.
(with
apologies to Longfellow)
.
…How good, how useful and when? -I am conscious that it may seem somewhat bizarre - in an account which not only champions the cause of bridge evaluation systems but which also seeks to add to their number- to query their value.
It is apparent that a significant fraction of bridge players do in fact see a need for some means of hand assessment, which will help them and their partners reach their par contract.
To that end most usually begin by considering their hand shape and their simple total of High-CardPoints. Some then go on to make adjustments to this basic count for suit length or quality, while others may undertake an assessment of their Losing Trick Count. And increasingly - and especially in competitive auctions - some will resort to the Law of Total Tricks.
The result is that there is already a substantial body of literature on hand evaluation and new books and articles - often with proposals for improved procedures- appear regularly. Furthermore, the proponents of the various systems are usually in no doubt about their relevance and their respective merits.
The problem which these claims pose, is that they face the average player with the difficulty of knowing how to choose between the various systems and just when to use them. Moreover, when they are taken together, they expose a significant and largely unexplained measure of incompatibility and they raise a fundamental question.
.
Why, if the respective hand-evaluation systems along with their adjustments and corrections are each as good as is claimed, have they failed to gain universal acceptance by the bridge community? And why, too, do new ‘improved’ versions continue to appear?
.
Nor is the situation helped by the way in which (with one or two notable exceptions) such claims tend to be largely unquantified.
In the light of this, my aim in respect of my own claims regarding the merits of the Winning Trick Count is to seek to fill this gap by providing, in the sections, which follow, a detailed consideration of its accuracy and of the possible use of corrections and adjustments to improve its performance.
.__________________________
.
…So how can we evaluate the evaluation procedures? - To even begin to answer the question we need a convincing and qualitative means of assessing and comparing the accuracy of the various systems. The problem, however, is that this quite fundamental and seemingly simple requirement turns out to be surprisingly challenging and difficult to satisfy.
So
much so that it has led me to resort to two quite distinct procedures to
enable me to gauge the accuracy of the respective trick-taking forecasts.
Each has its limitations but, as we shall see, when they are applied jointly
to a sufficiently large number of hands, they provide a convincing and
powerful measure of performance:
.
- The first method, which is simple and familiar to all bridge players, is to examine a board, which has been played and where the result is known; and to then compare the evaluation forecasts with the contract, which was reached, and the number of tricks, which were actually made.
On the other hand even a cursory inspection of the score sheets of most match-pointed events will usually show a range of outcomes on some of the boards. In turn - and insofar as it may then be difficult to assign a correct contract to such deals - it is apparent that this may somewhat limit the scope of this assessment procedure.
In practice, however, it transpired that this did not prove to be an unduly serious constraint and I found that I was able to apply the procedure quite systematically to over three quarters of the 255 boards, which were played in the Semi-Finals and the Finals of the Bermuda Bowl and the Venice Cup of the 1991 World Bridge Championships. This had the advantage that it combined a wide selection of randomly dealt hands with the reasonable presumption that the results reflected a consistently high standard of bidding and play.
The analysis also benefited from the fact that the same deals were used for both competitions which meant that they had all been played at least twice and some as many as eight times. Moreover, the highly competitive bidding meant that a significant fraction of the boards, which were considered, had resulted in both N/S and E/W contracts and hence provided a total of over 260 results for the evaluation exercise.
.
- The second method, which is also simple, is to examine just one of the two pairs of partnership hands of any randomly-dealt deal and to then estimate the number of tricks, which they could expect to make if they played in their best suit fit and if their opponents' cards were concealed.
This assessment,
which for convenience I shall refer to as the Estimated Trick Count
(ETC)of a pair of hands, can then be compared with the respective
forecasts of the evaluation systems for the same pair of hands.
Although this method sometimes involves a measure of judgement it is usually quite easy to apply on most deals and it is well established as a means of bridge-hand assessment.
Thus,
Ron Klinger describes it as the ‘Partnership Playing Strength’ in
his book The Modern Losing Trick Count, and he defines it
aptly as ‘the number of tricks you can expect to win if suits break
normally and half of your finesses work. In other words the number of tricks
that will be won most of the time’
In order to obtain a measure of the validity and the accuracy of the Estimated Trick Count I applied it to the World Bridge Championships boards described above. A more detailed account of this, and the various other evaluation analyses will be provided in the following chapter, but at this stage I will simply note that the outcome was surprisingly reassuring.
In fact, and despite my presumption that such an elementary assessment would at best be a rough approximation of the way in which experts would play such hands, it transpired that on almost every contract where it was possible to make an Estimated Trick forecast this turned out to be within one trick of the number of tricks which were actually made when the hands were played in the World Championship
In addition – and in contrast with the first procedure outlined above which can only be applied to contracts that have been bid and played - the Estimated Trick Count has the singular advantage that it can be used to compare the trick-taking prospects with the evaluation forecasts for bothpairs of hands on any board.
It thus provides a powerful means of assessing and comparing the accuracy of evaluation systems for weak as well as strong hands and hence can be applied to a very much wider range of bidding situations. Because of this broad scope it has been used for a substantial fraction of the evaluation comparisons and analyses, which follow.
And as we
will see later it can also be used very effectively to assess the merits
and the shortcomings of the wide variety of evaluation adjustments and
corrections, which have been proposed.