## LOTT versus "Got More, Bid More"

« The Law Of Total Tricks »     by Colin Ward

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The Law of Total Tricks ("LOTT") is a very simple theory.
It postulates that, in a competitive or pre-emptive auction, the total number of tricks available on any given hand is equal to the total number of trumps that the two pairs have in their respective longest suits.
 A Q x x x x x K J x A x x x x x K x A J 10 9 K Q x x x x x A x x x Q x x J 10 x J 10 9 x x x Q x x K x x x

 A Q x x x x x K J x A x x K x x x x A J 10 9 K Q x x x x x A x x x Q x x J 10 x J 10 9 x x x Q x x K x x x
In the above example, both sides have an 8-card fit.   This means that there should be (8 + 8) = 16 tricks to be had in total.
In the case of Hand A (left), N-S can make 2, while E-W can make 2.   By switching K from East to the "onside" position, N-S can make 3, while E-W can only make 7 tricks in .   The total number of tricks remains the same; only the distribution of those 16 tricks changes.
----- The Arithmetics of LOTT -----
Before we can appreciate LOTT, we need to consider how it works in regards to the scoring methods.   We will look at it from the point of view of a pair considering a sacrifice in 4 over the opponents' 4.
Consider this scale, where
“F” means Favourable vulnerability (them vul, us not),
“B” means Both are vul,
“N” means Neither vul, and
“U” means Unfavourable vulnerability (us vul, them not).
The first five lines show that, with 16 total trumps, sacrificing is never profitable.  It is only marginally profitable with 17 total trumps, when we are not vulnerable versus vulnerable opponents.
 Total Tricks for Scores for IMP Result Tricks Them Us Their 4 Our 4 for Our 4 16 10 6 F: +620 vs −800 −6 16 10 6 B: +620 vs −1100 −10 16 10 6 N: +420 vs −800 −9 16 10 6 U: +420 vs −1100 −12 16 9 7 F: −100 vs −500 −12 17 10 7 F: +620 vs −500 +3 17 10 7 B: +620 vs −800 −5 17 10 7 N: +420 vs −500 −2 17 10 7 U: +420 vs −800 −9 17 9 8 F: −100 vs −300 −9 18 10 8 F: +620 vs −300 +8 18 10 8 B: +620 vs −500 +3 18 10 8 N: +420 vs −300 +3 18 10 8 U: +420 vs −500 −2 19 10 9 F: +620 vs −100 +11 19 10 9 B: +620 vs −200 +9 19 10 9 N: +420 vs −100 +8 19 10 9 U: +420 vs −200 +6 19 9 10 F: −100 vs +420 +8 19 9 10 B: −100 vs +620 +11 19 9 10 N: −50 vs +420 +9 19 9 10 U: −50 vs +620 +11
At 18 trumps, the scales tip in favour of the 4 sacrificers, who will lose only at unfavourable vulnerability.   With 19 or more trumps, sacrificing is automatic.  With 20 trumps, both sides may be able to make game!
Our biggest problem is that we don't always know how many trumps the opponents have.   Hence, we often go by a more "simplified" (some would say "oversimplified") Law of Total Tricks: bid to your level of trumps.   We compete or pre-empt one trick for each trump that we have.   Hence, with nine hearts between partner and ourselves we might compete/pre-empt as far as 3 ... but no further.
----- Questions -----
1. I want to know how many tricks we can take.   Why should I care about how many both sides can take?
A x x    J x x x    x x x x    K x.
 LHO Pard RHO Me 1 2 pass 2/3?
Playing SAYC, after 1-2-Pass, knowing that partner's 2 is Michaels cuebid showing both majors, should I bid 3 ?
3. I'm an impatient type.   I want the bottom line now!   Does this "trumps = tricks" formula really work ?
4. Is there some way to test this theory before investing a few thousand IMPs or MPs in trying it ?
----- LOTT versus "Got More ?   Bid More ! " ------
There are two schools of thought regarding the basis for making bidding decisions.   The traditional method is to use what is euphemistically called "bridge judgement", following a "got more, bid more" approach.   The number of trumps that the pair holds plays a significant but not central role for traditionalists.   Factored equally into their calculations are texture, overall shape, position, cover cards, trump suit symmetry, non-trump suit asymmetry, High Card Points, and, yes, the number of trumps that the pair has.

