A great example of the utility of the Law of Total Tricks occurred in Hand #22 on Wednesday evening.
Board #22
East dealer
East-West vulnerable
| | North
♠ Q
♥ K J 9 8 7
♦ 7 4
♣ A J 9 5 3
| | West
♠ J 10 9 8 2
♥ 6 5
♦ Q 10 8 3
♣ 10 2
| | East
♠ A 7 6 4 3
♥ 3 2
♦ A K J 6 5
♣ Q
| | | South
♠ K 5
♥ A Q 10 4
♦ 9 2
♣ K 8 7 6 4
| |
|
| | | | |
| South | West | North | East |
| | | 1♠ |
| 2♣ | P | 2♥ | P |
| 3♥ | P | P | P |
The Law of Total Tricks (often abbreviated as "The LAW"1 or, less often, as "LoTT", was postulated by Jean-René Vernes for French bridge players in the fifties. The rest of the world learned about it little by little over the next three decades. It attained its current popularity only after it was featured in Larry Cohen's 1992 book, To Bid or Not to Bid.
The LAW states that in a competitive auction2 the total number of tricks available between the two sides is roughly equal3 to the total number of trumps that the two sides have in their best suits.
On this hand East-West's best suit is clearly spades. East and West both have five of them. North-South has ten clubs. The LAW predicts that twenty tricks will be available between the two sides. Deep Finesse calculated that North-South could take ten tricks in hearts or clubs. East west could take nine tricks in spades. So, the LAW's prediction is off by one trick: twenty trumps v. nineteen tricks.
At our table I, sitting East, opened 1♠, West overcalled 2♣, my partner passed, and our opponents ended up playing a partial in hearts. I took my three high honors, and we felt lucky that North-South did not bid game. We were therefore somewhat chagrined to discover that others bid 4♠ with our cards even though West had only three points. They only went down one. So, even though East-West was vulnerable, their -100 score was better than our -170.
How did they get to 4♠ when they only had a total of seventeen points? They followed Larry Cohen's advice because they felt "protected" by the LAW. He stated the "adjunct" of the LAW thusly: "You should always bid to the level equal to the combined number of trumps held by your side." In this case East-West has ten spades. If Larry Cohen (or someone who has read his books) had held West's motley assortment of cards, he would have immediately bid 4♠. That is probably what happened at the other tables.
As soon as West bids 4♠, North can place the total number of trumps at at least twenty—East-West's ten plus his own five plus the five that his partner promised. Unfortunately, there is no call that allows him to advertise his five-card support without going to the dreaded five level. He knows more than his partner and must decide on the spot whether to pass, double, or bid 5♣, which will be set by the end of trick 3. There would be no way to find the heart fit at that point.
Although the LAW applies equally well to all levels and all vulnerabilities, the adjunct works much better when your side is not vulnerable. If North decides to double the 4♠ bid, and East-West comes up one trick short, the penalty is 200, which is worth more than the 170 that our opponents won. If we had hot been vulnerable, then the 4♠ bid would have been the right decision no matter what North did.
So, my best advice is always to follow the LAW, but when applying the adjunct give a little consideration to the vulnerability.
1. A few years ago I sent Larry Cohen an email asking him why LAW was usually capitalized. He said that he did not know.
2. My recollection is that Vernes considered any auction in which both sides had at least seventeen points to be competitive.
3. Chapter 9 of Cohen's book lists major adjustments to the calculation. This part of the book is the most difficult to understand and apply.