A long running argument? Well let's attempt to put some clarity on it!

In this analysis we are taking into account only distributions NOT containing a 7+ card suit.

The probability of holding one or more 4+ card suits is 100% and for this to be a major: 56.94% whereas one or more 5+ card major is just 18.31%. This simplistic truism points the way: playing 4 card suits as biddable means being able to bid Naturaly, while insisting on 5 card means inevitable need of Artificialy!

There is a theoretical 3 times greater chance of opening a major playing 4+ card openings compared with 5+ card systems. A fundamental argument in favour of 4 card methods such as ACOL. This and the argument of Naturalness win me to the cause of 4 card Majors.

However the theory of information tells us that holding a 4 card Major and a 4 card minor - The minor should be opened! and so we do! In beta the opening of 1S will be 5 card >98% of the time

In 'Beta ACOL' the structural rules are significantly different to ACOL but it is still a natural 4 card based system - even more natural! Also beta has paid more lipservice to Tof I than ACOL does!

Standard Americain, known as SAYC is the prime example of 5 card systems - so popular it is easily the most played system in the world. In a way one of the conclusions of this analysis favours 5 card systems such as SAYC for its more systemic nature and its lower degree of complexity which has allowed it to assume its 'most adopted' position in the bridge world. Its opening bid frequencies are more aligned to the Tof I far more than ACOL is!

This gives Beta's frequency for a 1NT at least 1.6% less than in ACOL. Even more when singletons and some 5 card Majors creep in!

Probability of a specific 5-3 fit is 30.58% & 5-2 is 29.19% & 5-1 an unhealthy 33.75% & 5-3 or better is a great: 45%! The outlook for a fit is really excellent!

Probability of a specific 4-4 fit is 22%, 4-4+ fit is 34%, 4-3 fit is the most probable at 31% & 4-2 an unfortunate 24%.

As is to be expected a 5 card opening has a greater chance of finding an immediate fit.

With 6 card opening: probability of 6-2 fit is: 33.36% & 6-3 a healthy 27.8% & 6-4 12% - so nice to have a 6 card suit!

Lets look at probability of a fit holding hands with only a 4 card suit: 4333, 4432 & 4441. The probabilities are: 33.66, 60.31 & 80.3% respectively.

Two other important fit probabilities for some fairly common distributions:

- 5422: 74.2%
- 5431: 80.7%

- 4441: 80.3%
- 5440: 88.3%

- 4441: 20.3%
- 5440: 32%

Conclusions:

- The probability of holding a 5+ card major is a good 35% and probability of finding a fit (5-3 or 6-2) is 45%
- The probability of holding just a 4 card major is 34% and probability of finding a fit (4-4) is 33%.
- Of course in 4 card major systems 5 card major are opened equally easily (and the 5-3 fit found admittedly usually on rebids).
- In 5 card majors holding a 4 card major will find the fit, if it exists, on opener's rebid.

- For
these reasons 4 card major systems do not have any big disadvantage in
finding their 5-3 fit - just not IMMEDIATELY detected.

- However
the advantage argument does not end here. The effect on other openings
is also to be considered and we note that in 4 card systems like ACOL
or Beta, false 3 card openings are not found while in 5 card systems
they are frequently forced. So where natural systems are able to
show suits possessed at each of their first bids 5 card major systems
do not have this ability in any certitude. Advantage 4 card systems.
This advantage must not be underrated. Beta whose style resembles more
that of 5 card than 4 card systems ALSO benefits from this argument.

- Finally finding a 4-4 fit may be slightly more important than finding a 5-3 in the same hand as often the fomer can produce an all important additional trick at least at 2, 3 & 4 levels - 4 card systems will more easily locate a 4-4 fit
- But
4 card Major openings do not have all the advantages by any means! Five
card systems are
more systemic and easier to learn and less prone to variation in
interpretation - they are certainly the system beginners should try to
learn the game: NOT ACOL nor Beta for that matter. However Beta is an
attempt to have the best of both worlds with predominately 5 card major
openings with 4 card Spade openings quite rare and 4 card heat openings
around 15%.

Some Beta & ACOL differences:

- Beta has advantages on ACOL on distributional exactness in distinquishing 5 & 6 card holdings in a suit.
- 5-4 distributions are accurately discoverd in Beta where ACOL cannot always distinguish 5-4 from 4-4! , even 6-4! Acol may be even unable to show a second suit with clarity!
- 15+
NT declarations with only a 2 point variance (2N=21-22;
2D-2X-2N=19-20;1X-1Y-2N=17-18; 1X-1Y-1NT-2C-2N 15HCP & -3C 16HCP.

- Beta
has systemic facilities for 4441 3-suited hands - thereby removing the
ambiguity their presence can inflict on regular sequences: 1N can be
opened with a major singleton. With both Majors: 4-4 1H is always
opened.; with a minor singleton Beta opens in the other minor with
44{41}.

- So Beta has a clear advantage on clarity of distribution. Admittedly there is a small potential cost of getting to high!: A 2¦3-level rebid without jump may be <15HCP - but it is non-forcing. responder by passing, reverting to openers suit or rebidding his own 6+ card suit closes bidding from responder's viewpoint. 2NT conventionally denies both support for either suit leaving partner to decide! Finally bidding the UNBID minor or fourth suit is forcing, 3N is to play.