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The Winning Trick Count

When seeking a contract, you and Partner are interested in Winners - not Losers! Winners mean tricks and that is the essence of The Winning Trick Count (WTC). WTC directly addresses the question of how many tricks you might expect to make.

You pick up a hand with, say, 15 Points. That's all well and good and very familiar, but somewhat abstract, and the real question is how many tricks the hand may be worth. That's exactly where WTC comes in.

WTC is a more practical alternative to the rather abstract (though extremely familiar) Point count as a method of hand evaluation. Not surprisingly WTC and the traditional Point count are very closely related - see below.

How does WTC work? It's really simple.

But ... first things first.

Hand Types

When you pick up a hand, the very first thing to note (before counting Points or Winners) is the Type of the hand: whether it is Balanced, Distributional or 4441. These are the only three Types of hand.

In a Balanced hand the sum of the lengths of the two longest Suits is 8 or less and the hand contains no Singletons or Voids. There are only three hand patterns satisfying these criteria: 4333, 4432 and 5332. A Balanced hand may be opened, if at all, either in Notrumps or with a Suit bid.

In a Distributional hand the sum of the lengths of the two longest Suits is 9 or more. A Distributional hand is only openable, if at all, with a Suit bid; never with a Notrump bid.

A 4441 hand is best treated with caution and should probably not be opened with less than 14 Points - and then only with a Suit bid, using whatever rule you favour.

Having established the Type of the hand - Balanced, Distributional or 4441 - we can move on to WTC, the counting of 'Winners'.

Winners

Winners are Aces and reasonably guarded Kings and Queens, plus any extras for Shape.

Some examples - by no means exhaustive.
Axx, Axxx, Kxx, Kxxx, Qxx, Qxxx 1 Winner
AKx, AQx, AKxx, AQxx, KQx, KQxx 2 Winners
AKQ, AKQx, AKQxx, AKQxxx 3 Winners


Shape is about shortages (except in trumps, needless to say).
Doubleton 1 extra Winner
Singleton 2 extra Winners
Void 3 extra Winners


Some examples, including Shape Winners.
Jxx, xxx No Winners
Qx, Jx, xx 1 Winner
Kx, K, Q, x 2 Winners
AKQ, AK, A, Void 3 Winners


WTC is probably best when you and Partner have agreed trumps and seem to be heading for a Suit contract, rather than Notrumps. That is, where Suit agreement (at least 4 trump cards in each hand) can be established.

Although WTC might still be helpful when looking for a Notrump contract, a moment's thought will convince you that Shape Winners are far more problematical in Notrumps.

Before proceeding further, a word to the wise: common sense must rule at all times. For example, if you have less than four of Partner's Suit, with correspondingly less trumping potential, then it is prudent to reduce your count of Shape Winners accordingly.

Opening

Unless you are being pre-emptive, it's usually best not to open holding less than 5 Winners. Partner will normally assume that, if you open, you hold at least 5 Winners.

Let's say you pick up the following hand.

S A Q x x
H K J x x
D K x x
C Q x


The hand is 4432 and is therefore Balanced - but a shade strong for opening weak Notrumps!

Count your Winners: 2S + 1H + 1D + 1C = 5 Winners.

The hand satisfies the 5 Winners criterion and the obvious opening bid is 1H bearing in mind the usual rule for Balanced hands - open the lower ranking of two equal length Suits unless both Suits are red.

Note that, with a WTC of 8 or more, you would consider a strong opening, using whatever method you and Partner adopt.

See also Opening the bidding.

Responding

You are delighted to hear Partner open 1H when you pick up the following Balanced 4432 hand.

S J x
H Q x x x
D x x x
C A x x x


Suit agreement already!

Count your Winners: 1S + 1H + 0D + 1C = 3 Winners.

Partner has signalled at least 5 Winners. Adding these to your 3 Winners gives a total of 8 Winners. Clearly you can raise to 2H

Opener's Rebid

If you have heard Partner respond, and not simply Pass, you can review the situation.

When you have opened one of a Suit and Partner bids a single raise in your Suit, you now know that Partner probably has 4 of your Suit and also that Partner's WTC is 3 Winners. A double raise in your Suit tells you Partner has 4 Winners. And so on.

Bear in mind that, if you have opened with a Suit bid at the one level, you have told Partner that you have at least 5 Winners with that Suit as trumps.