LOTT, on the other hand, uses the total number of trumps that both sides have as the principle guideline.   Other considerations are "adjustments" (to use the LOTT terminology) to the total number of tricks we expect.
 A K 10 x x x x x x x x x x Q x x x x x x Q K J x x x A Q x x A Q x x K J x x x J x x A K J 10 9 x x x x x

Here E-W outgun N-S 24-16 in HCPs. The total number of trumps is (9 + 9) = 18.   Still, both sides can make eleven tricks!   That means that LOTT is "wrong" by (22 − 18) = four tricks in an auction which is bound to be hotly contested.   Again, LOTTers would say that the Total Number Of Tricks has to be "adjusted" upwards because of the double fits for both sides.   Skeptics would say that four tricks is a huge "adjustment".

----- A LOTT of Adjustments -----
While traditionalists consider Mike Lawrence's "Hand Evaluation" the definitive work on bridge bidding judgement, LOTTers regard "Following the Law", "Points Schmoints" and "To Bid or Not to Bid" as sacred texts.   If we read any of the literature on LOTT, we will see that the total number of tricks available "occasionally" has to be "adjusted" upwards or downwards on the basis of certain criteria.   These criteria are essentially the same ones developed by traditionalists: texture, overall shape, position, cover cards, trump suit symmetry, non-trump suit asymmetry.
Only High Card Points ("HCPs") are removed from the equation.   In a pre-emptive situation, HCPs are considered irrelevant because, by definition, we are conceding that they hold the majority of strength and we are not bidding to make.   We are simply trying to obstruct.   In a competitive situation, HCPs are disregarded by LOTTers, since they are presumed to break about 20-20 between the two pairs.
In Hand C above, we saw a case where the existence of a double fit increases the total number of tricks that the two sides can make.   Double fits, then, would require an "upward adjustment."   In the coming sections, we will examine the effects of the other critieria on the total number of tricks available.
----- Questions -----
1. If both schools use essentially the same criterion in their competitive decisions, what is the difference between them ?
2. LOTTers rely on the number of trumps that both sides have.   But how do they calculate this, without knowing for sure how many the opponents have ?
3. LOTT relies on knowing how many trumps partner holds.   Does this mean that LOTTers, with a six-card suit, are more inclined than non-LOTTers to jump overcall with decent hands ?   Would they bid 2 over RHO's 1 opening with:

 RHO LOTTer LHO Pard 1 2?
 x x x A K J 10 x x x Q x x ?

----- Texture and Mesh -----
The term "suit texture" refers to whether our long suits are supported by high cards − including good spot cards.
"Hand texture" describes whether or not our HCPs are in "controls" (Aces and Kings) or in "secondary honours" (Queens and Jacks).   Aces and Kings are considered "hard" values, while Queens and Jacks are regarded as "soft" values.   This assignation changes, though, once the bidding reveals how useful these values are likely to be.
Only after we have heard a few bids, can we make an estimate of how our High Cards will "mesh" with partner's hand.   According to Mike Lawrence's "In and Out" theory, Queens and Jacks in our long suits are "gold."   Queens and Jacks in the other suits are liable to be useless, if we end up declaring the hand − especially in a suit contract.
Mike ("O_Bones" on OKBridge) Dorn Wiss refers to such secondary honours outside our long suits as "QUACKS" (QUeens and jACKS), reminding us of their doubtful value to us declaring in any suit contract.   Our QJx opposite partner's xx will not help prevent them from cashing tricks in that suit, as Kx or A might.   Similarly, a King may be wasted opposite partner's singleton.   Even an Ace may be wasted, if opposite partner's void, but at least it will give us one pitch.
While QJx opposite our xx might not help our chances of making, say, 4, it may well prevent them from making 4.   Such secondary honours reduce the number of total tricks by reducing the opponents' expectations without enhancing ours.   LOTTers call this a "downward adjustment."   Non-LOTTers call these QUACKS "defensive values."

