.
I have so far steered clear
of any consideration of corrections or adjustments to the Winning Trick
Count.
Instead, my aim has been to demonstrate that this unconventional, but very simple, bridge-hand assessment procedure is significantly more accurate than the Losing Trick Count and that it will meet the evaluation needs on a substantial fraction of deals without any modification whatsoever.
In fact, as we have seen above it turns out, that the basic WinningTrick Count regularly provides an accurate forecast of the trick-taking prospects of a wide range of boards. It was within one trick of the right result around nine times out of ten and it predicted the correct outcome for over half of the 610 contracts, which were assessed. A score, which I shall examine in more detail below, but one, which I judge to be excellent by any standards.
Nevertheless, the analysis also shows that the estimates were, in fact, incorrect by one trick on almost half of the contracts and that they were out by two tricks or more on around 10%.
This poses the question: what – if anything – should we do about it?
.
The conventional answer is very simple. It is to recommend a range of carefully defined adjustments to take account of particular features of the quality and distribution of the hands.
And, of course, I similarly see the need to ensure that the Winning Trick Count provides the best possible evaluation on the widest possible range of hands. To that end, the account below of this important factor begins with a consideration both of the merits and of the significant limitations of such correction procedures.
In turn, this leads me to some rather unconventional conclusions about the applicability and the effective scope of the Winning Trick evaluation procedure.
.
9.1THE
MERITS AND LIMITATIONS OF EVALUATION CORRECTION PROCEDURES
.
The perceived need for a range of carefully defined corrections and adjustments to the various conventional bridge-hand evaluation procedures constitutes an important feature of the extensive literature on this subject.
On balance, the various improvements that are recommended usually appear eminently reasonable and they are routinely supported by convincing illustrations of contracts, which clearly demonstrate their successful application.
On other hand, as a more detailed consideration of such Losing Trick and Point Count evaluations will show, there is a rather disconcerting lack of consent among the proponents of such corrections in regard to the scale and the nature of some of the recommended adjustments.
Moreover, it is also the case that these various claims often lack the support of any systematic analysis of their real effectiveness when they are applied to a significant number of typical bridge hands, rather than to just one or two carefully selected examples.
In the light of this inconsistent and somewhat confusing situation I decided to undertake my own appraisal of their effectiveness and I began quite simply by applying two quite conventional corrections to a large fraction of the Losing Trick Count evaluations, which were considered earlier.
In the first test I simply followed the widely accepted and seemingly reasonable recommendation regarding the need to make some allowance for unsupported queens and I added half a loser to the Losing Trick Count for each occurrence of such a Qxx distribution.
Since I had begun with the reasonable assumption that this would result in at least some benefit, the outcome was unexpected. It transpired that there was indeed an improvement in the case of 42 of the estimates, but what was surprising was that another 61 were in fact worse following the adjustment!
For
the second test I followed Rubens’ advice regarding the balance of aces
and queens – If you have more aces than queens, subtract half a loser
for each extra ace; but if you have more queens than aces, add half a loser
for each extra queen.
This result in this case was even more unexpected. 56 of these corrected Losing Trick estimates were better, but 116 were worse!
I believe that it would be unwise to attach too much importance to a single statistical study such as this and it may be that a more rigorous and more extensive analysis would lead to a less disconcerting outcome. Nevertheless, this exercise certainly reinforced my qualms about the use of such structured adjustments and corrections and it strengthened my preference for a much more ad hoc approach to bridge-hand evaluation, as set out below.
That view was further supported by the outcome of a subsequent similar study of the effect of applying similar corrections to the Winning Trick Count itself.
I began by using the Rubens adjustment regarding the balance of aces and queens and I found that the outcome – 59 better, but 103 worse – was just as discouraging as that of the similar Losing Trick analysis above.
I then extended the Winning Trick exercise in line with the way in which the Losing Trick Count assessment is normally undertaken. To that end I corrected all of the forecasts by omitting any singleton kings or doubleton queens from the basic estimation of the honour-card trick total,
Once again, the result – 18 better, but 49 worse – pointed clearly to the merit of seeking to avoid, wherever possible, such structured adjustments or corrections to what is basically a simple and precise evaluation procedure.
.
