The Law of Total Tricks (the LAW for short) has been around for a few decades. It says that if the honor cards in a bridge hand are distributed roughly equally between the two teams, then the total number of tricks achievable by the two teams is equal to the total number of trump. If North-South is bidding spades, and East-West is bidding hearts, then the total number of potential tricks available to the two prospective declarers should be roughly equal to the number of spades held by North-South plus the number of clubs held by East-West. If North-South has nine spades, and East-West has eight hearts, the LAW predicts that seventeen total tricks are available, but it does not predict how many either side would take. If North-South can take ten tricks if spades are trump, then the prediction is that East-West can take seven if hearts are trump. If North-South can take only eight, then East-West should be able to garner nine.

In Wednesday’s game my partner and I tried to be LAWful, but we came a-cropper on one hand. Two green cards were in view as I examined this hand with neither side vulnerable:

♠75 ♥QJT62 ♦AQ84 ♣Q5This hand easily met my criteria for a third-seat opener, so I bid 1♥. RHO passed, and my partner bid 2♣ (three-piece Drury) with this aggregation:

♠9862 ♥AK4 ♦KJ6 ♣T63His bid said that he had 10-12 points and three hearts. I also knew that he did not have a singleton or void. A different bid is used for that holding. Seeing no chance for game I bid 2♥. After two more passes RHO ventured 2♠. I could see no extras in my hand, so I left it up to my partner. He elected to pass as well. The result was not good. They took eight tricks in the black suits. If hearts had been trump, we would have taken nine tricks in the red suits. We scored -110; East-West pairs that bid 3♥ made +140 points.

When I thought about this hand, I realized that the LAW had been violated. They had seven spades, and we had eight hearts. Fifteen trumps should generate fifteen tricks. However, a total of seventeen tricks were apparently available. Knowing that the LAW is very accurate, I felt a little cheated.

Well, that was not quite right. We could have set the spade contract by forcing declarer to trump the third round of diamonds. In fact, however, the opponents could have actually scored nine tricks if they had found their fit in clubs. So, the LAW’s prediction of sixteen tricks was still two short of what was really available. How could it be so far off?

1. The existence of a double fit, each side having eight cards or more in two suits. When this happens, the number of total tricks is frequently one trick greater than the general formula would indicate. This is the most important of the “extra factors.”
2. The possession of trump honors. The number of total tricks is often greater than predicted when each side has all the honors in its own trump suit. Likewise, the number is often lower than predicted when these honors are owned by the opponents. (It is the middle honors–king, queen, jack–that are of greatest importance.) Still, the effect of this factor is considerably less than one might suppose. So it does not seem necessary to have a formal “correction,” but merely to bear it in mind in close cases.
3. The distribution of the remaining (non-trump) suits. Up to now we have considered only how the cards are divided between the two sides, not how the cards of one suit are divided between two partners. This distribution has a very small, but not completely negligible, effect.

In this case the first correction probably adds at least one to the the prediction. Our second suit only had seven cards, but it was solid. The opponents had only seven trump, but their best side suit, clubs, consisted of eight cards. What made this hand unusual was the fact that the opponents had all of the black honors except the ♣Q, which was in a doubleton, and we had all of the red ones. So the first two factors combined to add two tricks to the total.

Is there any way that my partner or I could have divined this? I don’t think so, but I think that one of us should have bid 3♥ anyway. Here is why: Ordinarily, a bidder using the LAW knows that he is “protected” by the distribution if he bids up to the number of trump that his side holds. Our side held eight, so we were protected up to the two level. However, Vernes cited one exception in the last paragraph of his article: “This rule holds good at almost any level, up to a small slam (with only one exception: it will often pay to compete to the three level in a lower ranking suit when holding eight trumps).”

• We certainly had eight trumps.
• We had at least half of the honor values.
• We were not vulnerable.

Unfortunately, neither I nor my partner knew whether the opponents had seven, eight, or nine spades. Since my honors were concentrated in two suits, I think that I should have just taken the bull by the horns and bid 3♥.

That brings up another question: would the opponents have bid 3♠? I doubt it. Neither of them knew about the club fit, and neither had anything extra.