 Hand D: A x x x Q J x x x A x x x
 LHO Pard RHO Me 1 1 Pass ?
 LHO Pard RHO Me 1 1 Pass ?
 LHO Pard RHO Me 1 2 2 ?
The above hand D is far stronger in support of than and .   Indeed, were partner to overcall their 1 with 1, we would force to game.
After 1-1-Pass, though, the dubious value of the Heart QUACKS reduces this to an invitational hand.
After 1-2-2, advancer's A is considered to have a "pure" value opposite overcaller's likely singleton.
Similarly, xxxx would be a good holding for offence in that it would indicate that none of our overall values are liable to be wasted, if we play in .   However, Kxxx would be of questionable merit on offence after 1-2-2.
For decades, there existed the myth that Aces and Kings were better for suit contracts, while Queens and Jacks were better for NoTrump contracts.   This is only true, if both hands are flat.   If we are bidding NoTrump based on a long (likely minor) suit, we will need Aces − not Kings, Queens or Jacks − in the other suits.   In general, then, Aces and Kings are best for declaring, Queens and Jacks better for defending.

----- Overall Distribution -----
Flat hands require a downward adjustment, while double fits − which may include possible double fits − will require an upward adjustment in the total number of tricks.   In non-LOTTer parlance, we don't over-compete with flat hands.

 Hand E: Q 10 x x x Q J x x x Q x x
 Pard RHO Me LHO 1 DBL 3/4?
Over 1-Double, at equal or favourable vulnerability, most would simply leap to 4 with this hand E.   Ten trumps, ten tricks, 4.   However, the flat distribution is considered a downward adjustment; we should consider 3 as the limit of our hand's competitive potential.

 Hand F: J 10 x x x K Q x x x x x x
 Pard RHO Me LHO 1 DBL ?
Here, after 1-Double, the possibility of a double fit in the pointed suits (,) would require an upward adjustment.   LOTTers might wish to check for Diamond support from Opener and, if it is present, go to 4 on this hand.   The methods used to check for such a double fit may vary from partnership to partnership.

 Hand G: J 10 x x x A 10 x x x x x x
 Pard RHO Me LHO 1 DBL 4
Here, even a shortness in in Opener's hand may allow us to set the suit up with ruffs.   Bid 4 here.   LOTTers might consider the 6th Diamond an upward adjustment.
When competing (or considering a sacrifice), we should consider a doubleton xx in the opponents' suit a "death holding."
Even xxx is less obscene than xx, since it raises the possibility of partner having shortness in that suit.   Holding xxx, if the opponents are competing vigourously, we should assume that they have 9 trumps;   this marks partner with a singleton − one loser in that suit for us.
Holding xx in our hand, though, the opponents will have to have a 10-card fit, before partner can have a singleton and hold our losers to one.   Hence, tend to defend with a doubleton in their suit.   If they have sacrificed, just double.

