The Theory of Total Tricks: Part I – History and Application
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The Law of Total Tricks goes back to Jean-Rene Vernes in a Bridge World article from 1969(Vernes, June, 1969). Vernes found a statistical connection between the lengths of each side’s longest suits and the number of tricks available in those trump contracts. Vernes’ work was new and revolutionary, but only in the way it quantified the importance of trump length. As Danny Kleinman wrote(Kleinman, 2013) in a letter to me:

“The value of additional cards in a trump suit for offense was known, though not measured, from before the invention of contract bridge.”

As he pointed out, S. J. Simon had written, almost seventy years ago(Simon, 1946),

“It has probably never occurred to you that a fit in partner’s suit is a disadvantage in doubling a contract in another suit. Reflect on it and it becomes obvious. The fact that, between you, you hold most of the suit, means that the enemy holds few of it. And therefore you cannot hope to make many tricks in that suit.”

Kleinman actually published a penalty double rule well before the Vernes study:

Do not double an opponent’s suit for penalties at a level lower than the number of cards you have in your partner’s suit.

Replace “double … for penalties” with “sell out” and we have the modern playbook of competitive bidding written fifty years ago.

The Importance of Total Tricks

It is matchpoints, with no one vulnerable, and the bad guys have bid quickly up to three spades. Do you defend or take the plunge? Bidding to make is always nice, but you can gain even when you don’t make. Losing 100 in four clubs doubled is better than paying out 140 if three spades makes. This is where Total Tricks enters the arena. Suppose a little birdie whispered to you,

“There are 18 Total Tricks ready to take on this hand.”

By that, the birdie means

Tricks in spades (their way) + tricks in clubs (played our way) = 18.

It is then absolutely clear to bid. Let’s suss this out with a simple table:

 Tricks in Spades Tricks in Clubs Par Result Defending Par Result Bidding 7 11 300 400 (150) 8 10 100 130 9 9 -140 -100 10 8 -420 (-170) -300

Of course they haven’t bid their game yet in the last case, and partner might not raise four clubs to five in the first, so maybe those don’t count. Otherwise, bidding is a winner in every case, and wins easily in the two middle cases, which are more likely.

Do we have such a birdie? Yes, Vernes’ law is our birdie, since Vernes predicted:

The total number of tricks on a given deal is, on average, the total number of trumps held by each side.

So, let’s say the bidding goes

W
N
E
S
1
X
3
?

to you. You can expect partner to be approximately 1-4 in the majors. If you are 3-5 in the majors, then you can count a nine card spade fit, and a nine card heart fit. 18 trumps, and so 18 tricks. Your birdie tells you to bid four hearts without even looking at the rest of your hand.

This is an exaggeration, of course, and expert authors have written quite a bit on adjusting the Total Trick count, but estimating trumps, and using that to judge competitive auctions, has become the standard framework for all modern expert bridge players. Take a look at Kit’s Corner in this forum and you will see countless references to the number of expected total trumps in competitive decisions.

There was even a Rodwell invention in vogue for a short while: After a one heart opening and a one or two spade overcall,

4 = four more hearts than spades

4 = three more hearts than spades

4 = two more hearts than spades.

Using these methods, opener would know the exact total trump count should the next hand bid four spades, and would be incredibly well-placed to make a five-level decision. This invention certainly shows how deeply this Vernes Law has permeated modern bridge.

So, Vernes found a remarkable connection between the number of trumps held by both sides, and the tricks available on offense and defense. This statistical link has been verified in major studies, but, as of now, there doesn’t seem to be any theoretical basis for the amazing Law.

I find that very frustrating. Maybe it’s the mathematician in me, but I want to figure out how things work – I want to see the proof. I have spent quite a long time exploring total tricks, and trying to develop a working theory. Finally, things are falling into place. In this series, I am going to explore total tricks, trying to develop a complete theory, from the ground up. Stay tuned.

Bibliography

Bloom, S., & Colchamiro, M. (December, 2011). The Second Fit. The Bridge World .

Cohen, L. (1994). Following the Law. Master Point Press.

Cohen, L. (1992). To Bid or Not to Bid. Master Point Press.

Kleinman, D. (2013). Personal Correspondence.

Lawrence, M., & Wirgren, A. (2005). I Fought the Law. Mikeworks.

Simon, S. J. (1946). Why You Lose at Bridge. Simon and Schuster.

Vernes, J.-R. (June, 1969). The Law of Total Tricks. The Bridge World .

Part II of The Theory of Total Tricks