In the fanciful world of assessing the trick taking potential of a hand in contract bridge, we refer mainly to the highest cards, that is to the so-called “honors”, Ace, King, Queen and Jack, and sometimes we try to take in account even the highest spot cards such as 10, 9 and 8.
Quick Tricks
This term indicates the so-called “fast taking” tricks and dates back to the era  of Ely Culbertson. They represent the tricks cashable in the first two rounds of a suit, according to the table below.
2 quick trick = AK in the same suit
1.5 quick trick = AQ in the same suit
1 quick trick = A, or KQ in the same suit
0.5 quick trick = K protected
Quick Tricks (QT) have more or less the same validity both in attack and in defense, at suit contracts or at no-trump.
Quacks
That sounds like something derogatory and in fact Quack is a portmanteau, a contraction between Queen and Jack and indicates the “lower” honors. They gain “slower” tricks than Aces and Kings, are honors good to support the higher ones, valid more in no-trump contracts than at suit, are stoppers more than controls. A hand whose point count is made up mainly by Quacks, rather than by Quick Tricks, in general it is a hand worth less than the total point count indicates.
Quocks
By assonance or analogy, I christened Quock those combinations of honors that contain a top-spot, like ten, nine eight. A term, after all, quite easy to remember.
Actually, to make things simpler and more practical we will deal only with the combinations that contain a ten, certainly the most important ones from the point of view of the consequences that may have on the probability of taking tricks.
The 10 in theoretical assessments
The vast majority of players values their hands on a point count scale universally known as Milton Work, that is  Aces, Kings, Queens and Jacks as 4, 3, 2 and 1 honor points respectively (HCP).
What about the ten? It has always been, and it is still today, the focus of long discussions, debates and statistical research, in an attempt to give it some value that took into account his unquestionable potential of contributing to trick taking strength of the highest honors.
From time to time, doubt about a quantitative value to be attributed to it continue to arise in the arguments of the valuation theorists, armed with increasingly powerful computers and sophisticated simulation programs.
So we may range from the half point of the first draft of the Milton Work scale (true, but suppressed quickly), to the fractional values of Kaplan&Rubens, from the 0.25 point of Alex Martelli, to the full point of the Banzai scale.
In addition there are rather arbitrary alchemies proposed by bridge authorities that assign a value to the number of aces and ten (Pavliceck) or  compare their sum to the number of quacks (Bergen).
But are all this calculations worth the effort?
The 10 in computer simulations
If we suppose to ignore all the limits of a double-dummy analysis, the value measured in computer simulations for a ten is one sixth of a trick (about half a point), 2 ten represent one third of trick (1 PO), 3 ten 1,5 PO and 4 ten 2PO.
On the other hand, in theoretical scales that also take into account the 10, its value is about a quarter of a point (0.25), which means only 1 PO for the presence of all four ten. A conservative value compared to computer results?
But there is another truth out there.
Quocks are not all equal
In fact, the simulations take into account the number of ten and calculate an average value, regardless of their actual location respect to the other honors.
For example, you might have this figure in a suit: Kxx-10xx or this one K10x-xxx. In the first case the presence of the ten is absolutely irrelevant, in the second case the probability of producing a trick  with the King increases by almost 25% .
To get a more accurate idea of what a ten is actually worth, we need to distinguish different types of Quocks, based on their combination with one or more major honors.
Type 0 Quocks: when the ten is with no higher honor.
Type 1 Quocks: combinations of a ten and one higher honor.
Type 2 Quocks: combinations of a ten and two higher honors.
Type 3 Quocks: combinations of a ten with 3 higher honors, but generally the value of the 10 may be confused with the values of length.
A practical method for realistic results
To calculate a theoretical value ”a priori” for the major honors is already complicated in itself  and would be exceedingly complex and also, after all, useless for what concerns the ten. We can, however, more easily take into account the difference in probable tricks obtained “a posteriori” in combinations of honors with and without a ten. In simple terms we analyze a suit consisting of 3 cards against 3 cards, with all possible combinations of honors, assuming to have the entries and communication cards necessary to maneuver the suit correctly, and excluding the possibility of an immediate ruff.
I’ll save you tedious and impractical tables and report some considerations on the results, with the assumption that a trick is worth approximately 3 Milton Work points.