----- Position -----
Having strength in RHO's suits is good, since the chances of these cards taking tricks increases, as long as we apply the "play small towards big" rule from Rainbow Lesson #12.   Having length in RHO's suits is also good, since partner can over-ruff LHO (who, along with partner, is likely short in this suit).   Length or strength in LHO's suit should be devaluated.
Position of our lengths behind RHO (which is good for us) or in front of LHO (which is bad for us) does not affect the total number of tricks, generally.   It simply shifts them from one pair to the other.
--- Cover Cards and the 4-Point Principle ---
Any card which will cover one of partner's losers is a "cover card."   An Ace opposite a void may or may not cover one of partner's losers (depending on whether partner can cash this Ace, before the opponents cash their winners).   A King opposite a singleton is not a cover card.   Consistent with the "In and Out" theory above, secondary honours in partner's long suit should be viewed as cover cards.
It is a rule of thumb in bidding that we will take partner for one such cover card for every four HCPs that partner has shown in the auction.   This is called the "4-Point Principle."
For example, if partner opens 1NT, we would play him for (16 / 4 = ) four such cover cards, since 16 HCP is an average 1NT opening (15 to 17).   Similarly, after 1:2, Opener might guess that Responder will hold about (8 / 4 = ) two "cover cards", since 8 points is about average for such a raise.
Note: this 4-Point Principle is useful in constructive auctions as well as competitive ones.   Because it is part of the "got more, bid more" approach and does not affect the total number of tricks, it is not generally known or practiced by LOTTers.   It does help us determine how many tricks we can take, though.
----- Trump Suit Symmetry -----
 Hand H Opener A K Q x x K J x x A x x x Responder J 10 x x A Q x x x x x A x
Consider this common theme:
This pair can make 6 on a 3-2 trump break, by pitching a loser from dummy's hand on the fifth .
But, if is trump, 5 is the limit, since we will not have any pitches.   Hence, at higher levels especially, the balanced (4-4 here) fit is superior over the unbalanced (5-3 here) one.
This explains the popularity of jumping to game in partner's 5-card major with 5 of them ourselves.   Even if either of us does have a second suit, it will rarely be any more balanced than our major suit fit.
 Pard RHO Me LHO 1 2 DBL
In competition, then, it may be worthwhile to investigate the chances of a second, balanced fit via Negative Double or Snapdragon Double, rather than jumping on the first fit that comes along.   If the auction started with 1-2 or 1-2 on the above Hand H, then, a negative double might work out far better than any quick raise or cuebid.
LOTTers will note that choosing instead of on the above hand will reduce the number of actual trumps, but increase the number of total tricks by boosting our potential to 12.   LOTT uses the longest suit, though (9 spades in this case), even if that suit is not chosen as trumps.
----- Plain Suit Symmetry -----
The more asymmetrical our plain (i.e. non-trump) suits are, the more tricks we can take.   On Hand H in the above section, slam in is made, because we choose to be the NON-trump suit, where its asymmetry (5-4 rather than 4-4) permitted a pitch, which would be unavailable in 6.   This same theme popped up in Hand C, repeated here for convenience:

 A K 10 x x x x x x x x x x Q x x x x x x Q K J x x x A Q x x A Q x x K J x x x J x x A K J 10 9 x x x x x

 A K 10 x x x x x x x x x x Q x x x x x x Q K J x x x A Q x x A Q x x K J x x x J x x A K J 10 9 x x x x x
In the left Hand C, if N-S were vulnerable versus non-vulnerable opponents, we would have to infer that our 3-1 minor suit distribution might allow 5 or 5 to make, given the opponents' vigorous bidding the minors.   The one bidding 5 or 5 would have to conclude that their partner is short in their three-card minor.
But, in the revised case on the right, with four "death holdings" (i.e. doubletons) in the minor suits between them, N-S would have to avoid bidding 5 or 5 [against opponent's 5-minors.].
This is more than simply competing more with unbalanced hands — a theme that both groups embrace.   After all, both the 2-2 and 3-1 minor suit distributions would make the hands unbalanced, and would amount to the same number of Short-Suit Points (i.e. two) in both the North and South hands.   It is a matter of recognizing that partner is likely short in our 3-card minor suit and that doubletons are grim holdings.

