To what extent to inform ?

PAD

At any moment of the auction partner makes provisions for many allowable (more or less deviating from the model) holdings you can have. Thus, he knows that assuming an average (model) hand he makes an error – the greater, the more your hand deviates from the model.

A rough estimate of this uncertainty may be expressed by an average error.

The greater the value of this error, the greater uncertainty.

A simplified version of calculating this average error has been given by me in Pikier #1, in Distributional Uniformity Principle. he problem is how to calculate the average error. The issue is complex, and I will have to return to it later. Anyway, it seems necessary to treat the hand as a point in a four–dimensional space (each suit is equivalent to one dimension), and introduce a metric, taking into account both length and honors (plus priority of the major suits). However, intuitive „feeling” of the average error is fully satisfactory for our present needs.

The average error is, in fact, equivalent to AVERAGE DEVIATION from the model. The higher this deviation, the larger the dispersion of possible hands around the average. Therefore, from now on, we will replace (for simplicity but without considerable damage) „average error” with DISPERSION.

It is obvious that the general purpose of transmitting information is to minimize dispersion (which is a measure of lack of information). At the same time it is clear that dispersion cannot be totally eliminated (eg because of SAD), which leads us to the following problem:

What level of dispersion may be considered (in a given situation) adequately low, and how is partner to signal his desires in this respect ?

Look at a generally true formula: loss = (strength) x (dispersion)

Therefore, to minimize the loss (in points) it is necessary to minimize dispersion, and – the more so, the greater the strength. Hence:

PAD Precision Adjustment Directive
The more intensive the information exchange – the greater the strength or dispersion	with the word „or” not excluding „and” (obvious).

How can you recognize that partner is seeking wider information exchange ?

There are three symptoms, named: Firstly, Secondly, Thirdly...

FIRSTLY

Partner tries to keep the bidding as low as possible.

Thus:

PAD-1

The lower the bid – the greater the strength or dispersion

and, in a more practical formulation:

PAD-1a

The more your hand differs from the model – – the lower should the bidding be kept

The objection that this simplifies matters for opponents can be counterattacked with a statement that: The more they bid – the greater the knowledge obtained and therefore the lower the dispersion. Thus, sometimes (especially with strong hands) it might be profitable to allow opponents to bid (and to listen what they bid!).

SECONDLY

Partner selects bids after which the chance of your pass

(ie stopping exchange of information) is smaller.

Let's consider, from that viewpoint, three types of bids:

new suit no trump old suit

where:

new suit = a suit not bid by the partnership old suit = a suit already bid by the partnership

Note that „old suit” is the most likely bid to become a final contract (and to stop exchange of information), and „no trump” is more likely to end the bidding than „new suit”.

Thus, the second general subdirective:

PAD-2

The newer the suit – the greater the strength

which may be divided into the following statements:

PAD-2a	New suit is a positive suggestion (strongness)
PAD -2b	Old suit is a negative suggestion (weakness)
PAD -2c	No Trump is a neutral suggestion

This explains why in natural systems new suit is usually forcing.

Until now, I have been justifying Subdirectives #2 stating that „new suit” carries more information (ie signals less probable event) than „no trump” which, in turn, carries more information than „old suit”. Intuitively, this explanation seems to hold but I am unable to give a complete reasoning (maybe because I don't know how to measure deviations).

To illustrate PAD – the same exemplary situation:

W	E
1¨	1♠

?

The strength of bids from the viewpoint of:					HT = Honor Tricks Therefore, the final ( SAD & PAD ) sequence of bids according to their strength is: 1NT 2¨ 2§ 2♠ 2© 2NT and – as you see – is just the same as commonly used !
		SAD	PAD	SAD + PAD
1NT	=	3.5 HT		3.5
2§	=	3.9	+ 0.4	4.3
2¨	=	4.3	– 0.4	3.9
2©	=	4.7	+ 0.4	5.1
2♠	=	5.1	– 0.4	4.7
2NT	=	5.5 HT		5.5

THIRDLY

Partner uses special ways of bidding, favoring the exchange of information

( forcing bids, cue-bids, conventions, gadgets), or stresses his strength

Now, as we know how partner expresses his desire to exchange more information, we have to think of how we will meet his wish.

Partner is signaling that, from his point of view, dispersion is still too great !

Thus, it should be reduced, ie:

PAD-3

The more partner stresses his need to exchange information, or his overall strength – – the smaller Positive Deviations are allowed to be considered nonzero deviations

Thus, we move gradually from typical standard PoDs in the initial phase of the auction to showing smaller and smaller PoDs, going down into such details as confirming the king in a suit in which the model value has been a queen.

Precision Adjustment Directive ( PAD ), together with its SubDirectives, controls this process.

Here I end the first part of NASA and invite the reader not to waste time

All that was said (as it stands now) is already fully applicable !

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