BridgeHands

Law of Total Tricks - A bidding methodology predicated on suit length, emphasizing both constructive opportunities as well as preemptive properties.  Also see book Law of Total Tricks, The: To Bid Or Not To Bid and Following the Law of the Total Tricks.

In it's most simple form, "The Law" suggests a partnership bid to equal the number of combined suit length, with adjustments based on aggregate vulnerability and other factors.

For instance, if:

  Side A shows 9 Hearts collectively based on their bids and,

  Side B indicates 8 Spades then,

  The aggregate tricks total 9 + 8 = 17

Thus:

  If Side A's bidding indicates they can make 10 tricks in Hearts then,

  Side B can only make 7 tricks in Spades (17 - 10 = 7)

Assuming Side A is vulnerable and can make 620 points,

Side B can lose up to 3 tricks and still have a better score (4 Spades Doubled, down 3 = 500 points, 120 points better than losing 620 points).

Jean-Rene Vernes, who originally created "The Law" in a 1969 article in the Bridge World magazine, included illustrative hand # 93 from the 1958 World Championship:

	A 6 9 7 K 9 6 4 A Q 9 3 2
Q J 10 9 2 10 8 5 4 A Q 10 4	Trump: Clubs	K 8 7 A J 6 2 J 10 8 5 2 6
	5 4 3 K Q 3 7 3 K J 8 7 5

" In one room, the Italians arrived at a contract of four clubs, North-South; in the other room, they were allowed to play two spades, East-West. Analysis shows that the result was never in doubt. North made ten tricks in clubs, losing only one spade and two red aces, while West made eight tricks in spades at the other table, losing one spade, one diamond, one club and two hearts."

"Now I will ask the reader to consider an unfamiliar concept that I call 'total tricks'--the total of the tricks made by the two sides, each playing in its best trump suit. In the deal above, the number of total tricks is 18 (10 for North-South in clubs, plus 8 for East-West in spades)."

"Now, even though it is not possible, in the course of a competitive auction, to determine how many tricks the opponents will make, can it be possible to predict, on average, the number of total tricks? If so, this average figure cannot help but be of lively interest in making competitive decisions.

"In fact, this average exists, and can be expressed in an extremely simple law: the number of total tricks in a hand is approximately equal to the total number of trumps held by both sides, each in its respective suit. In the example above, North-South have ten clubs, East-West eight spades. Thus, the total number of trumps is 18, the same as the total number of tricks."

"You may notice that in this deal the number of trumps held by each side was equal to the number of tricks it actually made--ten for North-South, eight for East-West. That is pure coincidence. It is only the equality between the total number of trumps and the total number of tricks that obeys a general law."

Jean-Rene Vernes professed several adjustments were necessary to "The Law":

The article concludes, stating:

"Unfortunately, it is very difficult in practice to determine the total number of trumps. (Oddly, this calculation is often somewhat easier for the defending side than for opener's. For example, you can usually work out the total trumps with great precision when a reliable partner makes a takeout double of a major-suit opening.) Most often, though, players can tell exactly how many trumps their side has, but not how many the opponents have. However, this itself is sufficient to allow the law of total tricks to be applied with almost complete safety."

"Consider, for example, the second bidding sequence above, and suppose that South has four spades. After partner's one-spade overcall, he can count on him for at least five spades, or nine spades for his side. Thus, East-West have at most four spades among their 25 cards. In other words, they must have a minimum of eight trumps in one of the three remaining suits. Thus, South can count for the deal a minimum of 9+8=17 total tricks. So a bid of three spades is likely to show a profit, and at worst will break approximately even."

"A similar analysis shows that the situation is entirely different when South has only three spades, so that his side has a considerable chance of holding only eight of its trumps. To reach the figure of 18 total tricks, it is now necessary for East-West to hold ten cards in their suit--not impossible, but hardly likely. It is much more reasonable to presume that the deal will yield only 16 or 17 total tricks. Thus, it is wrong to go beyond the two level; three spades must lose or break even."

