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).
JeanRene Vernes,
who originally created "The Law" in a 1969 article in the
Bridge World magazine, included
illustrative hand # 93 from the 1958 World Championship:
" In one room,
the Italians arrived at a contract of four clubs, NorthSouth; in the other
room, they were allowed to play two spades, EastWest. 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 NorthSouth in
clubs, plus 8 for EastWest 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,
NorthSouth have ten clubs, EastWest 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 madeten for NorthSouth, eight for EastWest. 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."
JeanRene Vernes
professed several adjustments were necessary to "The Law":
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 honorsking, queen, jackthat 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 (nontrump) 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. 
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 majorsuit 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 onespade overcall, he can
count on him for at least five spades, or nine spades for his side. Thus,
EastWest 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 EastWest to hold ten cards in their suitnot
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 pointcount difference must not be too
great between the two sides, preferably no greater than 1723, certainly
no greater than 1525; (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 1819 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:
Playing in some number of
clubs, EastWest have 9 club trumps and NorthSouth have 9 spade trumps for
a total of 18 total tricks. Playing in clubs EastWest get five club tricks
and two diamond tricks. The critical card is who has the HK. For
NorthSouth, 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 1819 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:
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
EastWest.
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:
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
nonproductive.
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 EastWest tricks, making Diamonds
their best tricktaking 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 NorthSouth or EastWest 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
pointcount difference must not be too great between the two sides,
preferably no greater than 1723 HCP, certainly no greater than 1525 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:
With 9 Hearts and 9
Diamonds, the hands comprise 18 total tricks. In actuality,
NorthSouth takes 13 tricks in a Heart contract while EastWest is limited
to 5 Diamond tricks plus 1 Club trick. So the total should be 19 total
tricks.
However, moving
NorthSouth'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, pointcount 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
pointcount and control differences. When one side has at least 24
points, the accuracy decreased to 30 percent. When the points were in
the 1723 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.
