What is equally significant, however, is that this same procedure also allows us to use our own Winning Trick Count estimate as the basis for an assessment of our opponents’ trick-taking prospects in any competitive auction where we are able to judge the quality of their prospective trump holding.

This quite unique extension of the boundaries of conventional hand evaluation simply reflects the fact that the Winning Trick Countof the opposition is similarly the sum of their trump holding minus six, and their holding of honour cards – which you can also estimate as shown below:

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-The Honour-Card Linkage. There are always twelve prospective Honour Card Tricks (the sum of the A’s; K’s, and Q’s) in the two pairs of hands on every deal.

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It follows that on those deals where you have a measure of your own honour-card holding you simply need to subtract this estimate from twelve to assess your opponent’s strength

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Following which you simply need to add your estimate of their honour-card holding to your estimate of their trump holding minus six and you know how many tricks they are likely to make!

And similarly, of course, you can use such information, as their bidding will regularly provide on their strength and distribution to assist you with your own Winning Trick Count estimation.

We will come back to this singularly important feature of the linkages between the two pairs of hands but first let us see how they go on to provide us with a rather unexpected bond with the Law of Total Tricks and an even easier means of estimating the opposition prospects.

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3.1 THE WINNING TRICK COUNT- AND THE TOTAL TRICK COUNT

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Jean-René Vernes' Law of Total Tricks – one of the most recent arrivals on the evaluation scene - is achieving widespread acceptance as an effective and low-risk assessment strategy. It states that: 

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‘The number of total tricks in a hand is approximately equal to the number of trumps held by both sides, each in its respective suit’.

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A recent commentary in BRIDGE WORLD notes that: ‘ The Law of Total Tricks is currently the most widely used guideline in competitive bidding … recentresearch, spurred by the availability of cheap computing power, has shown that the Law is remarkably accurate’.

However, while it is increasingly evident that this remarkably simple estimate of the overall trick-taking prospects provides an effective and low-risk bidding strategy for competitive auctions, its weakness is that it tells us nothing at all about how the total will be divided. In addition the proponents of the ‘LAW’offer no plausible explanation for this seemingly improbable link between the total number of tricks and the total number of trumps.

In contrast, we find that we can obtain an insight into both of these questions by just adding together the Winning Trick estimates for both sides each in its respective suit.

The resulting Winning Trick Total Count on any deal is made up of:

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-The sum of the trump holdings minus six for each side - but this is simply the sum of their combined trump holdings minus twelve.

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Plus

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-The sum of the honour-card holdings for each side - but as we saw above this must always be twelve

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And when we add these together we see that:

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-The sum of the two Winning Trick estimates - the total number of tricks, which would be available if each side were to play in their best contract – is simply the sum of their combined trump holdings.

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The result – the Winning Trick Total Count - is precisely the same as the Law of Total Tricks!

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From which it follows that it must similarly share the same remarkable accuracy but with the important distinction that it also provides us with an even easier means of assessing our opponents’ prospects on those competitive auctions where we can make such an estimate of the total number of trumps. In which case:

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-We simply need to subtract our Winning Trick Count from our estimate of the total number of trumps to obtain the Winning Trick Count for the opposition!

3.2THE WINNING TRICK COUNT- AND THE SUIT-LENGTH LINKAGE

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In the account above we have seen how the simple and quite inevitable linkage between your honour-card or point strength and that of the oppositionallows you to estimate their Winning Trick Count in any competitive auction where you are also able to judge the quality of their prospective trump fit.

What is especially fortunate, moreover, is that, even on those deals where we seemingly have an indication of the strength of only one of the two trump holdings, we can often exploit the correlations between the card distributions in the two pairs of hands to make an estimate of the total trump count.

While the somewhat belated recognition that these linkages are quite well defined has made no significant impact in respect of conventional bridge-hand evaluation procedures, it has proved to be particularly instrumental in extending the scope and accuracy of Vernes’ Law of Total Tricks.

This emerges very clearly, for example, in Dick Payne and Joe Amesbury’s book TNT and COMPETITIVE BIDDING, where they question Vernes’ own conclusion that: ‘it is very difficult in practice to determine the total number of trumps'- and go on to show how their concept of ‘total distribution’ can be used to assist such estimations.

They note that bridge players are primarily concerned with the patterns of single hands – ‘these are after all the ‘raw material of the uncontested auction’. But they go on to stress that, when it comes to competitive bidding, it is: ‘the total pattern of twenty-six cards that you and your partner hold’ which is of vital importance.

They illustrate the value of this approach to the estimation of the total-trick count (or, as they designate it, the TNT - the total number of tricks) with a helpful listing of the most common hand patterns.

In the first instance their table provides useful guidance on the likelihood that you and your partner will have a worthwhile suit fit. But, more importantly, it then goes on to demonstrate the extent to which your partnership trump holding will also be very strongly linked to that of your opponents on a wide range of deals. And Larry Cohen provides a somewhat analogous chart of such correlations in his book Following the LAW. 

Some of the more important linkages, which result from these and related considerations of hand distribution, are listed below:

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Although these correlations between the suit lengths in the two pairs of hands are not as precise as the honour-card linkage described above, they are robust and they are especially useful on those competitive deals where it becomes clear from the bidding that one of the two pairs has a good suit fit since, as the table shows:

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- The better the trump fit of one side, the more assured their opponents can be that they too will have a good fit in one of the other suits.

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They clearly help to explain the increasing acceptance of the Law of Total Tricks as an effective and low-risk assessment strategy.

What is more important, however, in this consideration of the Winning Trick Count is that they enable us to make an estimate of the total number of trumps on a wide range of deals. Following which, as we saw in the previous section:

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- We simply need to subtract our Winning Trick Count from our estimate of the total number of trumps to obtain the Winning Trick Count for the opposition!