"As we examine one after another of the competitive problems at various levels, we find that the practical rule appropriate to each particular case can be expressed as a quite simple general rule: You are protected by "security of distribution" in bidding for as many tricks as your side holds trumps. Thus, with eight trumps, you can bid practically without danger to the two level, with nine trumps to the three level, with ten to the four level, etc., because you will have either a good chance to make your contract or a good save against the enemy contract."

"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). Of course, the use of this rule presupposes two conditions: (1) the point-count difference must not be too great between the two sides, preferably no greater than 17-23, certainly no greater than 15-25; (2) the vulnerability must be equal or favorable. For this rule to operate on unfavorable vulnerability, your side must have as many high cards as the opponents (or more)."

"The Law" was popularized by Larry Cohen in 1992, who wrote several book on the topic.  Best known is "To Bid or Not to Bid", followed by "Following The Law" which provided adjustments to the law.  Larry Cohen and his partner, Marty Bergen, devised many conventions based on the concept of the law of total tricks - particularly with a very good trump fit (9+ cards).

Also see Hand Evaluation Books
 

In the May 1992 issue of Bridge World, Andrew Wirgren took a critical view of the law of total tricks from an analytical perspective, titled "The Anarchy of Actual Tricks".  Andrew's article highlighted the difference between a side's longest suit (the original concept of "The Law") and the one that produces the most tricks. Andrew pointed out that studying actual tricks is more important than studying total tricks.

Andrew used a hand generation simulator, Scania BridgeDealer, to generate deals. Surprisingly, he found "The Law" only worked correctly 35 percent of the time.  Next, he studied three world championship books:

1981 Bermuda Bowl final = 31 percent "Law" accuracy

1982 Rosenblum Cup final = 36 percent "Law" accuracy

1983 Bermuda Bowl final = 41 percent "Law" accuracy

Next Andrew studied the adjustment factors to "The Law" in Larry Cohen's second book. Negative Adjustment Factors would suggest that the Total Tricks will be less than the number of trumps while Positive Adjustment Factors would suggest that the Total Tricks will be greater than the number of trumps.

Negative Adjustment Factors included:

Negative Purity honors in opponent’s suits and/ or poor interiors in your own suit

Negative Fit ( misfits)

Negative Shape (flat hands)

Positive Adjustment Factors included:

Positive Purity (no minor honors in opponents’ suits and/or good interiors in your own suits

Positive fit (double/double fit

Positive Shape (extra length or voids).

Andrew Wirgren concluded that accurate use of "The Law" suffers deficiencies.

Location of High Cards

Larry states in his book "To Bid or Not to Bid", pages 18-19 that:
1) "Finesses that are onside for one pair will be offside for the other. The Total Trick count is constant". Andrew strongly disagrees as the following random deal exemplifies:

	A Q 8 3 A Q J 9 2 A 6 3 2
7 4 ? ? Q J 9 K J 9 8 5 3	Trump: Clubs	6 2 ? ? ? K 10 5 2 Q 10 7 4
	K J 10 9 5 10 8 7 8 7 4 A 6

Playing in some number of clubs, East-West have 9 club trumps and North-South have 9 spade trumps for a total of 18 total tricks. Playing in clubs East-West get five club tricks and two diamond tricks. The critical card is who has the HK. For North-South, the position of the HK is worth three tricks when the DA is knocked out at trick one. If West has it, the total trick count is 20, but if East has it, then there are only 18 total tricks. This shows that the position of the high cards is not irrelevant and does not balance themselves out. Thus, the total trick count is not always constant when formulating the Law.