If you did indeed open with exactly 5 Winners and heard Partner bid a single raise to 2 of your Suit, there is probably little more to be said: your 5 Winners plus Partner's 3 Winners makes 8 Winners and 2 of a Suit contract is probably where you should stick.

If you have more than the minimum 5 Winners, you may decide, having done the arithmetic based on your knowledge of the total number of Winners in the two hands, to bid to the appropriate level, or at least let Partner know that, in fact, you have more than you have claimed.

The obvious example: you have opened one of a Major with 6 Winners (not just 5) and heard Partner jump to the three level in your Suit, meaning that Partner claims to have 4 Winners. Since 6 plus 4 is 10 you can bid to Game without more ado.

Responding - again

Again you are delighted to hear Partner open 1S when you pick up the following 4441 hand. Not quite Distributional but, with the Singleton, certainly not Balanced so you can expect help from the Shape characteristics.

S J x x x
H K
D K Q x x
C J x x x


It must be your lucky day: Suit agreement - again!

Count your Winners, being careful to note that the Singleton HK only counts as 2 Winners, not 3: 0S + 2H + 2D + 0C = 4 Winners. Partner has signalled at least 5 Winners. Adding these to your 4 Winners gives a total of 9 Winners. Time for a jump raise to 3S even though your Points look thin!

When holding less than four of Partner's Suit, it's prudent to reduce your WTC accordingly. For example, holding only three cards in Partner's Suit, reduce your Winners by one. As always, common sense must prevail!

Opening - again

Finally, let us look at the stronger end of the spectrum. It is, indeed, your birthday and the following picture gallery comes your way:

S A Q J 8 7 5
H A J
D J
C A Q x x


You have no less then 2S + 2H + 2D + 2C = 8 Winners. Playing Weak Twos in the Majors, this is a golden opportunity to brandish your Strong Two with an opening Reverse Benjamin 2D - your Suit to be specified by following Partner's relay 2H with a glorious 2S of course!

A little bit of Theory - strictly for Masochists!

Readers may be interested to learn that, by analysing lots of dealt hands, it's possible to demonstrate a fairly clear (statistical) relationship between Winners (including Shape Winners) and Points. Quite simply, it is
P = 2W + 1

where P denotes the number of Points and W the number of Winners.

However, don't forget that a statistical relationship is not an exact relationship: it only relates to averages, so that, if you count W Winners in your hand, you will, on average, find that it contains 2W + 1 Points.

On average, you can expect to pick up one Ace, one King and one Queen. So the average number of AKQ Winners is 3, but there are also, on average, 1.5 Shape Winners. This means that the mythical 'average' hand will contain 3 + 1.5 = 4.5 Winners.

Entering W = 4.5 into the above formula gives, not surprisingly, the average number of Points

P = 2W + 1
   = 9 + 1
   = 10

The above suggestion, that one may consider opening with 5 Winners, is thus equivalent to saying one would not normally open with less than 11 Points - even this being a shade competitive, but not too reckless!

Furthermore ...

Clearly, since there are only 12 AKQs in the pack (not 13), the number of Winners, as defined above, in any one hand can never exceed 12. If, as is highly likely, you have less than 12 Winners, then you have some Losers. Your Losers are exactly as usually calculated in the Losing Trick Count (LTC).

Counting the number of Winners (W), as prescribed above, and Losers (L) in the usual way you therefore find that the following relation always applies to your hand.

W + L = 12

To repeat: this has to be the case since the pack contains 12 AKQs. W is the number you've got in your hand and L is the rest. So, if you know W then you know L and vice versa. Everything you may (or may not) want to know about W or L follows from that simple equation.

So, for opener's hand (using 0 for opener)

W0 + L0 = 12

where the assumption is that opener's W0 is at least 5 or, equivalently, L0 is at most 7.

And for responder's hand (using 1 for responder)

W1 + L1 = 12

Adding the two

W0 + L0 + W1 + L1 = 24

After slight rearrangement, the total Winners between the two hands is

W0 + W1 = 24 - (L0 + L1)

Hence you get the usual LTC formula, by adding your Losers to partner's Losers and subtracting this sum from 24, the number of TRICKS you might expect to make - or, more commonly, subtracting from 18 = 24 - 6 to get the BID. So the usual LTC BID formula is

BID = 18 - (L0 + L1)

Incidentally, since this formula always applies, you can obviously greatly simplify the usual LTC calculation by assuming, for opener

L0 = 7

and thus

BID = 11 - L1

In other words, a simpler LTC method would be: just take your Losers away from 11 to get responder's BID.

