Early in the new millennium I worked a few years for the Internet company e-bridge. One of the things I wrote for them was a series of articles looking critically at the Law of Total Tricks. To my knowledge, it was the first time somebody openly questioned this so popular theory, which, after Larry Cohen’s blockbusters To Bid or Not to Bid (1992) and Following the Law (1994), had made a big impact on bridge players all over the world.

But something was wrong with the Law. No doubt about it. What bothered me most was that the foundation for the theory was clearly false. For instance, it was said that if you changed the distribution within a pair, the total trick count wasn’t changed, since “good distribution for one side is bad distribution for the other.” And yes, a change in the distribution that gains our side one trick on offense, may at the same time reduce the opponents’ tricks by one if they declare, but it is far from always the case. Maybe it’s not even the norm. And the same could be said about the other motivation. The claim that “honors that are onside for one side are offside for the other” and that the total number of tricks isn’t changed, was also false, since quite often one side gains more on one honor being onside than the other.

Later I rewrote parts of the material and published it in The Bridge World and Bridgetidningen, the Swedish magazine. Eric Kokish, who was responsible for all content on e-bridge (at that time), urged me to write a book on my findings. That sounded like good advice, so I started. Then roughly three years ago I got an e-mail from Mike Lawrence. Through Kokish he had heard about my plans on a critical Law book, and he had long thought about writing one himself. We discussed the issue for a while and finally decided to write a book together.

I studied many thousands of deals, looking at the material from many different angles, testing lots of hypotheses. I had, for instance, checked what happens if one side plays in its second best trump suit while the other side play in its best trump suit, or if either side plays the contract from the wrong side. Both these factors are important, but the Law had been embarrassingly silent – probably because if it had taken these factors into account, it would have been even more inaccurate than it is. When Jean-René Vernes wrote his article “The Law of Total Tricks” in The Bridge World 1969, he talked about an average, nothing else. And if you take, say, 100 deals, and calculate the average total trumps and the average total tricks, they will indeed be almost equal. But it doesn’t mean that the Law is correct on most of the deals. Yes, Larry Cohen claims in Following the Law that “On most deals … tricks will exactly equal trumps“ (page 49), and originator of the theory Jean-René Vernes’ wrote that “on well over half the cases” total trumps would equal total tricks. Both statements are wrong. The truth is that the Law is right on roughly 40% of all deals.

The two longest suits
The question I was obsessed with during my work was: Why should total tricks and total trumps be equal? Incidentally, this was my first reaction when, in the early 70’s, I heard about the Law for the first time. And I still had no answer. During the summer of 2002 I got an idea. Why only look at two suits (our trump and theirs)? What happens if we instead look at each side’s two longest suits?

The first thing I realized was that the sum of North-South’s two longest suits had to be the same as the sum of East-West’s two longest suits. Since it may not be obvious why, here comes a short explanation. Suppose North-South has the majors, East-West the minors. Since the sum of North-South’s cards is 26, and the sum of North-South’s majors and East-West’s majors also is 26, it follows that the sum of North-South’s majors must be the same as the sum of East-West minors. So if North-South have 17 cards in the majors, distributed 9-8, East-West must have 17 cards in the minors – but they don’t have to be distributed 9-8. They may also be 10-7, 11-6 or 12-5. But they can’t be 13-4, since then North-South will have nine cards in one of the minors, making their two longest suits not 17 but 18 (9+9; one major and one minor).

I looked at my statistics again to see if the second longest suit had any relevance – and it sure looked like it had! I compared all deals with 17 total trumps. When one side's two longest suits were 9+7 and the other side's two longest suits were 8+8, there were more tricks on average than when one side's two longest suits were 9+6 and the other side's two longest suits were 8+7. In both cases, the total tricks are 17 (nine for one side, eight for the other). Furthermore, for all numbers of total trumps, it appeared to be true that “the more cards one side has in its two longest suits, the more total tricks there are on the deal.” As a former philosophy student, I immediately wondered why.

I had already suspected that it would be like this. In his article in The Bridge World 1969, one of the things Vernes mentioned was that there are often extra tricks when both sides have eight or more cards in two suits. That was a correct statement. But he didn’t mention anything for the cases where only one side has two trump suits (e.g., 9+7 versus 8+8 instead of 9+6 versus 8+7). And what about the cases where neither side has two trump suits (e.g., 11+7 versus 11+7 instead of 11+6 versus 11+6). Was it realistic to expect more tricks in those cases, too? The statistics said yes. The problem was that I didn’t know why. And I wanted to.

