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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 - it is important that you are able to use it intelligently.


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-card fit in your prospective trump suit, and that your opponents have an eight-card fit in theirs.

That is - seventeen total trumps.

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.


Tactics


Sixteen total tricks


Suppose that you have identified an eight-card fit with partner.

The odds very much favour the possibility that your opponents also have an eight-card fit.  They might have a bigger fit, and they could just possibly have three seven-card fits, but an eight-card fit facing an eight-card fit is the most common layout.


Given that there are two eight-card fits then there will be sixteen total trumps.

According to the law of total tricks there will therefore be sixteen total tricks.


The first corollary is that, in a competitive part-score auction, you should compete to ‘the level of the fit’.

That is, with an eight-card fit you should contract to make eight tricks - i.e. you should bid to the two-level.

Let’s face it, if you aren’t making eight tricks then the opponents are making nine - you can certainly afford to lose 50 or 100 as opposed to their 110 or 140 - just be a little bit careful if you are vulnerable against trigger-happy doubling opponents - -200 could be expensive, but a penalty double at the two-level is relatively rare.

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-ranking suit then you will already have achieved this aim.  They have already bid to the level of their fit at the two-level, and you have been able to match them.  In fact, they should in general bid one more as we shall see below so as to deny you the pleasure of playing at the level of your fit, but they will not be as comfortable as they were at the two-level.


If yours is the lower-ranking suit then you will have been outbid at the two-level.  You must bid one more rather than leave them to play at the level of their fit.

If you are making nine tricks then bidding to the three-level is clearly the right action.

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-card fit with partner.

Your opponents will inevitably have at least one eight-card fit - leading to seventeen total trumps and therefore seventeen total tricks.


You have to compete to the three-level don’t you?

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-level and you have a nine-card fit in a higher-ranking suit then you must compete at the three-level.


Eighteen or more total tricks


As soon as the combined holding reaches eighteen or more (9-9 fits or better) then we are moving out of the part-score zone - someone will be hoping to make game.

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 - particularly if vulnerable against not when two down doubled scores badly against the opponents’ making game.


Are you making game?


Note that I prefaced the above by referencing ‘a competitive part-score auction’.


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 - it is about how high you can afford to compete, more or less irrespective of whether or not you have any hopes of making the contract.


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-making contract.

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-level and partner raised by one means or another to the three-level then you can place him with at least four-card support, and if partner overcalled the opponents’ opening bid then you can be all but certain that he holds at least a five-card suit, and in some circumstances it will be more than reasonable to assume a six-card holding.

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-card fit then your opponents are more than likely to hold at least an eight-card fit also, and if you can identify a nine-card fit then the opponents must inevitably hold at least one eight-card fit.


Weak opening bids


This theory also lies behind weak opening bids and the weak jump overcalls.


If you have a six-card suit then partner will have at least two cards with you most of the time.  That makes an eight-card fit, so get in with a two-level bid as quickly as you can.  And if you have a seven-card suit then partner will have two cards with you almost exactly half the time, making a nine-card fit.  What more reason do you need for a three-level preempt?

(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-count.  Quite simply, those small cards in the second suit will represent winners, whereas in a poorer fit their potential will be far less.

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-taking potential as well.

This situation will clearly lead to a greater number of tricks being available on the deal.

For example if each partnership has a nine-card fit then the law of total tricks would suggest that eighteen tricks are available on the deal, and this will be the case if the other two suits are more or less equally distributed between the four hands.

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 - if they contain top losers then the extra tricks might not be available.


N

A Q T 5 4

T

A K Q J 8 4

8


S

K J 3 2

7 5 4

7 2

T 7 5 4


W

9 6

A K 9 8 6

T 6 5 3

K 6


E

8 7

Q J 3 2

9

A Q J 9 3 2

On an unadjusted count, N/S have twenty combined points and a nine-card fit in spades.

E/W also have twenty points together with a nine-card fit in hearts.


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 - in each case the powerful second suit in one hand creates a trick-taking potential well beyond whatever the point-count might suggest.


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-card trump fit.

Without the second-suit fit you must compete to the three-level.

Now add a second-suit fit to the equation.  You must compete to a higher level.  There might easily be twenty total tricks available on the hand.  If you aren’t making eleven tricks then your opponents will be making a game.


If either member of the partnership holds a quality side-suit of any length then this situation will be evident to them and they will be in a position to compete beyond the usual level.

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 - the fit-jump - showing agreement with partner’s suit together with a good holding in a side-suit.  Partner will then know whether or not such a double-fit exists, and he will be in an excellent position to determine how far to compete as the auction continues.


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.

Follow these links for discussions of its place as a support bid for partner’s opening bid or for partner’s suit overcall.


For a full analytic treatment of ‘the law of total tricks’ follow this link.

N/S have a nine-card fit in spades and E/W have a ten card fit in hearts.


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 1-3 and 3-1 and E/W will be able to make eleven tricks for a total of 22.


The reason lies in the double-fit.

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.


N

A Q T 5 4

T 9

A K J 8 4

8


S

K J 3 2

7

Q 7 3 2

T 7 5 4


W

9 6

A K 8 6 5 4

T 6

K J 6


E

8 7

Q J 3 2

9 5

A Q 9 3 2

This page last revised 10th Nov 2017