4 Card Majors v 5 Card Majors?

     

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!

Some important statistics:

The probaility of holding two 4 card suits (excluding all hands with a 5+ card suit)  is 23.75%  20.6% of these, that's 4.89% will be in the 12-14 range where many ACOL players mostly opens1NT, but Beta will not open 1NT  if 4-4 in majors or with a distribution of 4-32 in the majors - eliminating at least (as some hands with xxx in the other minor are not opened 1NT in Beta either) 1/3 of these 4-4-3-2 hands from a 1NT opening.
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!

Now let's examine the 'fit'  probability of  5 versus 4 card openings

Let's take 5 card major openings first :
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:
Probability of a  fit with 3-suited hands are very good;
Probability of a double fit is also fair:
 
Conclusions:
  1. 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%
  2. The probability of holding just a 4 card major is 34% and probability of finding a fit (4-4) is 33%.
  3. Of course in 4 card major systems 5 card major are opened equally easily (and the 5-3 fit found admittedly usually on rebids).
  4. In 5 card majors holding a 4 card major will find the fit, if it exists, on opener's rebid.
Deeper analysis:
Semi  4 card systems, such as Beta, while harder to master than 5 card systems, once mastered advantage is clear in terms of distributional exactness and  in conveyance of information

Some Beta & ACOL differences:
  Nevertheless, Beta & classic ACOL, despite their differences, are both firm adherents to 4 card suit openings in hands lacking a 5 card suit. Beta NEVER opens a short minor!