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:
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!