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**The Total Number of Tricks available on any deal is approximately equal to the Total number of Trumps**

If this were an algorithm, life would be simple. We add up the number of cards in our longest suit, add up the number of cards in our opponents' longest suit and the sum is approximately the same as the total number of tricks we can make playing with our suit as trumps, together with the total number of tricks our opponents can make with their suit as trumps.

However, it is not an algorithm, it is a heuristic: there are many other factors that affect the total number of tricks that can be made and when the law should be applied.

**A simple**** Rationale**

- There are four suits in the pack (if not certain of this I suggest you re-read your first bridge book.)
- Two of the suits are the 'trump suits' (They are unlikely to be the same, except in contrived situations)
- Two of the suits are 'neutral' suits
- Given an even distribution 3 tricks will be fought over in each of the neutral suits. It makes no difference who wins how many; the total number of tricks will be 6
- Now look at how many tricks you will make in your trump suit.

- If you hold 7 trumps, the likely distribution is 4-3 : you will make 4 tricks
- If you hold 8 trumps the likely distribution is 4-4 or 5-3: if it is 5-3 you make 5 tricks, if it is 4-4 you will probably get a ruff, making 5 tricks (this ruff may be the outstanding card in one of the neutral suits, or the opponents' trump suit)
- If you hold 9 trumps the likely distribution is 5-4:You will make 6 tricks if you can ruff in the short hand (or twice in the long hand, or if the suit splits 6-3)
- If you hold 10 trumps, however, you will only make 7 tricks if the suit is 7-3: 6-4 you need a ruff in the short hand, 5-5 you need 2 ruffs.

- Thus for 7,8 or 9 trumps, you make
**3 tricks fewer**than you have trumps. - However you make 3 tricks from the neutral suits (on average)
- Thus the expected number of tricks you make in a hand is equal to the number of trumps you hold!
- If you only make 2 tricks from the neutral suits then your opponents usually make 4, so the total tricks made is constant.

**The flaw in the**** argument**

- The primary assumption is that there a 3 tricks in each neutral suit. Keen mathematicians will realise that this leaves one card left over. If the card is ruffed then it either means the 5th trick for the 4-4 split (one for each hand), or is ruffed by the short trump holding for 9 or 10 trumps, or is ruffed in the long trump hand (and hence reduces the total number of tricks for 9 or 10 tricks).
- It is,however, possible (or even probable) that the long card (or cards) become an extra trick, by itself. In this case the total number of tricks in the neutral suits increases to 7 or 8. Note that if the opponent's cards are split 4-2 then the extra trick is compensated for by a third round ruff.
- Holding a large number of cards in a neutral suit, therefore, increases the number of tricks that a side can win from 3 to 4 (or 5).
- Similarly a shortage in one neutral suit means both sides may gain extra tricks - thus increasing the total tricks.
- If the defence can ruff a trick in the short suit then the total tricks that can be made goes down - since the tricks that the declarer can make with their chosen trumps has been reduced. Note that this does not affect the tricks that the defence can make if they themselves were declarer.
- The neutral suit length must, of course be equal to or less than the trump length. (Note that a 4-4 trump fit is quite likely to increase the number of tricks that can be taken by one since a ruff in either hand adds up to 5. For a 5-4 trumps split, an extra trick is only produced if the hand with 4 trumps has fewer cards in a suit than that with 5 trumps. This is less likely due to the law of vacant spaces.

Let's analyse a simple hand (taken from Mr Cohen's follow-up book on The Law.

West

♠

76

♥

8642

♦

KQ108

♣

KQ3

North

♠

Q1052

♥

AQ3

♦

A3

♣

10972

East

♠

83

♥

K75

♦

J654

♣

AJ64

South

♠

AKJ94

♥

J109

♦

972

♣

85

D

- ♠ 5 tricks due to the fit: the extra trick (to make 6) comes from ruffing the diamond OR ruffing 2 clubs (there will always be a 2-card suit when there is a 5-card suit).
- ♥ 3 tricks (2 for NS, one for EW) as expected
- ♦ 5 tricks (3 for EW, 1 for NS in top cards, one extra for ruffing the heart
- ♣ 3 tricks. As you can see EW can make 4 BUT NS have the tempo to take their tricks in spades before the extra trick can be used. This requires optimum defence (which the Law assumes). In practice, due to misdefence, more tricks may be made than The Law suggests - certainly at the 2 or 3 level.