An experiment
To see if I was on the right track with this “two longest suits” hypothesis, I decided to make an experiment, just like a good scientist. I intended to look through all possible cases the suits could be distributed given these conditions: (a) North-South’s two longest suits are the majors, (b) East-West’s two longest suits are the minors, (c) all suits are as evenly distributed as possible within each pair, (d) North-South have all major-suit honors, (d) East-West have all minor-suit honors.

This might look like an odd experiment, since you usually have honors not only in your two longest suits and some of the suits are usually unevenly distributed between the players in a pair. But by keeping the rules strict, I hoped to learn something. Now, when neither side have slow losers in their long suits and neither side have better distribution than their opponents, I wanted to see if the second longest suit had any role to play. My instincts said it should have, since by looking at the two longest suits for each side, I in fact looked at all four suits instead of focusing at two of them – the trump suits – and tried to predict from them solely. I hoped that the more factors I could consider, the better my conclusions would be.

Since I planned to look at all possible distributions, from the most balanced (two seven-card suits and two six-card suits for each side) to the most unbalanced (two 13-card suits for each side), I needed a way of describing them. Since the terms “distribution” and “pattern” refer to 13 cards (one hand or one suit), and I was going to look at 26 cards, I needed a new term. I chose “deal pattern” to make it clear I was looking at the whole deal, not a part of it.

Sometimes the two sides have exactly the same lengths, like when you have two seven- and two six-card suits, while at other times the lengths are different, e.g., when we have one eight-card suit and three six-card suits, while our opponents have three seven-card suits and one five-card suit. When both sides have the same lengths, it’s enough to give the deal pattern with four figures, e.g. 7-7-6-6 or 13-12-1-0, but when the sides are different it’s more clear if you give the lengths for both sides, like 8-6-6-6/7-7-7-5. In all these cases, the suits are given in descending order, and when one side’s longest suit is longer than the other’s, the side with the longest trump suit is given first.

Then I set off. 7-7-6-6 was easy. For each side, the defenders could cash the first six tricks, so Vernes was right here: 14 trumps produced 14 tricks.

And when I continued with 8-6-6-6 versus 7-7-7-5 the Law was once again correct. With 15 trumps, there were 15 tricks. Or was the Law really correct?

From diagram 1 North has got a spade from West in exchange for a heart. That means East-West can take eight tricks, while North-South still only take seven. Fifteen trumps and fifteen tricks, oh yes … but North-South was the side that got an extra trump. How come East-West is the side gaining from the swap?

Let us continue.

From diagram 2, North has given West a club and got a heart back. That means both sides have eight trumps and that the deal pattern is 8-7-6-5. As you can see, both sides can take eight tricks, so the Law is still correct.

But the same thing that happened from diagram 1 to diagram 2 happened again: One side got a trump (this time East-West), but it was the other side which gained a trick. What is really happening?

Let’s move on from 16 to 17 total trumps:

A heart to East, a spade to North – still in accordance with the principle that all suits are as evenly distributed as possible between the players in a pair. But now something new happened. Neither North-South nor East-West gained a trick. 17 trumps but 16 tricks – one trick fewer than the trumps.

And if we move up from 17 to 18 trumps, the same thing happens again:

A heart to South, a club to East. 18 trumps, but still 16 total tricks. Just like the previous case, neither side gained anything from the swap. Now there are two fewer tricks than trumps.

Slightly dizzy and confused I went back to diagram 3, but this time I didn’t change the number of trumps; I changed the deal pattern from 8-7-6-5 to 8-8-5-5 by swapping two side suit cards instead. Then something new happened again:

A heart to South and a diamond to East, and now both sides can take nine tricks. This time neither side gained a trump but both sides gained a trick. All of a sudden we have 18 total tricks with 16 total trumps. In the previous case we had 18 trumps but 16 tricks. The difference is two for the second time, but this time we have two more tricks than trumps. Proponents of the “Law” like to say, “trumps are everything,” but at this point I wondered if it wouldn’t be wiser to say, “trumps are nothing!”

Now it was 100% clear to me that trumps and tricks had nothing to do with each other. Had there been the slightest relationship between them, what I had just done would be impossible. So, forgive me for saying so, but my little experiment had been a stroke of genius, and all of a sudden I could prove that there was no relationship between trumps and tricks. If they happened to be the same on a given deal, it was more like a side effect.