Distribution of the Suits

Larry also states in his book To Bid or Not to Bid on Pages 18-19 that "bad breaks for one side translate into good breaks for the other. The Total Trick count is constant." This is not always the case as Andrew points out with the following example hand:

	10 9 8 7 3 2 K Q J 10 A 6 5
3 2 10 9 8 7 A 6 5 K Q J 10	Trump: Clubs	6 5 4 A K Q J 4 3 2 9 8 7
	A K Q J 6 5 4 9 8 7 4 3 2

Both sides can take eight tricks, first drawing trump then removing the minor suit Ace from the defense.  By moving all the 5s, the total trick count changes dramatically. Now both sides can make 10 tricks for 20 total tricks, two more than expected. Moving the C5 from North to South meant that one club loser disappeared and moving the H5 from the South to the North hand meant that a heart loser vanished at the same time. The same goes for East-West.

This simple example shows two important things. The first is that an extra trump for one side does not automatically mean one extra total trick. The second is that distribution is important as theorized by Andrew disagreeing with the opposite view of Cohen. Therefore, the total number of tricks on any deal depends not only on the total number of trumps, but also how the suits are distributed.

A third factor challenging "The Law" is the belief that the trick count remains constant when honors are moved from one hand to the other. The following is an example deal that was played by Andrew Wirgren in the 2001 Hecht Cup in Copenhagen showing that this is not always true:

	10 10 6 5 4 2 A K 10 8 K J 6
K Q 6 5 J 8 7 9 7 5 4 8 2		A J 4 3 K Q Q J 6 3 A 9 4
	9 8 7 2 A 9 3 2 Q 10 7 5 3

Assuming both sides can make 17 total tricks and both sides have found a black suit fit, should West overcall 3C to 3S?  Wirgen did getting a 48% score, while 3C by opponents would be down two for a 78 percent game (93 percent if Doubled).  Thus, when a side is bidding a suit other than their best (starting out with Hearts here), using the Law is non-productive.

While moving the HA to from South to North still produces 17 total tricks, their side can take 7 tricks in Clubs or 9 in Hearts.  Interestingly, doing so also changes the East-West tricks, making Diamonds their best trick-taking suit.  So while the Law purports "shifting honors" does not influence the outcome, here it causes the trick taking swing from 14 to 17 actual tricks.  Ironically, exchanging the 5s between North-South or East-West hands allows the side to make 10 tricks (20 total)!

Finally, Wirgren argues that point count, control, and vulnerability hypothesis of the Law are not always valid, citing:

"(1) the point-count difference must not be too great between the two sides, preferably no greater than 17-23 HCP, certainly no greater than 15-25 HCP; (2) the vulnerability must be equal or favorable. For this rule to operate on unfavorable vulnerability, your side must have as many high cards as the opponents (or more)."

Originally, Vernes considered the point count difference important without an explanation, however the topic was not addressed in "The Law of Total Tricks".

Wigren provides the following illustrative example:

K Q J 2 K 9 6 4 A 8 4 K 7   5 8 5 K Q J 9 5 3 J 10 9 4   10 8 7 6 3 10 2 10 7 4 8 5 3   A 9 4 A Q J 7 3 6 A Q 6 2

With 9 Hearts and 9 Diamonds, the hands comprise 18 total tricks.  In actuality, North-South takes 13 tricks in a Heart contract while East-West is limited to 5 Diamond tricks plus 1 Club trick.  So the total should be 19 total tricks.

However, moving North-South's Aces to East, things change dramatically.  Here, a Spade lead against South's Heart contract provides the defense 2 additional tricks - SA and a Spade ruff.   In the Diamond contract, the SA was only worth 1 trick. Thus, when player's strength/controls become unbalanced, it becomes more unlikely that trumps will provide an accurate evaluation of aggregate tricks.   In conclusion, point-count and control differences can greatly affect trick taking based on associated controls.

Wirgen studied 352 deals from world championships finals, noting the accuracy of the Law a 37 percent based on point-count and control differences.  When one side has at least 24 points, the accuracy decreased to 30 percent.  When the points were in the 17-23 range, the accuracy increased to 42 percent.

In conclusion, according to Andrew Wirgen, "The Law" is better served in competitive part score auction and the strength is balanced.  Unlike the hypothesis in the Law, Andrew Wirgen has attempted to provide definitive data where the Law is inaccurate.