9.2THE
APPLICABILITY AND EFFECTIVE SCOPE OF THE WINNING TRICK COUNT
.
My
somewhat heretical conclusion above there would be little benefit in seeking
to improve the accuracy of the Winning
Trick forecasts
by following the conventional practice of formulating a series of detailed
corrections was reinforced when I considered the way in which this unusually
simple Winning
Trick procedure
was likely to be used to best effect with the two most important categories
of hands which are likely to present the player with evaluation problems
at the bridge table.
In
the case of the first category – that
significant fraction of boards (around one in four) where one side has
a point count of around 26, or more and
usually an excellent opportunity of bidding and making game - I
believe that the basic Winning
Trick Count can
often contribute by providing them with an accurate pointer to their trick-taking
prospects at a very early stage of the auction.
On
the other hand, for the majority of such deals, the score sheets of duplicate
bridge events show that a large number of players routinely succeed in
reaching the correct contract with the aid of their normal bidding systems
and I see little need for the more refined evaluation procedures involving
the assessment of cover cards and controls, which are sometimes proposed.
Their
success often reflects the use of the broadly accepted presumption that
the basic prospects for a suit contract can
be defined very simply in terms of their partnership point count as follows:
.
-Consider
bidding a game in a major with twenty-six points or more.
-Consider
bidding a game in a minor with twenty-nine points or more
-Consider
bidding a small slam with thirty two points or more
-Consider
bidding a grand slam with thirty five points or more
.
Following
which, they are then usually able to use their normal bidding procedures
and conventions to establish that they have a sufficient measure of control
to prevent the opposition using such high-card strength (typically A’s
and K’s) as they may have to defeat the contract. This is an especially
important factor in the case of the slam and the minor game hands.
In
the case of the second category – that much larger fraction
of boards where the points are more evenly distributed and where the side
which has the balance of strength is much more likely to face competition
from their weaker opponents,- I
believe that the very simple and basic Winning
Trick Count again
has the important advantage that it can routinely provide both sides with
a reasonably accurate indication of their trick-taking prospects at an
early stage of the auction.
Following
which, however, I then judge that the opportunity to then introduce the
kind of correction and adjustments which are a feature of more traditional
evaluation methods, is usually seriously restricted both by the limited
bidding space and by the increasingly contentious nature of such auctions.
This
view is supported too, I believe, by the way in which the Law
of Total Tricks
is increasingly gaining favour as a bidding aid for such deals. This despite
the fact that, in contrast with more conventional hand-evaluation, it simply
provides an indication of the combined trick count.
.
9.3THE
WINNING TRICK COUNT AT THE BRIDGE TABLE
.
My judgement above about the limited value of the kind of structured refinements which are a feature of some bridge-hand evaluation methods does not, of course, reduce the scope for players to seek to improve their forecast on deals where their own experience (or intuition) points clearly to the need to adjust the basic evaluation. My conclusion, however, is that each such case should be assessed on its merits and then corrected in a quite ad hoc way which seeks to reflect the shape and quality of that particular hand and such indications of unusual distributions as may have emerged during the auction.
For
example, in
a competitive bidding situation, a player can usually judge that a holding
of three or four small cards in the opponents’ agreed suit may merit a
positive adjustment, since it means that partner probably has only a singleton,
or a void.
In
the same way, a holding of KJx clearly has much more value when it is held
over a bid in that suit by the opposition, than when it is under such a
bid.
And
there is similarly a range of examples involving unusual distributions
(such as deals with voids or a good fit in two suits) which I believe are
best assessed and then corrected on a case-by-case basis by
the players themselves on the basis of such indications of the shape and
quality of the hands as may have emerged during the auction
In the light of this situation my broad and somewhat unconventional conclusion is that formal hand-evaluation procedures should be kept as simple as possible and that they should be regarded as a complement, rather than as an alternative, to the judgements and experience, which underlie the well-established bidding procedures of Contract Bridge.
To
that end I believe that the Winning Trick Count has two important
advantages over the established hand-assessment methods. The first, that
it simply requires an estimate of the partnership point count and trump
strength in order to provide an unusually accurate guide to the trick-taking
prospects on a large number of deals. The second, that in many competitive
auctions, it is capable of breaking down the Total Trick Count into
the more valuable forecast of the prospects for each side.