Quite sensibly, bridge books don't go into all the above but if you really want to understand LTC - and hopefully improve on LTC - you've got to!

But the whole point of The Winning Trick Count is that, since you know W0 and W1 anyway, why not just calculate the Winners W0 + W1 straight away; it's more intuitive, since you're really looking for Winners, not Losers; and its almost always simpler since you usually have less Winners in each hand than Losers!

Epilogue: Winning and Losing

This is a rather sad story. As the Bard wrote, 'If you have tears, prepare to shed them now'. Well, actually it's not all that bad, really, I suppose, but it felt like it at the time.

The story begins in the Summer of 1988, during a Saturday evening game of 'kitchen Bridge'. Someone introduced me to the Losing Trick Count (LTC). From the very start I was uneasy about it.

For one thing, LTC puts the main emphasis on losing tricks, not winning them. Now, as any of my partners will tell you, I'm as skilled at losing tricks as the next man, but it's not my real aim in life at the Bridge table. And when my partner and I are struggling towards a contract, our bidding refers to the tricks we are hoping to make, not lose!

And then there's the crazy arithmetic. I mean: you are supposed to count your losers, then add your losers to Partner's and, to cap it all, take the number you last thought of away from 18 of all things! Well, what could it all mean? I thought, this is not for me; I've spent my whole life avoiding daft arithmetic and I'm not about to start doing it now.

The day after my first encounter with LTC was a lovely sunny Sunday, but I'm afraid I wasted the whole afternoon figuring out how LTC worked and, more to the point, how I could improve upon it. The alternative I came up with I naturally called the Winning Trick Count (WTC) and I was quite proud of my new method. But, as the saying goes, 'pride comes before a fall'. We're approaching the tearful bit.

Over the intervening 15 years I explained WTC to a few acquaintances, some of whom were quite enthusiastic while others (who clearly love talking about losers and doing dodgy arithmetic) told me, essentially, that they were too old and set in their ways to bother with anything better than LTC.

Anyway, to cut a long story short, I eventually listened to unwise advice and, much against my better judgement, in June 2003 published an article about WTC in one of the bridge magazines. Needless to say, I expected a flood of adulatory correspondence about my wonderful new method and I eagerly awaited the next edition of the magazine.

A single letter flooded in (from a correspondent living in North Wales, sadly not a Mrs Trellis, for those who know about her). The writer stated that he agreed with almost every single word of my article because - wait for it - he first came across the method in a book entitled 'The Phoney Club' by David Allen published in 1992! (I've not been able to get hold of this book, by the way.)

Worse still, the editor of the magazine added a note about a booklet called - believe it or not - 'The Winning Trick Count' published by a Dr Leslie Ellis in 2001. I've since been in correspondence with Leslie Ellis and he has been kind enough to send me a copy of his very interesting booklet (which he uses for teaching at his club in Tichfield, Hampshire). Sure enough, his method is more or less identical to mine.

The magazine editor (who shall be nameless) also rather caustically mentioned the website of a Norwegian called Hahkon Hallingstad devoted to a bidding scheme he also calls 'The Winning Trick Count'. As it happened, I already knew about this website and had confirmed that his method seemed to bear no relation to my WTC - a fact which the editor should also have checked first, but that's life.

Finally came the biggest blow. Nothing could have prepared me for this ultimate twist in the tale. I already knew that the inventor of LTC was one F Dudley Courtenay (in about 1934) and, indeed, I made reference to him in my article. My correspondent, Leslie Ellis, kindly sent me a photocopy of some pages from a pamphlet called 'The Standardised Code of Contract Bridge' published in 1937 by Courtenay (edited by Col. Walshe, who he?). As soon as I saw these it was quite obvious to me that 'the Courtenay Code' bore a strong resemblance to my beloved WTC! In short, I had had the embarrassing experience of more or less 'reinventing the wheel' - more than 50 years too late! There must be a moral here somewhere. Perhaps it is: never publish or you will be damned!

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