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, and do not doubt the power of this theory,  whether applied to discrete systems like in bridge, human languages, 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 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 the broader the information it contains must be. And put more quantitatively the amount of information 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.
So, the theory would expect that economical bids like PASS, double or next bid 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 further bids pass far different information from that would be passed directly - including further 'doubler' bids! It would also suggest that in opening bids such as 'PASS' should have the highest frequency (it most certainly does! >40%).
 Let's take a 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!
Well in 'beta ACOL' we do address this failure in ACOL: increasing the frequency of 1 & 1 at the expense of 4 card openings in 1H, 1S and particularly 1NT.  This is a powerful endorsement of beta ACOL over ACOL.
If the principles of information are taken to the limit in a bidding system even beta ACOL would be shown up!
A futuristic system following the Tof I would open 1
most frequently - may become as wide as for example: 'any balanced hand in a range of 11-15 points, followed by a 1 response with a very wide spectrum too. Well I'm not about to go about constructing such a futuristic system right now, although admittedly I have given it some thought!
I guess, also 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 disaster when misunderstandings occur!
Finally how do the most common systems of today measure up to this theory? Conclusion none is better than any other!

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 over-protection of ACOL.

I strongly advocate that beginers in bridge learn a 5 card major system SAYC which will be a much quicker, easier and more effective entry to competitive bridge.