Quad combinations
 

" wrote...
Can anyone tell me how to adapt the follwing formula so kindly
provided by Mr. Grove, to enable Excel to generate all the possible
combin(49,4):
...

You really want all 211876 combinations of 4 numbers from 49 numbers without
replacement (i.e., no duplicates)? Results in multiple 4-column ranges all the
way from row 1 down to row 65536?

Far more efficient to use 4 columns.

A1: 1 B1: 2 C1: 3 D1: 4

Then enter the following formulas.

A2: =A1+(B1=47)
B2: =IF(C1<48,B1,IF(B1<47,B1,A2)+1)
C2: =IF(D1<49,C1,IF(C1<48,C1,B2)+1)
D2: =IF(D1<49,D1,C2)+1

F1: =A65536+(B65536=47)
G1: =IF(C65536<48,B65536,IF(B65536<47,B65536,F1)+1)
H1: =IF(D65536<49,C65536,IF(C65536<48,C65536,G1)+1)
I1: =IF(D65536<49,D65536,H1)+1

Select F1:I1, copy, and paste into K1:N1 *and* P1:S1. Don't worry about the
values they show at this point.

Select A2:D2, and fill down into A3:D65536. Then select A2:D65536, copy, and
paste into F2:I65536 and K2:N65536. Select A2:D2, copy, and paste into
P2:S15268.

How you choose to work with this is up to you.

Inaddition can someone provide the most efficient formula that would
enable me to determine the frequency of repetitive quad combinations
in a sample of lottery results.

I have a lottery table with all lottery results in (Columns B:H). The
lottery has 49 balls and 6 balls and the bonus ball are drawn.

B C etc....
1st No 2nd No etc....

Meaning any combination of 4 of the 7 balls in column B through H? That's 35
possible combinations from each row. So, you'd be better off hardcoding all
combinations of (7 choose 4) in another range, namely,

1 2 3 4
1 2 3 5
1 2 3 6
1 2 3 7
1 2 4 5
1 2 4 6
1 2 4 7
1 2 5 6
1 2 5 7
1 2 6 7
1 3 4 5
1 3 4 6
1 3 4 7
1 3 5 6
1 3 5 7
1 3 6 7
1 4 5 6
1 4 5 7
1 4 6 7
1 5 6 7
2 3 4 5
2 3 4 6
2 3 4 7
2 3 5 6
2 3 5 7
2 3 6 7
2 4 5 6
2 4 5 7
2 4 6 7
2 5 6 7
3 4 5 6
3 4 5 7
3 4 6 7
3 5 6 7
4 5 6 7

and call that Comb_7_4. If your range of samples (B2:H99, for example) were
named Samples, then in yet another range, the top-left cell of which I'll name
Quads, generate the combinations of 4 out of 7 using these formulas.

the Quads cell itself:
=INDEX(Samples,1+INT((ROW()-ROW(Quads))/35),
INDEX(Comb_7_4,1+MOD(ROW()-ROW(Quads),35),COLUMN()-COLUMN(Quads)+1))

Fill this right into the next 3 columns. Select this 4-column by 1-row range,
and fill down into the next 3429 rows (this is specific to the number of rows
needed for Samples being B2:H99, i.e., 35 * 98 = 3430).

In the column to the right of this range of formulas enter a formula like (this
one assumes Quads is W2)

4 columns to the right of Quads (AA2 in this example):
=W2&" "&X2&" "&Y2&" "&Z2

and fill this down into the same row as the range of formulas to the left of it.
To the right of that enter another formula.

5 columns to the right of Quads (AB2 in this example):
=COUNTIF($AA$2:$AA$3431,AA2)

and fill this down into the same row as the range of formulas to the left of it.
Then enter dummy field names like A and B in AA1 and AB1, respectively. Select
AA1:AB3431 and run an advanced filter (Data Filter Advanced Filter...),
select 'Copy to another location', check 'Unique records only', and in the 'Copy
to' field select yet another range, and click OK. When the result will be the
4-ball combinations in the left column and the number of times they appeared in
Samples in the right column.

Knowing how to do this stuff is possibly valuable. Spending time doing this sort
of stuff to play lotteries is a monumental waste of time. Find the most frequent
'quad' in the first half of your samples, then see how often it appears in the
second half. Note: if you're thinking about playing the most frequent 'quad'
along with all other combinations of 2 numbers, be aware that that'd require 990
sets of numbers (45 choose 2 = 45 * 44 / 2). Your odds of winning by doing this
would be slightly worse than 1 out of 14,125.

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Quad combinations
 

Dearest Mr. Grove,

I am eternally grateful for all your assistance and i'm humbly working
through your latest formulae.

As a senior contributor who views my endeavors as absurd and futile,
when I hit the Big-one, can I presume you will be presented with an
ethical dilemma on whether or not to forgo your 10% commission? ;)

Thanks once again.

Samuel.

Please remove obvious spam trap if u wish to reply by email.

Quad combinations
 

" wrote...
...
As a senior contributor who views my endeavors as absurd and futile,
when I hit the Big-one, can I presume you will be presented with an
ethical dilemma on whether or not to forgo your 10% commission? ;)
...

Tell ya what, put 1% of your lottery spending into an escrow account for my
benefit. If you bankrupt yourself before winning the big one, I get the money.
If you do win, you get it. Certainly someone with such accumen as you possess
could see such a gamble is virtually a guaranteed winner for you.

Lightning strikes people all the time, and not because they consciously chose to
stand in the wrong place. Purely fortuitous good things happen too, even to
people who believe they caused their own good fortune.

If lotteries were predictable, there's be very, very few fully employed
mathematicians and statisticians. Consider the logical implications of this.

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Quad combinations
 

Did you mean acumen?

