Analysis of Beta 1level Openings
There are 2 main aims in this analysis

Here we make an analysis of each 1level opening bid in Beta ACOL

Then we will give a theoretical probability for each opening bid
PASS
This is the
most frequent of all opening bid so it deserves some mention! It
describes a hand unsuitable for any other system bid:
 Opening 1level bids focused on in this analysis  about 37%,
however Beta's 1C opening will be up to 910% , thats nearly 1 in 10!
1N about 56%, and D, H, S each about 67% . This all fits well with
the 'theory of information'!
 Other openings: 2C, 2D, 2Ma, 2NT, 3mi (2suited)  about 6%
 Preemptive openings  2D & 3H and beyond, characterised by weak 6 & 7+ card suit respectively  about 7% of all hands
 PASS the rest: 50% by difference
There
is a little shift towards PASS with unfavourable vulnerability say up
to 1%, mainly deducted from preemptive2openings but not exclusively, otherwise the choices
between these 4 groups are well demarcated.
1.
Beta'a 1C
denies a 5+ card suit in any other denomination. Beyond this whatever
your HCP for 1NT 1C will be used whenever the restrictions required for
1NT are not present.
Beta's 1C opening is alertable as it cab be just 2 cards.
Many balanced
hands with 4 or 5 Clubs & 1214 will be opened 1NT however the
other minor needs to be Hxx or xxxx and Majors 42 or
43. 44 in minors will also be opened 1NT with the majors 32
& occasionally 41 (singleton A or K). However with 5C & 4 D 1NT is opened only when 22 in the majors!  otherwise 1C.
1216 balanced hands (4333, 4432 & 5332, 54xx) will be opened 1 and rebid 1NT where possible AND 1718 balanced hands with a 2N rebid
With 19+ HCP balanced hands are opened with 2 (1920) or 2 (23+) or 2NT (2122).
With 19+ 6 card Club suit or 5Clubs & another 4 card are opened 1 too, upwards until qualifying for a 2 opening with <=3 1/2 LTC.
Estimated frequency of a Beta 1 opening is: 9.8%!
1
Very similar to 1:
needs to be the longest suit and 5 card, 5.5%
1
Its very different to the minor's scenario above.
Firstly 5 Card
Hearts are opened from 10HCP & with 44 in the Majors also from 10 HCP.
Also 5 card majors are never opened 1NT, still some 4 card majors are
opened with 1NT or 1C.
With 1518 a 5+ card 1 is opened if the longest suit and even with 4 cards if and only if the only other 4 card suit is Spades.
5+4+ Distributions with a 34LTC hands are opened 2. 3 1/2 LTC qualifies it for a 2 opening. Also balanced 1922 hands are opened 2 or 2NT.
Estimated frequency for 1 is 6.5%.
1
Opened if the longest suit or if 5+ cards there is a second suit of the same length.
As above for Hearts in the range 1214 a certain number of balanced hands are opened 1NT.
However unlike Hearts, Spades are opened with 10+HCP with 6 + cards (not 2).
15+ are similar to 1, 2, 2 and 2 openings. Except 2S may not have Hearts as a 2nd suit.
Estimated frequency for 1 is 6.5%
1NT
The following defines a Beta 1NT opening:
 1214 HCP may be shaded to 11 in 3rd & 4th position openings
 Minor suit holdings MUST total 7 or 8 cards either:
 A 3 card minor must be headed by A, K or Q
 Suit distributions allowed are:
 4333 (4 card minor)
 5332 (53 card minors)
 4432 (NOT 44 in Majors)
 2245 (thats 5C & 4D)
A 1NT opening works out at about 6%
The overall result is pleasing in that there is a fairly even distribution over
1level openings. Very different for ACOL where the 5 percentages
increase where Beta's decrease! Mainly due to:
 Beta's restrictions on a 1NT opening & ACOL's 1NT
overbelief in its preemptive value makes this bid at least 3% more
frequent
 Beta's nonadherence to ACOL's principal of 'preparedness'
& ACOL's almost strict adherenceincreases Major openings, lowers
frequency of minor openings
 Beta's nonforcing 2 of a Major openings & ACOL's 2's
(mostly through 'Benji' ), Game force opening has a slightly
lower frequency in ACOL
 ACOL
makes weak preempts and weak jump overcalls in minors, where Beta does
not:: so preemptive opening bids are more frequent in ACOL
The total % for 1level openings 37%
All these calculations are more complicated than i thought and it
has taken more than a full
days struggle and now needs verification over the next few
hundreds of deals by Beta players as there were certain calculations
that were guesstimated as so much can depends on vulnerability, support
by key middle cards like Ten or Nine & distribution of honours. knowing my habits in doubt I rounded up a bit!