As many experts know the Law of Total Tricks is a very useful tool for judging how high to bid in competitive auctions. To apply 'The Law' you add the number of trumps your side has in your best suit to the number of trumps the opponents have in their best suit. This number will be equal to the total number of tricks each side can make if they play in their respective best suit.
This may sound to you either fishy or trivial. The amazing part is that it really works. Say for example that you (N-S) have nine-card heart fit and the opponents have ten card diamond fit. The total trick expectation therefore is 9+10 = 19.
Now comes the useful conclusion: if N-S can make ten tricks E-W can make nine. If N-S can make eight tricks E-W can make eleven. And so on. Clearly the number of tricks each side can make on a particular deal depends on the lay of cards: are the finesses on, do suits split, etc. But the total numbers are fixed. As an illustration consider the following deal (to be fair I gave each side 20 HCP):
| Dealer: | North | ||||||
| Vul: |  |
7 4 2 | |||||
 |
A Q 9 4 2 | ||||||
 |
9 | ||||||
 |
A Q J 7 | ||||||
| West | East | ||||||
|
A 8 5 | |
K 6 3 | ||||
|
7 6 3 | |
5 | ||||
|
K 10 5 4 | |
A Q J 8 6 | ||||
|
K 9 3 | |
10 6 4 2 | ||||
| South | |||||||
|
Q J 10 9 | ||||||
|
K J 10 8 | ||||||
|
7 3 2 | ||||||
|
8 5 | ||||||
Assuming that defenders take all their tricks, N-S will lose two spades and a diamond taking ten tricks in hearts.
With the same perfect defense E-W playing in diamonds lose one spade, one heart and three clubs taking therefore eight tricks. The total number of tricks is 10+8 = 18. What about the total number of trumps? It is 9 hearts for NS plus 9 diamonds for E-W = 18 again. Isn't it cute?
Now, switch North and South hands:
| Dealer: | North | ||||||
| Vul: | |
Q J 10 9 | |||||
|
K J 10 8 | ||||||
|
7 3 2 | ||||||
|
8 5 | ||||||
| West | East | ||||||
|
A 8 5 | |
K 6 3 | ||||
|
7 6 3 | |
5 | ||||
|
K 10 5 4 | |
A Q J 8 6 | ||||
|
K 9 3 | |
10 6 4 2 | ||||
| South | |||||||
|
7 4 2 | ||||||
|
A Q 9 4 2 | ||||||
|
9 | ||||||
|
A Q J 7 | ||||||
In this lay-out the club finesse is off for N-S and they can take only nine tricks in hearts. What about E-W? They have to lose only four tricks now so the total is again 9+9=18.
So here it is: in a competitive auction with the strength roughly equally divided you should compete to the level of your fit: bid three and expect to take nine tricks with nine card-fit, four with ten-card fit etc.
Here is another example of application of The Law.
| Dealer: East | North | ||||||
| Vul: None | |
A 3 | |||||
|
7 3 | ||||||
|
A Q 9 5 3 | ||||||
|
K 9 7 4 | ||||||
| West | East | ||||||
|
Q J 10 8 2 | |
K 9 7 | ||||
|
J 8 5 | |
A 10 6 4 2 | ||||
|
6 4 | |
10 | ||||
|
A Q J | |
10 8 6 2 | ||||
| South | |||||||
|
6 5 4 | ||||||
|
K Q 9 | ||||||
|
K J 8 7 2 | ||||||
|
5 3 | ||||||
| West | North | East | South | ||
| - | - | Pass | Pass | ||
| 1 |
2 |
2 |
3 |
||
| Pass | Pass | 3 |
4 |
||
| (all pass) | |||||
| Other table: | |||||
| - | - | Pass | Pass | ||
| Pass | 1 |
Pass | 2 |
||
| 2 |
(all pass) |
What does The Law tell us here? NS have ten trumps in diamonds and EW have eight trumps in spades. According to The Law this makes the total number of tricks available on this deal equal to 18, which, according to The Law is equal to the total number of trumps.
Is this true? Who can make what on this deal? Easy to see that NS can take 10 tricks in diamonds losing only one spade and two red aces. This is equal to the combined number of trumps they have. EW can take eight tricks in spades losing one spade, one diamond, one club and two hearts. The sum of NS and EW tricks is therefore actually equal to 18.
South at the first table knew his side has ten trumps and felt comfortable bidding 4D. He rightfully expected the Law to protect him. West at the second table also knew that her side with eight trumps should be able to make eight tricks. If opponents competed with 3D she might be willing to bid one more, just because -100 is better than -110.