Type 0 Quocks
The difference in tricks is only significant in combinations such as:
10xx-KJx  + 0.28 tricks
10xx-QJx  + 0.24 tricks
About a quarter of a trick, but in this two cases the MW value is higher than the actual value and already taken into account.
Therefore, in the case of a Quock of type 0 there is no variation to be made or, in other words, you should ignore ten without an higher honor in the same suit.
Type 1 Quocks
Only in combinations such as:
J10x-AQx   + 0.45 tricks
Q10x-AJx   + 0.45 tricks
A10x-QJx  + 0.45 tricks
The increase is almost half a trick and the MW point count underestimates the value for -0,17 trick, equal to about half a PO, value that should be added to the total point count, but “a priori” you can not be sure of the presence of the necessary honor fit and after all are only 3 combinations out of 28.
Note, in all three combinations, the absence of a King.
Then also holding a ten with one tiger honor, you should add no additional point.
Type 2 Quocks
The error is approximately half a point for the following combinations:
QJ10-AXX
KJ10-xxx
AJ10-xxx
AJ10-Qxx
AQ10-Jxx
which are, therefore, slightly underestimated (-0.17 tricks). But they are only 5 combinations out of 24 possible type 2 Quocks, while all the others are widely covered by the Milton Work point count, provided that one trick is worth about 3 HCP. In addition, if we happen to have 4 type 2 Quocks of those listed above, assuming that there are all the conditions required by our hypotheses to move the suits correctly, the increment to add would be only 0.68 tricks, equal to 2 Milton Work points.
The true value of a ten
A quarter of a point, half a point, a full point? Or even two?
How much is a 10 ultimately worth?
The most interesting thing that emerges from our analysis is that a hand without 10, or with type 0 Quocks, is generally overrated by the Milton Work point count. A hand with Type 1 Quocks should be revalued but only in very few cases and at most half a point for Quock and the same is true for the presence of Type 2 Quocks.
On the other hand, it should not be forgotten that the combinations analyzed are valid “a posteriori” and warn us about a possible”a priori” evaluation.
That is, having an AJ10 in a suit, we should add half a point only if we find in front of 3 spot cards or a protected Queen, but not if we find the King. And having KJ10 we should reevaluate the hand only in the hope of finding 3 spot cards from the partner and not the Queen or the Ace.
A rather difficult and imprecise assessment to make “a priori”.
One last consideration. The cases in which the presence of a ten shows a significant contribution in increasing the probability of trick taking of the higher honors it supports are very few compared to all possible combinations of Quocks (15 quock-0, 28 quock-1, 24 quock-2). A total of 67 combinations, of which only 8 are significant, with their limits, and would each entail the addition of at most half a point.
The conclusion, and it’s my advice, is quite simple, although not quite intuitive:
do not count the ten and devalue the hand that is without them (if you want, about 1 point).
The astonishing power of the ten
Now enough with the theory. I’m going to offer you an interesting hand.
Est, all non-vulnerable MP, you hold:
T82 QT8 AT86 QT6.
West, dealer, opens 1 NT (15-17 HCP), Nord pass.
To invite game (8-9 HCP), you can use Stayman  or 2 NT.  If you decide to invite, your partner, who have a minimum, will pass.
This deal came out tome in a simultaneous tournament (I played it in Est):
Q765
973
94
AK32
AK9   T82
KJ64 QT8
KJ73 AT86
74    QT6
J43
A52
Q52
J985
As you can see, 9 tricks are cold. Of course, if Nord leads a small club, you’re gonna be a bit in trouble, but your only chance is to find clubs 4-4 with AK on side and you should put up the Queen.
Do you regret not having called the game directly? Should you have upgrade your point count, thanks to those magnificent 4 ten?
I must confess I tried to invite and my partner passed. The doubt has tormented me throughout the evening.
Out of scruple I have changed a little bit the hand of Est taking away one or more ten and assigning them to the opponents.
Here is one of those hands (the others are quite equivalent).
Q765
T93
T9
AK52
AK9  832
KJ64  Q82
KJ73  A864
74     Q63
JT4
A75
Q52
JT98
East no longer has even a ten, which have gone to strengthen the South Jacks and the North 9s. Well the result I would say that it is just astonishing:  3 NT are still unbeatable.
Bridge, after all, is an amazing funny game. Love it.
Keep bridge alive…and us.

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