The law of total tricks

Total tricks is the number of tricks your side can take playing in its best trump fit plus the number the opponents can take playing in theirs. Total trumps is your side's trumps in that fit plus their trumps in theirs. The law says the two numbers are about equal. If your side holds nine spades and they hold eight hearts, there are 17 total trumps, and the law expects 17 total tricks: 9 for you and 8 for them, or 10 and 7, or 8 and 9.

Cohen's working rule follows from it. In a competitive auction, bid to the level of your side's trumps. Contract for as many tricks as you hold trumps, and no more.

Why is this safe? Take the 17-trump deal above. If you bid 3♠ with your nine spades and go down one, you took 8 tricks, so the law gives the opponents 9 in hearts. Not vulnerable, your 3♠ down one costs 50 points, and they would have scored 140 playing in hearts. Vulnerable, down one costs 100, still less than their 140. Either you make your contract or you lose less than their part score was worth. The exception is being doubled when vulnerable. 3♠ doubled down one vulnerable is 200, more than any part score they could make.

Going beyond the safety level is a different bet. If you hold eight trumps and they hold eight, there are 16 tricks to share, and the side that buys the contract at the three level usually goes down. Cohen's short version is that with only eight trumps you should not bid three over their three.

You know your own hand, and partner's bids tell you a minimum length. Add the two and you have your side's trumps. These are the usual promises in Standard American; check them against your own agreements.

The opponents' trumps are a guess from their auction. If one of them bids a suit and the other raises, place them with at least eight. When your side holds few cards in their suit, they likely hold more: if you and partner have four hearts between you, the opponents have nine.

Counting your own side is the part that wins points, and it decides the raise. Holding four-card support for partner's five-card major, you have nine trumps, so a weak raise goes straight to the three level. That is the idea behind Bergen raises and the weak jump raise in competition. Holding three cards opposite a weak two, you have nine trumps again, and the raise to three is a preempt and partner passes it.

Neither side is vulnerable. North opens 1♠, East overcalls 2♥, South raises to 2♠ and West competes with 3♥. North holds 14 points and wonders about 3♠.

South's simple raise promised three spades, so North knows the side has eight trumps, and West's raise suggests the opponents have eight hearts. The law expects 16 tricks. Double dummy, North-South take exactly 8 tricks in spades and East-West exactly 8 in hearts. 3♥ goes down one for +50 to North-South. Had North bid 3♠, it would also go down one, for -50. Passing is worth 100 points on this deal.

West's 3♥ was itself a bid above the law's level, and it happened to work. If West had passed, 2♠ would have made for 110 to North-South, so going down 50 in 3♥ saved 60. On this 16-trick deal both three-level contracts fail, so whichever side bids last at the three level loses.

Neither side is vulnerable. North opens 1♠ and East overcalls 2♥. South has only 6 points but four spades, which makes nine trumps.

Double dummy, North-South take 9 tricks in spades and East-West take 8 in hearts, so the law is exactly right here. 3♠ makes for +140. The jump also did its second job. West, with 9 points and three hearts, might have competed with 3♥ over a quiet 2♠, but over 3♠ there is no room left below the four level, and the law gives East-West no reason to go there with eight trumps.

We solved 10,000 random deals double dummy, put each side in its longest fit, and compared total tricks with total trumps. The law was exactly right on 39.6% of deals and within one trick on 87.0%. It missed by two or more on 13.0%. Those figures barely moved when we kept only the deals where the high-card points were split close to evenly, the competitive part-score deals the law was written for.

The pattern in the last column is the useful part. On deals with few total trumps there tend to be slightly more tricks than trumps, and on deals with many there tend to be fewer. The law is a good estimate, not an exact count, and the adjustments below are how strong players decide which way a given deal leans.

Cohen and later writers list the features that push the trick count above or below the trump count. They are judgment calls. Most players treat each as worth about half a trick to a trick.

• A double fit adds tricks. When your side also has a second eight-card or longer fit, the long side suit runs and the trick total often beats the trump total by one or two.
• Flat shape costs tricks. If your hand is 4-3-3-3, nothing ruffs and no long suit sets up. Count one trick less, and two flat hands opposite each other are worse.
• Soft honors in their suit cost tricks. Queens and jacks in the opponents' trump suit, such as Qx or QJx, are worth something in defense but little when you declare, and they suggest the deal will produce fewer total tricks.
• Honors in your own long suits add tricks. Kings and queens that fill out your trumps and side suit carry their full value whoever declares.
• Trump spots matter at the edges. A suit like AJ1098 loses fewer tricks than A7542, and good intermediates make the higher number more likely.

Here is a deal where everything points down. Every hand is balanced, and South's Q93 in hearts sits in the opponents' suit.

A North-South pair who followed the bare law to 3♠ with their nine trumps would go down one. An adjusted count of one trick less, for the flat South hand with heart values, keeps them at 2♠, which makes.

The double fit works the other way. On the deal below North-South have nine spades and ten diamonds, East-West ten hearts and nine clubs.

North-South make 11 tricks in spades, East-West make 10 in hearts. Both sides have a second fit and short suits to ruff with, and the total runs two tricks above the trumps. If East-West bid 4♥, North-South do best to bid 4♠, which makes with an overtrick for 450 not vulnerable, rather than defend against a making 4♥ worth 420 to the opponents.

• Game and slam decisions. When your side holds most of the high cards, the question is whether game makes, and that turns on points and fit. Total trumps do not answer it. The law is a tool for deals where both sides can compete.
• Notrump. The law counts trump contracts. It says nothing about 3NT.
• Unknown lengths. If you cannot tell how many trumps the opponents hold, the total is a guess and the law is only half used. Your own side's count, which you usually do know, is the half that sets your bidding level.
• Vulnerability and doubles. The law estimates tricks and leaves the scoring to you. Bidding to the level of your trumps is safe in the sense that you lose less than their part score, but vulnerable and doubled, down one is 200 and down two is 500.
• The five level. Eleven trumps permit the five level by the law, but a five-level save that turns out wrong is expensive, and experienced players bid it less often than the bare count suggests.

The law also has its critics. Mike Lawrence and Anders Wirgren argued in I Fought the Law of Total Tricks (2004) that the law is less accurate than its followers believe, and proposed counting short suits instead. Their counts are harder to use at the table, and most club players keep the law as the starting estimate and adjust from there.

1. 1.Counting partner for more trumps than promised. A raise shows three. Unless the bidding has shown a fourth, do not count it.
2. 2.Bidding three over three with eight trumps. On a 16-trump deal both sides usually go down at the three level, so let them play there.
3. 3.Using the law to bid games. Raising a weak two to game with four trumps is a preempt. It is not a game try, and partner must not treat it as one.
4. 4.Forgetting the adjustments. Two flat hands with queens in the opponents' suit will rarely produce the full total. Shade the count down.
5. 5.Ignoring the score. Vulnerable against not vulnerable, the doubled penalty for going down can exceed the part score you were trying to stop.