Total trumps (9+8) = 17. Total tricks (6+3+5+3) = 17.

However - let us change a couple of cards

West

♠

76

♥

8642

♦

KQ108

♣

KQ3

North

♠

Q1052

♥

AQJ3

♦

A

♣

10972

East

♠

83

♥

K75

♦

J654

♣

AJ64

South

♠

AKJ94

♥

109

♦

9732

♣

85

D

Now the total number of cards in each suit is the same and EW can still make their 8 tricks. But NS can now make 11. there is no change in the 'purity' of the hand. So what has gone wrong?

West

♠

76

♥

8642

♦

KQ108

♣

KQ3

North

♠

Q1052

♥

AQJ3

♦

A

♣

10972

East

♠

83

♥

K75

♦

J654

♣

AJ64

South

♠

AKJ94

♥

109

♦

9732

♣

85

D

The key change, obviously, is the fact that hearts (the neutral suit), now plays for 4 tricks in total. Not only that, the 9 cards in the trump suit now produce 7 tricks.

**Mino****r**** Honours **

Mr Cohen, quite rightly, explains that holding **unsupported** minor honours can reduce the total number of tricks. With both sides holding nearly the same number of high card points it is quite likely that a suit with minor honours is 'frozen' (neither side can play the suit without losing a trick in it). In this case, the number of tricks that can be made in the suit will depend on who has to open up the suit. When the balance of high card points becomes more skewed then these minor honours are less likely to be unsupported. The fact that a trick may not be made in a suit, or indeed that a trick may only be made by defenders, reduces the tricks that a side might make.

West

♠

A6

♥

Q974

♦

Q762

♣

K75

North

♠

Q72

♥

865

♦

104

♣

AJ1083

East

♠

KJ4

♥

KJ103

♦

K983

♣

64

South

♠

109853

♥

A2

♦

AJ5

♣

Q92

D

In this hand the fate of the ♠J is discussed - move it from EW to NS then NS gain an extra trick but EW do not lose one. The reason for this is described as the Jack being a 'minor honour'. However that is not the reason.

The reason why EW don't lose a trick is that the third spade goes on the 4th heart. The 'extra' spade trick is in fact a mirage as West has nothing to throw away on it!

**Double Fits**** **

Everyone knows that a 'double, double fit' increases the total number of tricks on a hand (often considerably more). However it is NOT the fact of the fit per se, it is the fact that the secondary suit contributes more than the expected three tricks. **A strong 4-3 fit** is sufficient to increase the total number of tricks. (As indeed can be witnessed in the very first hand of the article). A weak 4-3 fit usually results in the long card having to be ruffed, which merely increases a 4-4 fit to the expected 5 tricks or, if it is ruffed in the short hand, increases the 5-4 fit to 6 tricks.

West

♠

A10653

♥

A952

♦

95

♣

A3

North

♠

Q7

♥

8

♦

KQJ106

♣

KQJ76

East

♠

9842

♥

K10643

♦

A2

♣

108

South

♠

KJ

♥

QJ7

♦

8743

♣

9542

D

A nice double-double fit - 18 combined trumps and a double fit should produce more than 18 tricks. But it doesn';t. Why?

One problem is that neither the EW, nor NS 9-card fits generate the expected 6 tricks. There is no ruffung value in the short trump hand. The second problem is that the heart suit doesn't generate a guaranteed 5 tricks in total since the 5th trick ownership depends on who plays the suit.

As an aside - 5-5 hands are regarded, rightly, as being trick generators (provided there is a reasonable fit). The reason is that, with a fit, partner can ruff the secondary suit (generating 6 tricks in the trump suit, which is the correct number on a 5-4 fit and one more than needed with a 5-3 fit) setting it up (thus increasing the total tricks in the neutral suits.)

