W in clubs.
A Q T 5 4
A K J 8 4
K J 3 2
Q 7 3 2
T 7 5 4
A K 8 6 5 4
K J 6
Q J 3 2
A Q 9 3 2
This page last revised 10th Nov 2017
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