Math3

4 Card Majors v 5 Card Majors?

A long running argument? Well let's attempt to put some clarity on it!
Our conclusion is that there is not much in 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 very high and for this to be a major: 28.47% 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 possible Artificialy! in minor openings. Five card majors spells some lack of definition in minor openings. In Beta this is more than halved with the introduction of 5 card 1

openings.

Therfore there is a theoretical 1.6 times greater chance of opening a major playing 4+ card openings compared with 5+ card systems. A fundamental argument used in favour of 4 card methods such as ACOL. This and the argument of Naturalness win me to the cause of 4 card Majors. In Beta 3rd hand & 4th hand openings may be 4 card!

However theory of Information suggests that 1C should bear a higher frequency and this consideration steers Beta away from 4 card majors even 4 cards Diamonds! In Beta 1C and 1N (the latter much lower in frequency) handle hands NOT containing 5+ card suits.

The Tof I suggests that beta should consider increasing the frequency of 1D opening beyond its current specification. (these considerations are complex and not included at present).

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 100% of the time in 1st and 2nd positions. Even simple Major simple o'calls are likely to be 5 card...however Beta encourages quality 4 card Major, especially spade, overcalls.

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' see Math 1, than ACOL does!

Standard Americain, known as SAYC is the prime example of 5 card Major 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! Its also easier to learn - a far more sensible system for those learning bridge. Their initial sucess and earlier gained confidence would reduce losses in new players we see in the ACOL world!

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 even with a distribution of 4-3 in the majors - eliminating at least (as hands with xxx in a minor are not opened 1NT in Beta either).
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 creeping into the ACOL 1NT opening! Beta 1NT are always balanced - no 5 card suit (except clubs) and never singletons or voids.

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 a far less: 22%, With a 4-4+hand a fit is more likely at: 34%, 4-3 fit is the most probable for a particular 4 card suit 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. This is great news for Beta's Break-out bids!!
Two other important fit probabilities for some fairly common 2 suited distributions:

5422: 74.2%
5431: 80.7%

Probability of a fit with 3-suited hands are even better:;

4441: 80.3%
5440: 88.3%

Probability of a double fit is also fair:

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 high too: 45%
The probability of holding just a 4 card major is 34% and probability of finding a fit (4-4) is only 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 major systems holding a 4 card major will also find the fit, if it exists, usually in the 2nd round of bidding. Note in Beta our 1C opening denying a 5 card Major will always locate a 5-3 or 6-2 or 4-4 by the 2-level by design!

Deeper analysis:

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, false 3 card openings are not so frequent due to weak 1NT; while in 5 card systems they are frequently forced and augmented by the stronger 1NT opening.. Beta avoids this dilemma. 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 apparent style resembles more that of 5 card than 4 card systems ALSO benefits from its strong formal usage of its 1 opening in discovering 4-4 fits indeed also 5-3 and even 6-2 fits by the 2-level! 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 like ACOL with its 4 card openings or BETA with its 1 opening will even more easily locate any 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 with - NOT ACOL nor Beta for that matter -. However Beta is an attempt to have the best of both worlds with predominately 5 card openings (with 4 card Spade openings quite rare - 3rd hand openings - and betas use o f 1H opening for precisely 4-4 in majors otherwise strictly 5+ card Hearts AND its detailed 1 opening & sequences).

Some other Beta & ACOL differences:

Beta has provided specific sequences to anoounce 5-5 or better hands by the 3 level either from the opening bid or a direct overcall! This means also that all other sequences do NOT concern themselves with 5-5 or better distributions! The then will not have ambiguity between 6-4 and 5-5 for example!
Beta has advantages on ACOL on distributional exactness in distinquishing e.g distinquishing 5 & 6 card holdings in a suit. When Acol rebids a Major one cannot distinquish 5 &6 card holdings with any certainty. In Beta rebidding shows 6 cards always!
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 due to lacking reversing values!
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(12-16)-2C(inquiry)-2N (14)15HCP & -3C 16HCP -2D possibly Diamonds regardless 12-(14) -2H(5 if X=H) or (3 if Y=H) (4 if previously NOT bid). Again ACOL 2N is 20-22 - a wider range.
Over the years Beta has evolved further and further away from its ACOL birthplace. It is now a system in its own right. ACOL & Beta can no longer related! Indeed BETA owes a good deal to 5 card Major systems and Italian ideas.