Theory of Information

We must always bear in mind that our bridge bidding is a highly restricted language (just 35 + 3 elements and a restrictive grammar too) and therefore perfection is simply not possible!
At the same time then; the greater should be our concern to get the most out of its limited possibilities! Would you not agree?
When one considers that the possible number of deals is: 53,644,737,765,488,792,839,237,440,000. On the other hand
the total number of possible bidding sequences is also very large, but a large percentage are unusable.

There is a mathematical theory of the information applicable to any system with a continuous field or (as is the case with our bidding language) a system of discrete values ...the legal bids available in any context.... Do not doubt the power of this theory, whether applied to discrete systems like in bridge, human languages, or the electron states of a Hydrogen atom or in non-discrete physical systems such as fluiddynamics, general relativity, electrodynamics etc.
This theory is known as 'Fisher Information'. If one stops to realise that this theory can be used to derive many of the most important mathematical representations of the physical world, such as, fluiddynamics (Stokes), General relativity (Einstein) and even Quantum Mechanics etc - it is indeed a mathematical and a little known unification of physics!
It can most definetely be applied to bridge bidding - a discrete system - too!

What it tells us is that the maximum information that can be passed at any bid depends on the proper use of all available bids and crucially the more economical a bid is to carry a broader scope of information. And put more quantitatively the frequency of usage must decline, quite rapidly according to theory, with with each possible available bid and a recognition that the information in each possible bid will decrease, that is 'become more specific', as more bidding space is consumed. This will not come as a surprise, I'm sure, but what maybe a big surprise is that there is a more rapid decay in the amount of information with each successive bid should convey than you may expect.

I know of no bidding system that comes even close to this. This is not surprising as it would inevitably cause intense artificiality and given that most of our bidding systems have naturalness at their heart the outcome is clear: a battle between naturalness (easier to acquire) and coded (higher precision).
So, the theory would expect that economical bids like PASS, double, redouble or the next available n(1-7) of (

NT should be very general and the more of precious bidding space that is consumed the less information, that is more specific, will be inferred.
This is a clear endorsement of 'doubler' bids, bids that make require further bids to unravel their meaning further - including further 'doubler' bids! It would also suggest that in opening bids such as 'PASS' should have the highest frequency (it most certainly does! c40%) - it also suggests the concept of a forcing opening bid of PASS is sound! Frequencies for 2 and higher level openings are all lower in frequency.

Let's take a closer look at ACOL:
1

should be the most frequent bid - this is far from true in ACOL.
Indeed frequency seems to increase from 1

through to a lordly 1NT! whose frequency has increased with the decades!

Consider precision's 1

opening which comes in at just under 9%. But while precision showed strength & 1

has a slightly greater frequencey than Major openings.

In Beta 1 1

> NT The frequency of opening steadily decreases. Beta denies presence of a 5 card in

and

's frequency is higher than Major openings as it covers a higher CPU range while Major openings are limited by Beta's strongish 2Ma openings. Betas 1

openings are all about the 7.5 to 8% with D's>H's>S's> 1NT at only 6% So we observe a tailing off of probabilities as required AND crucially more in line with Fisher than ACOL!
In Beta 2C's 6%, 2D's (3-way) 5% 2Ma each 2% 2N(21-22) which may contain a 5 card Major: 0.5%
Well in 'beta we do address this failure in ACOL: increasing the frequency of 1

at the expense of 4 card openings in 1

& 1

and particularly a far more constrained 1NT. This is a powerful endorsement of beta ACOL over ACOL.
In conclusion if the principles of information are ever taken to the limit in a bidding system even beta ACOL would be shown up but we would have totally artificial system - harder to master and likely more prone to disaster even fro EXPERTS!

Well I'm not about to go about constructing such a futuristic system right now, although admittedly I have given it some thought! Personally, I still believe in a balance between 'naturalness' & 'artificiality', the former more human and easier on the memory while the latter requiring considerable mental effort and dare I say prone to somewhat more prone to disaster when misunderstandings occur! One option i do commend wholeheartedly is that the next bid is conventional - which is frequently the case in Beta incidentally. Beta has artificial sequences like many systems.

Finally how do the most common systems of today measure up to this theory? Conclusion none is much better than any other! But Beta has made a considerable effort!

What of beta ACOL as compared to ACOL, well I claim a definite improvement! Consider these:

1 in Beta is the most frequent opening.
Secondly, our restrictions on 1NT reduce the frequency of this bid in favour of , & openings
Thirdly, our showing of 2 suits: in responding to T-O Doubles and in protective bidding: carry more information

Also in showing or asking for guards or help in common classical sequences, inverted minors, and trial bids sequences,

Fourthly our somewhat increased frequency of usage in both 2 & especially our 2 openings; the former handling 'near' game going hands & the latter a 3-way 'multi' including not just weak 2 twos - these in turn reducing top-end loading on 2/ openings (now non-forcing and strict 5-4 or better distribution with a 4-5LTC). Instead of ACOL's more frequent and rather wide-ranging weak twos (beta's 2 caters for weak Major 2's just as effectively) and a 2NT more precise opening 21-22HCP instead of ACOL's 20-22 wider range- small but significant! With 2D opening also catering for a balanced 19-20HCP
Fifthly, following our 2 opening, a prolific use of a question/response forcing style as an economic ongoing structural schema for precision bidding in hands where one hand is much stronger than the other in a Q & A style.
Lastly, in defensive bidding: our more general approach to a T-O Double, based only on strength, not too much emphasis on Major suits & also with a very much increased frequency of use and showcasting a powerful Forcing 1NT response to a take-out Double. Also our 1NT overcall, promoted to a far more useful role - all these innovative use of these bids are made to carry more information in an economical manner. They have long deserved a more prominent role.

The above is not an exhaustive list! and Its also arguable that the EBU's straightjackets have and still will resist innovation in an over-protective attitude towards ACOL.

I strongly advocate that beginers in bridge learn a 5 card major bidding system SAYC or even PRECISION which will be a much quicker, easier and more effective entry to competitive bridge. ACOL on the other hand demands far more experience to succeed putting beginners in a very weak position at the table!

Worldwide bridge as seen on BRIDGEBASE for example are largely 5 card major systems and even strong NT. A much more comfortable envirnment for beginners than the local clubs in the UK pushing and protecting ACOL. The lockdown may well have brought this to the attention of many a bridge player in the UK in the last 18 months!