The Law

by Steve Turner

Let's start by reviewing the question, "At what level do most competitive auctions begin and end? If your experience tells you "at the one and two-level," you probably need to reconsider your competitive philosophy.

So...wouldn't it be nice if we had a couple of tools to decide how and when to compete against those folks who always seem to get into our face, and settle into their comfortable part score with their 8-card or 9-card fit?

Thus, the purpose of the concept known as "The Law of Total Tricks."

How do we define the Law?

The total # of tricks available in a given deal is = to the number of trumps available (to BOTH sides combined). An example. If we have a 9-card fit and the opponents have an 8-card fit, then the combined trump length is 17, true? By definition, there are then 17 total tricks available. This concept is the basis for what is to follow.

How do we apply the Law?

Let's take an example. You pick up this hand SKQJxxx HKJx DQx Cxx

We would open 1S, right? OK, your opponent overcalls 2C, partner raises to 2S, followed by 3C on your right. Hmmm...what to do? Here's how we decide.

Premise:  We bid to the level of the number of trumps we have.

Adjunct #1: Usually outbid the opponents at the 3-level with 17 total trumps, especially non-VUL (it can be shown that this applies even if the opponents have the 9-card fit and we have the 8-card fit).

In the above example, we have a 9-card fit and the opponents have an 8-card or 9-card fit (usually). So, there are 17 or 18 tricks available between the combined hands. If we want to bid our share of the tricks, then we need to decide if it is right to bid again. Mathematically, using a chart for 17 total trumps, and non-vulnerable, it can be proven that you need to compete, regardless of the outcome. Read Larry Cohen's book (To Bid or Not to Bid), page 27. If the opponents have a 9-card fit instead of an 8-card fit, creating a total of 18 tricks available), it is even more critical to compete (see page 29).

Another example. You hold SAQxx HKJx DJxx CQxx. In 1st chair you open 1C, hearing 1H on your left, and a negative double by partner. Your RHO bids 2H, and you bid 2S. It goes P - P - 3H on your right. What now?

Adjunct #2:  Never outbid the opponents at the 3-level with 16 total trumps.

OK, let's take a look: What is the likely fit their way - probably 8, due to the simple overcall and a single raise, right? (often, good opponents are not giving up versus 2S, a known 8-card fit). Now...what is our fit? EXACTLY 8. Take that to the bank (partner did not bid 1S, but instead doubled). So, it's fair to say that the likely total tricks available is 16, according to our definition. Looking at Rule 1 - have we yet bid to the level indicated by the number of trumps we hold? YES. Then pull out the Green card.

Same example, but change the auction slightly. Your LHO overcalls 1H, 1S by partner, 3H by RHO.....your call. This one is a little more tricky. Do the opponents probably have 9 trumps? Do we also have 9 trumps? Do we have extras? Does it matter?

Adjunct #3:  Always outbid the opponents at the 3-level with 18 total trumps.

FOLLOW the LAW. Bid 3S here.

COROLLARY:  Make every effort to not allow the opponents to play at a level equal to their number of trumps.

The ultimate proof in any concept is in the results. Consider this. If most of the time the following statement would hold up, would you consider its use?

"No matter how many tricks you go down, the LAW protects you from suffering a larger penalty than what their contract is worth."
Matt Ginsberg, for an article in The Bridge World, used a double-dummy solver to investigate how often the Law is correct. Ginsberg is also the author of GIB, one of the world's first expert-level bridge-playing programs which is based upon this double-dummy solver. Matt's results were very interesting and are summarized here:

"As the total number of trumps increases, the less reliable are the LAW concepts. Thus, at higher levels, the LAW tends to overestimate the trick-taking capability. Generally, the LAW is very consistent through the 4-level, with potential flaws above the level at which more than 20 total trumps combined exist. Some degree of judgment then enters into the picture."

Now, in lower-level competition, the solver showed that the LAW is accurate 67% of the time. How about you? Should you follow the LAW? Here's the answer.

"Take a look at your competitive judgment. Can you judge correctly more or less than 70% of the time without it?"

The original article describing the Law of Total tricks was published in 1969 by Jean-Rene Vernes in The Bridge World. (An excerpt is here.) The Law has become very popular following the publication of two books on the subject by Larry Cohen. These are To Bid or Not to Bid, the Law of Total Tricks (1992) and Following the Law (1995). A recent contrary opinion has been published by Mike Lawrence and Anders Wirgren in I Fought The Law Of Total Tricks (2004). Matt Ginsberg's article is available here.