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THE WINNING TRICK COUNT AT THE BRIDGE TABLE

There have been some significant developments following Maurice Harrison-Gray’s enthusiastic endorsement of the Losing Trick Count around 1959 when he noted:

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‘Experts sometimes claim that they bid on inspection, but the less gifted of our clan prefer some form of ready reckoner. Judging from my correspondence, the Losing Trick Count alleviates many of their former headaches’.

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These include a number of detailed proposals for corrections and adjustments both to the Losing Trick Countitself and to the various High Card Point Count assessment procedures, which are also widely used, while the more recent Law of Total Tricks has provided a powerful additional guideline to the trick-taking prospects in competitive bidding situations.

Despite this, the evaluation challenge really hasn’t changed very much. The problem, which we continue to face on most boards, is that our aim of reaching our par contract is dependant solely on the view that we take about the value of the cards that we can see in our own hand, along with such limited – and often imprecise - information as may emerge during the auction. The situation is not helped by the fact that we need to form a judgement without undue hesitation.

It seems clear, however that many players - regardless of which evaluation method they may eventually use - usually begin by attempting to make an estimate of their partnership strength (as measured by their combined point count) and by seeking to establish if they have a prospective trump fit.

But, as we have already seen, for a large number of deals, this is precisely the information which the two point-count versions of the Winning Trick Count described above in Chapters 4 & 5 require in order to provide an accurate forecast of their partnership trick-taking prospects at an early stage of the auction.

Moreover, I judge that both evaluation procedures are so easy to use at the bridge table that such players are more likely to be convinced of their merits by simply testing them themselves with some typical hands rather than by a more extensive consideration of selected deals.

In addition, however, as we can see in the two examples below, the Winning Trick Count can be used just as effectively by those players who are more accustomed to make their evaluation of their partnership prospects by considering the hands separately rather than jointly.

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Board 1 - 

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North dealer – N/S vulnerable.

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	NORTH S 9 H KQ843 D Q72 C 1065
WEST S K632 H 652 D 943 C J74		EAST S AQ1084 H 9 D J105 C KQ98
	SOUTH S J75 H AJ107 D AK86 C A32

When I considered this deal, earlier, in Chapter 4, I noted that N/S with 24 points and a nine-card heart suit had an excellent prospect of making game, while E/W who have a similar nine-card spade fit but only 16 points, would probably only succeed in making eight tricks.

I went on to point out that both the honour-card and the point-count versions of the Winning Trick Count provide the correct evaluation for each pair of hands:

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-N/S 10 tricks - Made up seven honour cards (3A's; 2K's, and 2Q's) - or seven point-count tricks (24 points) - plus three trump tricks (a nine-card suit minus six).

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-E/W 8 tricks – Made up of the remaining five honour cards – or five point-count tricks (16 points) - plus three trump tricks (a nine-card suit minus six).

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However, if we now consider the deal from the very much more restricted viewpoint of the E/W players at the bridge table who do not have the luxury of such an overview of the full deal, we see that East is likely to open the auction with a perfectly reasonable one spade bid.

Following which, West is immediately able to use the consideration of the honour-card and the trump-fit linkages described above to provide him with a Winning Trick Count insight into the overall trick-taking prospects for both sides.

One moreover, which - despite his quite uninspiring flat hand with its meagre 4 points – already allows him to begin to formulate a very positive strategy for the impending auction.

If he begins by estimating his partner’s strength - using, for example, the honour-card version of the Winning Trick Count - and he assumes that he has a made a normal opening bid of perhaps 12-13 points, he can judge that this will correspond to a holding of around four honour-card tricks

In addition, if - like many partnerships - they are playing a five card-major system he knows that his partner has at least five spades[1].

In which case he can go on to judge that his partner will probably have a Winning Trick Count in spades of at least six - made up of his four honour-card tricks and two trump tricks (five trumps minus three).

Thus - and notwithstanding his own very modest estimate of only two Winning Tricks(made up of his sole honour card and his fourth trump) - West already knows that his partnership has aWTC expectation of making at least eight tricks.

While this points to the prospect of a reasonably safe two-spade contract, he can also see that a game in spades is only likely to succeed if his partner has an unusually strong opening hand.

Furthermore, in the light of the hand-strength and suit-length linkages described earlier, West can already see that if his partner does, in fact, have a normal opening it follows that N/S will almost certainly contend the auction.

Clearly, they must have the seven or so outstanding honour cards. Moreover, as we have seen above, a simple consideration of the probable card distribution for both pairs of hands shows that they must also have a prospective trump fit of at least eight - and very probably more - in one of the other suits.

Since this assures them a Winning Trick Count of at least nine tricks (made up of seven honour-card and two trump tricks), and quite possibly ten or more, West can go on to judge that he should be prepared to contend up to 3 spades – either as a worthwhile sacrifice; or perhaps even making if partner has a good opening.

Moreover - and still before South has even made a bid! - West can already envisage the prospect of a making an E/W sacrifice in four spades in the event that N/S should identify a heart fit and bid confidently to game. In which case, his overall Winning Trick Count evaluation correctly indicates that the resulting score of two, or possibly even three, down doubled would have a high probability of providing a good result.

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Board 2 – 

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In some auctions – for example, those with an opening pre-emptive bid, which offer the prospect of a large total trump count – we find that we can often apply the evaluation linkages described earlier with even more assurance.

Thus, on the deal below, where it seems likely that North may be given the opportunity to make a pre-emptive 3H opening, we see that the TotalTrick Count – the sum of the combined trump holdings - is twenty (10H for N/S and 10S for E/W). 

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South dealer – E/W vulnerable.

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	NORTH S 106 H AQ109652 D 32 C J4
WEST S K97543 H K D 85 C K1065		EAST S AJ82 H 73 D AKJ C Q873
	SOUTH S Q H J84 D Q109764 C A92

We also see that that both the honour-card and the point-count versions of the Winning Trick Count correctly break this total down to the number of tricks which each side is likely to make if they were allowed to play the contract[2]:

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-N/S 9 tricks in hearts - Made up of five honour cards (2A’s, and 3Q’s)- or five point-count tricks (16 points) - plus four trump tricks (a ten-card suit minus six).

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-E/W 11 tricks in spades - Made up of the remaining seven honour cards (2A’s; 4K’s, and 1Q) – or seven point-count tricks (24 points) - plus four trump tricks (also a ten-card suit minus six).

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However, if we now consider the deal from South’s much more restricted viewpoint at the bridge table, we see that as soon as his partner makes his non-vulnerable pre-emptive opening bid he can already envisage a partnership Winning Trick Count of at least nine tricks in hearts.

Thus, in addition to his own three honour-card tricks (1A and 2Q’s) and his valuable three-card trump support, he can reasonably assume that North’s pre-empt, probably made up of at least a seven card suit (and hence at least four prospective trump tricks) and perhaps two honour cards should also provide six tricks.

Moreover, South should also be aware that his opponents who have the remaining seven honour cards also have a high probability of at least a nine-card suit and that if – as seems probable - this is in spades they are likely to be able to make a vulnerable game.

In which case, and again even before East has bid, South can see that a sacrificial bid of 5 hearts over 4 spades will almost certainly be worthwhile.

Sadly, however, when this board was played in the Semi-Finals of the 1991 World Championships and North did in fact make such a pre-emptive bid at one table, South then failed to match this Winning Trick Count insight into the partnership prospects.

The bidding went as follows: After passes by South and West, North opened with a pre-emptive bid of 3 hearts; East then doubled; South raised to 4 hearts but did not compete again over 4 spades from West. In consequence E/W were allowed to make the winning score of a vulnerable game in spades.