**Summary - the theory**

- The 'Law' (note the word' approximately) is pretty accurate BUT has to be taken with a pinch of logic and deduction.
- The more trumps you hold, the more likely it is that the Law will overestimate the tricks you will make.
- Uneven trump holdings are more likely to result in an accurate result according to the Law. 5-3 fits definitely fit, a 4-4 fit probably will.
- Although a ninth trump is useful for ensuring you don't lose control, it is dangerous when applying the law - unless you can see a use for it - since a ruff is a requirement to uphold the Law (unless the 5-card suit can be used to ruff twice - e.g. dummy reversal)
- Conversly where a hand can generate two extra tricks by ruffing in the short trump hand, a 9-card fit is worth an extra trick. A ten-card fit requires these two ruffs merely to comply with the law (on a 5-5 fit), although only one ruff is needed on a 6-4 fit.
- A neutral suit that will generate more than 3 tricks by strength will increase the total number of tricks that can be made.
- Suit holdings that will generate a trick in defence, but not one in offence reduce the total number of tricks.
- If the defence manage to obtain a ruff in a neutral suit, this reduces the total tricks.

**Application - find how good your fit is.**** **

- In competitive auctions the key factors are : Trump fit (both sides) and Distribution.
- It is important for your side to know:

- The total number of trumps you hold.
- This means that you should have agreements as to what you would call based on length of suits. Thus differentiation on length by using support doubles (3-card rather than 4-card support), or defining your negative doubles (a double shows 4 cards in the other major, a bid shows 5)
- An opening bid that shows 5 cards (or more) in a suit is more precise than one that shows 4 cards (or more). A 5-3 fit is indicative that your side meets the requirements for The Law to be accurate. (The downside of course is that it takes more calls to find a 4-4 fit).
- Is there a secondary fit - a 'double double fit'? Fit jumps (and Fit non-jumps) are thus an important construct in any bidding system based on The Law. Knowing whether there is a secondary fit gives your side a decided advantage in knowing the total tricks.
- Pre-empting with fewer than the agreed number of cards is dangerous if the auction rates to be competitive. Partner will overestimate the total tricks available. A pre-empt in 2nd position (where it is most likely that a competitive auction status will arise) should be sound with regards to suit length. In 3rd position the aim is solely in-fast, out-fast and disruption is the main concern, suit length is less important. In 1st position, my preference is for a sound 6-card suit as a minimum. (Many players differentiate between a sound 6-card suit and a weak one, by using the Multi 2-diamonds convention and weak 2s)

**Application - work out how good your opponent's fit is.**** **

- This information mainly comes through their bidding. Obviously if partner splinters/ could have splintered but didn't then that helps.
- In a competitive auction, if opponents struggle into a suit, then it is likely that their fit is only 8 (or even 7) cards.
- Find out whether they have options for specific suit lengths that they haven't used. (Yes they should alert a bid if they use support doubles in that situation, but some may not realise the requirement)

You should have sufficient information from the bidding to decide the total trumps and hence the total tricks.

The rest is simple calculation:

- If the opponents can make their contract, how many tricks will your side make? What are the relative scores?
- If you have to decide to bid on - consider how many tricks the opponents would make if your side makes the contract - and if you go off. You may be amazed at how often this will suggest defending and taking the money.
- Every trump you hold in the opponent's suit is valuable. Even if they are only the 2345 the fact that you hold them means the opponents do not - they have fewer trumps to ruff and may need to waste their high trumps to draw yours. Holding 4 trumps and the shorter trump hand definitely suggests defending in close decisions.

**Application - pre-emptive raises**

- There is no doubt that playing 5-card majors is a great benefit when considering major-suit contracts.
- You can always raise to the 2-level with 3 trumps
- To raise to the three level requires 4 trumps and a ruffing value: i.e. anything other than 4-3-3-3.
- Raising to the four level requires two ruffing values if partner may have 5. If partner has 6 then only one is needed.
- Pre-emption works, excessive pre-emption, when the distribution is balanced is just another way of giving up 5 imps. Beware of hands where you have a massive trump fit - but nothing to use the trumps on.

Finally Authorship of the hands is acknowledged. Further research is recommended as these are my own thoughts, which may be controversial or unfounded.

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