Law of Total Tricks: Bid to the Level of Your Trumps

The law of total tricks says that the total number of tricks available on a deal is about equal to the total number of trumps: your side's longest fit plus the opponents' longest fit. From it comes a simple bidding rule: in a competitive auction, bid to the level equal to the number of trumps your side holds, eight trumps to the two level, nine to the three level, ten to the four level.

The law was first published by the French expert Jean-René Vernes in the 1960s and became famous through Larry Cohen's 1992 book To Bid or Not to Bid. It is a tool for partscore battles, and players in every system use it, from Standard American and 2/1 to Acol.

Two numbers drive the law:

• Total trumps: your side's best fit plus the opponents' best fit. If you have eight hearts and they have nine spades, total trumps = 17.
• Total tricks: the tricks your side takes in hearts plus the tricks they take in spades, each as declarer in its own suit.

The law says the two numbers are about equal. If total trumps are 17, then when you can take 8 tricks in hearts they can take about 9 in spades, and when you can take 9 they can take 8.

You do not need to know the split to use the law. The practical rule is the one you bid by: with eight trumps, compete to the two level; with nine, to the three level; with ten, to the four level. If the opponents also have a fit, bidding to that level is safe, because either you make it or they could have made something too.

You cannot see partner's hand, so you count what partner has promised:

Add your own length. If partner opened 1♥ and you hold four hearts, you have nine trumps: you are entitled to compete to 3♥, and you may jump there at once to take space away from the opponents. If partner overcalled 1♠ and you hold three, you have eight: compete to 2♠, not higher.

Count the opponents' trumps the same way. An overcall shows five, a raise of it shows three more, a jump raise four more. Your own shortness is a clue too: if you and partner hold only three spades between you, the opponents hold ten, and the total is bigger than it looks. A big total is a signal to compete harder, because both sides take a lot of tricks. A small total, with one side short of a fit, is a signal to defend.

Keep the count running through the whole auction. Each bid either confirms what you assumed or changes it, and the count you held after the first round is often wrong by the third.

You have 14 HCP and five hearts. Partner's 2♥ promised three: eight trumps. The opponents have shown about eight spades (five for the overcall, three for the raise). Total trumps: 16.

The law says total tricks are about 16. If you can take nine tricks in hearts, they can take only seven in spades, and the other way round. Most of the time the split is eight and eight: both 2♥ and 2♠ make, and both 3♥ and 3♠ go down.

That is exactly what happens here. Double dummy, North-South take eight tricks in hearts and East-West take eight in spades. If you bid 3♥ you go down one. If you pass, 2♠ makes. The best result for you is to pass now and hope they bid 3♠ over your silence, which also goes down. Your hand has no extra shape and no extra trump: with eight trumps, stop at the two level.

You hold 4 HCP and four hearts. Partner has five, so you have nine trumps: the law lets you go to the three level. In competition most pairs play the jump raise to 3♥ as preemptive, a weak hand with four trumps. With a good hand you would cue-bid 2♠ instead to show a limit raise or better. To compare how 2/1, SAYC, Acol, Precision and Polish Club read the jump, see what 3♥ means in every system.

The jump makes life hard for West. With a quiet 1♥ - 1♠ - 2♥, West bids 2♠ or 3♠ at leisure. Now West has to decide at the three level, without knowing whether East has a minimum.

Here the total trumps are 18 (nine hearts and nine spades), and the double dummy total is 18: nine tricks in hearts for North-South and nine tricks in spades for East-West. Your 3♥ makes. If West competes to 3♠, that makes too, and neither side should bid four: 4♥ and 4♠ both go down one. The law told you where to stop on both sides.

The law is an estimate, not a promise. To measure it we ran 2,000 random deals through a double dummy solver, took each side's longest fit and the tricks each side makes in it, and compared totals:

So the law is exact on about 40% of deals and within one trick on about 87%. The average error was close to zero. Studies by other researchers report figures in the same range. That is good enough to guide partscore decisions, and it explains why the adjustments in the next section matter: they push the estimate up or down by the trick it often misses.

Upgrade (the total is likely higher, so bid one more or compete harder):

• A double fit. When both sides have a second fit as well, total tricks often exceed total trumps.
• Pure honors. Your honors are in your long suits, not in the opponents' suit.
• Shape. Singletons and voids, especially in the opponents' suit.

Downgrade (the total is likely lower, so bid less or defend):

• Honors in the opponents' suit. A ♠KQ sitting over the spade bidder is worth tricks on defense, not on offense.
• Flat hands. 4-3-3-3 opposite partner's raise rarely produces extra tricks.
• Short trumps. A raise on three small trumps plays worse than one on four.

Vulnerability also matters, though it does not change the total. Going down one doubled when vulnerable costs 200, more than the 110 or 140 the opponents would score. Not vulnerable, minus 100 against their partscore is a good trade.

• Notrump. There is no trump suit, so there is nothing to count.
• Game and slam decisions. The law tells you the total, not how it is split. Whether your side has ten tricks depends on high cards. Use points, the losing trick count and judgment.
• Misfits. If neither side has an eight-card fit, the law has little to say.
• When one side has most of the strength. The law assumes both sides compete. When one side holds 30 points, it plays the hand and the total does not matter.

• Counting trumps partner never promised. A 1♦ opening may hold three diamonds. A single raise usually shows three trumps, not four.
• Bidding the extra level "because I have points". High cards decide who makes what, not the total. With eight trumps and 15 HCP, you still sell out at the two level more often than not.
• Applying the law in an uncontested auction. If the opponents are silent, bid your values.
• Forgetting the preemptive side. The law is a weapon: a fast raise to the level of your fit, like 3♥ on the deal above, takes space away at once.
• Treating the law as exact. Use the adjustments, especially for honors in the opponents' suit.

You will meet these choices all the time in BridgeDummy bidding puzzles: you are South, you choose a call, and each option is played out double dummy on many deals that fit the auction. Over many puzzles you see when the law holds and when the adjustments win. Related reading: the Rule of 17 for raising weak twos, overcalls, preempts and Bergen raises.