----- Pre-Empting with LOTT -----
Many non-LOTTers would be surprised to learn that the tendency to pre-empt at the TWO level with a SIX card suit, at the THREE level with SEVEN, is an application of LOTT.
Consider this: you have SIX spades.   There are SEVEN left.   Divide them equally, and partner rates to have 2+1/3 spades − closer to two than three.   This means that, on average, we have EIGHT trumps in that suit.   Hence, we open 2 as a weak 2-bid with the appropriate overall strength.
With seven cards in, say, hearts, we should expect the remaining six hearts to divide 2-2-2 on average.   Hence, we should expect nine hearts in total (7 + 2), and will therefore bid with 3.
In responding to such a pre-empt, we will often raise briskly to the appropriate level.   For example, opposite partner's non-vulnerable 2 opening, we might bid 3 with any hand of 0-17 HCPs that has three spades!   With four spades, we would venture to 4, if our point total is 0-14; only with 15-17, will we balk at the notion of taking a likely minus against a game, which is not a favourite to make.
Among the many modifications to modern bidding structures that have been inspired by LOTT is the Bergen raise.   1:3 and 1:3 become pre-emptive, while responses of 3 or 3 show a 4-card support for 1 or 1 Opener's major.   The cost of this approach is that the declaration of a nine-card fit so early in the auction assures the opponents of a similar fit of their own.   This hand featured may of the themes discussed here, along with an inspired defensive SnapDragon Double by advancer:

 Both Vul. A Q 10 x x x x J x x A Q J x x x x J 10 x x A K x x A K 10 x x Q x x x 10 x x x x K J x x Q x x x x K x x x

 West North East South 1 Pass 3* X 3 X* Pass 4 Pass Pass Pass
3 is a Bergen raise,
showing 8-10 pts with 4 spades.
Double of  3 is Snapdragon,
showing 4+ Hearts,
Diamond tolerance and
defensive values (see Lesson #3).

The knowledge that N-S had nine spades allowed West to double 3 here (or bid 3, if South had bid 3 instead) with virtual impunity.   When the opponents have a nine-card fit, we are guaranteed an eight-card fit, and will usually have either a 9-carder ourselves or two 8-carders.
This result was a rare +620s for E-W in 4, while many N-S pairs were able to buy this one in 2.   LOTTers, then, must always ask themselves, if the knowledge that partner has four trumps (rather than 3+ trumps) is more valuable to us than to them.

----- Discussing LOTT with partner -----
It is a good idea for any pickup partnership to discern how closely wedded to LOTT they and their opponents are.   Many pairs mention LOTT in their stats (e.g. "Out, Law" versus "Law Abider") and/or on their convention cards.   Since this is a matter of style, it is possible for a LOTTer and non-LOTTer to play together as long as both they and their opponents are aware of who does what in this critical regard.
----- In Closing -----
Few controversies make this game more interesting than LOTT.   One might make the mistake of presuming that LOTTers prefer to play against others of their ilk so that they can accurately assess the total number of trumps/tricks during competitive auctions.   Not true!   Ask any LOTTer and they will tell you that they prefer playing against critics of the theory.   As for the skeptics, they will respond with one voice:   "Sit yourselves down, LOTTers, and DEAL THEM PASTEBOARDS!" :)
The beauty of the Law Of Total Tricks cannot be found in the prose describing it.   Rather, it lies in the theory's inherit simplicity.   As the Romans would say: simplex signum veritatis.
No theory in any game has ever caused such a revolution in popular thinking.   Even the greatest of its critics may find themselves counting their trumps in close competitive auctions.

---- Final Quiz -----
 K x x x x x x x K x x x x

 West North East South 1 Pass 2 3 Pass Pass ?
What would you bid
as responder ?
 K x x x x K x x x x x x x

 West North East South 1 Pass 2 3 Pass Pass ?
What would you bid
as responder ?
 K x x A x x Q 10 x x x x x

 West North East South 1 Pass 2 3 Pass Pass ?
What would you bid
as responder ?
 K x x K 10 9 x x x x x x x

 West North East South 1 Pass 2 3 Pass Pass ?
What would you bid
as responder ?
 K Q x x x x Q x x x x x x

 West North East South 1 2 2 3 Pass Pass ?
Non Vul.  IMPs.
What LOTTers are liable
to do here ?
 K Q x x x x Q x x x x x x

 West North East South 1 2 2 3 Pass Pass ?
Non Vul.  IMPs.
What will anyone