But that wasn’t all. I also knew why the tricks sometimes went up and sometimes didn’t. It had to do with losers. In diagram 1 both sides have six losers. So they take seven tricks each. In diagram 2 North-South gained a trump but gained no tricks; their losers were still six. But East-West got rid of a loser (in spades) and therefore took one more trick than before. In diagram 3 East-West gained a trump but North-South gained from the swap, since it was their side which got rid of a loser. In diagram 4 and 5 nothing happened: neither side got rid of a loser, so neither side gained a trick. And not once did I have to use the word “trumps,” talking about “losers” was enough.

In diagram 6, where I moved two side suit cards, both sides gained a trick. They did it because both sides reduced their losers from five to four. Therefore, going from 8-7-6-5 to 8-8-5-5 was a gain of two tricks.

A swap gains a side a trick, if and only if they get rid of a loser. Not once will the side that gains a trump gain a trick. NOT ONCE! If you don’t believe me, try it out for yourself.

Let’s go back to deal 5:

Let East give a club to West and get a spade back. This means all suits won't be as evenly distributed as possible within a pair. This is something different:

Now East-West take one more trick in a club contract than in deal 5, since they have only one spade loser, while they had two before.

When Vernes wrote his famous article, he mentioned that “… how the cards of one suit are divided between two partners … has a very small, but not completely negligible, effect.”

What do you think about that claim? Imagine that nobody has objected to it for 36 years!

In diagram No. 5, where East-West’s spades are 2-2 they will take one trick less than in diagram 7, where their spades are 3-1. But to North-South it doesn’t matter how the spades are in the defenders’ hands. A gain in distribution is often a gain for one side only.

Right and wrong reason
Now let us compare diagram 1 and diagram 3.

What has happened is that North has given West a club and got a spade in return. Since this swap means that both sides gained a trump and a trick, it is understandable that you get the impression that tricks and trumps are related. But by now you know better. What has happened is that both sides got rid of a loser and both sides gained a trick. The fact that both sides also gained one trump each is only a side effect.

Short – not long
At this stage I realized that my little experiment had been highly successful. Now I had an irrefutable proof that there was no relation between total trumps and total tricks. I had managed to kill the Law.

But the goal of my study wasn’t this (that was just another side effect). I wanted to see if one side’s two longest suits could be used for predicting total tricks. But it didn’t seem so. The difference between deal No. 5 and deal No. 7, for instance, couldn’t be explained, since both sides had the same number of cards in their long suits. So where was the relationship?

Then I saw it. My wife use to say I solve problems by turning things upside-down (going from the other way, starting with the last page, etc). And once again that was the right thing to do: Instead of looking at the two longest suits, I should concentrate on the short ones. When I did so, everything fell into place, everything was clear and in perfect harmony.

If we start with deal No. 1:

North-South have three cards in each hand in both of their short suits. Their total length in their short suits is therefore 6, which also is how many tricks they lose on that deal. On deal No. 2:

North-South got an extra trump, but their short suit total (SST) is still 6, and therefore they take no more tricks in spite of getting an extra trump. But East-West improved their SST from 6 to 5, and therefore they will take one more trick than in diagram 1.

And now it’s no mystery that there is a difference of two tricks between deal No. 3 (8-7-6-5) and deal No. 6 (8-8-5-5):

In the first case the SST for both sides is 5, in the second case it’s 4. No surprise that it resulted in two extra tricks!

When I realized this very obvious fact – which nobody before me had observed – I realized I not only could prove that there was no relation between total trumps and total tricks, but I had also found something vastly superior to the Law of Total Tricks. High time to put the Law in an envelope, seal it and save it in the box labeled “Obscure Twentieth Century theories.”

When I let Mike in on my discovery, he became just as enthusiastic as I had been. That meant the book we were writing together had to be rewritten to a large extent, and the time it took to put it together was longer than expected. But who cares if the result is – according to our esteemed editor Matthew Granovetter in his review for the Jerusalem Post – “the most controversial book of 2005, maybe the decade.“ The title is “I Fought the Law of Total Tricks.“

To continue the discussion we started in our book, we have put up a website. Go there and ask a question or read what others have said. You find it at

I can assure you that much of the stuff you’ll find there will surprise you.