Mr Grove, if you're going to post condescending retorts, you should at
least get the spelling right; misspellings tend to throw the reader
off the content.


Samuel.

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Quad combinations
 

misspellings tend to throw the reader
off the content.

Apparently.

Seems to me, Harlan invested some time answering your original question and
provided some sage advice at the end. You are the one that baited him.

In fact, if Harlan correctly interpreted your strategy, you are decreasing
your chances. As an example,

Assume 4 letters A, B, C, D

with 3 letter combinations being chosen in a drawing. The combinatorial
possibilities a

ABC
ABD
ACD
BCD

Assume 3 drawings have been held and the results were
ABD
ACD
ABC

As we know, each combination will, over time be chosen an equal number of
times. Picking a combination containing A, your strategy, would actually
lessen your chances, since 3 successes have already been "consumed."

of course, unless the selection system is flawed, each drawing result is
independent of past experience, but if one believes an infinitesimal gain
can be made, you should do the opposite of the most frequently selected
quad.

--
Regards,
Tom Ogilvy



wrote in message
om...
Did you mean acumen?

Mr Grove, if you're going to post condescending retorts, you should at
least get the spelling right; misspellings tend to throw the reader
off the content.


Samuel.

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Quad combinations
 

Harlan,

I'd be very surprised
if there weren't regulations requiring that balls be changed if any
particular number were drawn too many times in a short period of time

Directly from the New York Lottery Site:

<snip
How often are the ballsets changed?
For Lotto and Take Five, three sets of ballsets are changed
every three months. Numbers and Win 4 are changed every
month (both the midday and evening sets). Pick 10 also has
three ballsets and they are changed every two months. For
information about the Mega Millions ballsets and drawings, visit
the official Mega Millions site at: www.megamillions.com
<snip

And from the MegaMillions site they're changed for ever draw:
<snip
The drawing machines and ball sets for each game are randomly
selected and certified by outside auditors, to ensure that balls and
equipment allow each number an equal chance of being drawn.
Each Lottery drawing machine and ball set used goes through a
series of pre-drawing tests to ensure the absolute randomness of
the results.
There also are a series of post-drawing tests, which are conducted
as part of the certification process.
Two draw officials who are lottery employees and one member of an
independent auditing firm administer tests.
In addition to these measures, all of these steps are videotaped to further
ensure the integrity of the process.
All draw equipment is securely maintained with limited access to draw officials
only.
<snip

I'd feel safe in assuming that every major lottery has similar
rules/guidelines with respect to changing the balls/whatever
they were using.

John

Quad combinations
 

"Tom Ogilvy" wrote in message ...
Think you need to reread what I wrote...

Unless you have some new revelation on the basic concepts of probability
related to lottery numbers that I don't understand, and I doubt it, don't
see much reason to waste further disk space on this.

Emphatic and succinctly put, my sentiments entirely.

Samuel.

Please remove obvious spam trap if u wish to reply by email.

Quad combinations
 

"Tom Ogilvy" wrote...
Think you need to reread what I wrote - as I stated and you have agreed, the
independent nature of the draws obviates the analysis - I am well aware of
that.
...
[reordered]
Harlan Grove wrote in message
"Tom Ogilvy" wrote...
...
In fact, if Harlan correctly interpreted your strategy, you are decreasing
your chances. As an example,
...

The remainder of your argument (which I recognize was toungue in cheek) relied
upon the OP either accepting that all outcomes should occur as frequently as any
others based on the flawed assumption that there's some sort of self-correcting
mechanism to do so or you're interpretting the OP's intent opposite to how I've
done.

It's bad enough to find the most frequent historical 4-ball combination and
assume that means it's more likely to recur, then augment it with all other
2-ball combinations to pick 'winning' numbers - given 49 balls, (45 choose 2) =
990 6-ball combinations. If the most frequent 4-ball combination is considered
*unlikely* to recur, there'd be (46 choose 6) - (45 choose 2) = 13,982,826
possible 6-ball combinations that have no more than 3 out of 4 of the numbers
from the historically most frequent 4-ball combination.

If you had meant to dissuade the OP from proceeding with this exercise, I
believe you should have been more explicit.

Unless you have some new revelation on the basic concepts of probability
related to lottery numbers that I don't understand, and I doubt it, don't
see much reason to waste further disk space on this.

Provided above. Guess this allows me to repost, hunh?

In case it hasn't become obvious to you, I have no qualms about wasting badwidth
on pointless replies. Thanks for the invitation.

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Quad combinations
 

" wrote...
...
Emphatic and succinctly put, my sentiments entirely.

How nice. Too bad your sentiments are as likely to be disappointed as your money
is to be squandered. Please hurry up. The sooner you spend your money on lottery
tickets, the sooner you'll need to cancel your Internet service.

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Quad combinations
 

Harlan wrote in message ...
" wrote...
..
Emphatic and succinctly put, my sentiments entirely.

How nice. Too bad your sentiments are as likely to be disappointed as your money
is to be squandered. Please hurry up. The sooner you spend your money on lottery
tickets, the sooner you'll need to cancel your Internet service.

Mr. Grove, you need to take a look at the illiterate content of your own posts
before handing out advice.

Samuel.

Quad combinations
 

wrote...
....
Mr. Grove, you need to take a look at the illiterate content of your
own posts before handing out advice.

Can't you do better than that?

Playing the lottery is a pleasant way to spend a *few* bucks.

Spending a lot on playing the lottery is unwise.

Spending a lot of time analyzing past lottery winning numbers in the
ignorant hope of increasing your odds of winning is a particularly acute
form of willful stupidity.

Given the content of my posts, it's easy to prove I'm nasty and careless
(when it comes to spelling). Given the contents of yours, it's easy to prove
you're an idiot.