One for the math-heads
FakeLake
I've struck a bit of a mathematical problem.
I'm in the process of writing a lottery number analysis program, and as one
aspect to my research towards it, I have made a file containing all possible
6/49 combinations. They are stored in a very orderly manner:
1,2,3,4,5,6
1,2,3,4,5,7
1,2,3,4,5,8
...
etc
...
43,44,45,46,47,48
43,44,45,46,47,49
44,45,46,47,48,49
The reason I did this is to try and work out a system of giving all
combinations and ID number from 1 to 13983816. My problem is that I can't!
I've hit a stumbling block and my mind has gone blank!
Can anyone see how I can work out the ID number from a given combination,
i.e. what is the ID number of 5,24,26,31,44,47 ?
I've been wracking my brains for hours but my mind has gone blank!
Any help would be much appreciated!
Peace,
FakeLake.
RayJ
What is the size of the file???
I'm not even going to ask how you will be using this "ID",
but why not let the computer generate it? I'm assuming you
programmed a loop to create the above file? Stick a counter
in there to count the iterations. You could modify this to
accept an input number (e.g 5,24,26,31,44,47) and spit out
the "ID" (counter).
Good luck,
Ray
Gerry
This is interesting. You come in here and insult a few
people and then ask for help on how to figure out your
problem.
Peace back to you.
Gerry
Sean B
maths.
Sean B
Ramsay D. Seielstad, KC2GMW
Try using the first 49 prime numbers and multiplication, you'll have a
unique ID for every combination ...
In article <9hsohl$lkq$1...@plutonium.btinternet.com>,
"FakeLake" <nos...@me.com> wrote:
- ->Hey there everyone.
- ->
- ->I've struck a bit of a mathematical problem.
- ->
- ->I'm in the process of writing a lottery number analysis program, and as one
- ->aspect to my research towards it, I have made a file containing all possible
- ->6/49 combinations. They are stored in a very orderly manner:
- ->
- ->1,2,3,4,5,6
- ->1,2,3,4,5,7
- ->1,2,3,4,5,8
- ->...
- ->etc
- ->...
- ->43,44,45,46,47,48
- ->43,44,45,46,47,49
- ->44,45,46,47,48,49
- ->
- ->The reason I did this is to try and work out a system of giving all
- ->combinations and ID number from 1 to 13983816. My problem is that I can't!
- ->I've hit a stumbling block and my mind has gone blank!
- ->
- ->Can anyone see how I can work out the ID number from a given combination,
- ->i.e. what is the ID number of 5,24,26,31,44,47 ?
- ->
- ->I've been wracking my brains for hours but my mind has gone blank!
- ->
- ->Any help would be much appreciated!
- ->
- ->Peace,
- ->FakeLake.
- ->
- ->
- --
+-----------------------------------------------------------------------------+
| Ramsay D. Seielstad KC2GMW | mrh...@worldnet.att.net; kc2...@arrl.net |
| Schenectady, NY, USA | ~~~~~~~~~~~~~~~~~~~~~~~ |
+-=-=-=-=-=-=-=-=-=-=-=-=-=-=+=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-+
| "An average working stiff, A bunch of unrelated hobbyist activities, which |
| have no significant value or use other than to occupy my free time and |
| amuse myself ... and trust me, this ain't my employer's opinion or view. |
+-----------------------------------------------------------------------------+
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FakeLake
news:ei85kts6f75kam1i6...@4ax.com...
> It can be calculated by simple elementary
> maths.
>
> Sean B
As I have said before, I have a degree in maths, but as I also said before,
I also have a mental block!
Please explain, as you obviously know.
Peace,
FakeLake.
Gerry
Drink a 6 pack of beer and stand on your head
for a half hour. Works every time ;-)
Gerry
Royce Penny
FakeLake wrote:
-----------------------------------
There is a formula that Don had passed on to the group a year or so back - and
it is not a simple formula to figure out. Perhaps if Don is lurking from
somewhere downunder in Australia he could repost it.
--
Royce Penny
Royce Penny's Money Machine
http://www.geocities.com/lottoking.geo
Nick Koutras
This has come up a few times.
So I created an Excel worksheet that will do that.
You can download the sheet here:
http://groups.yahoo.com/group/LottoDesigner/files/Excel%20Downloads/
The algorithm I used can be found below.
file 515
keywords combinations
gams B,C1
title COMB
for generates a vector from a lexicographical index
, That is, let C1, C2, ... Cm be the set of
, combinations of n items taken p at a time arranged in lexographical
, order. Given an integer i, this routine finds Ci
by B.P. Buckles and M. Lybanon
ref ACM TOMS 3 (1977) 180-182
Regards,
Nick Koutras
"Greek by Design"
FakeLake
download anything but text and audio-visuals from newsgroups (I'm not saying
for one minute that you spread viruses, but some people do, and you can
never tell), but I'm sure it's just what I'm after (which is annoying, but
due to my paranoia I might never find out!).
Peace,
FakeLake
Nick Koutras <tl...@hotmail.com> wrote in message
news:3B433A50...@hotmail.com...
FakeLake
they aren't needed here. In my mind I can see a blurred vision of an altered
base-49 number system, but again... the mental block... lol
As I said in my original question, I already have a way of numbering them:
0: 1,2,3,4,5,6
1: 1,2,3,4,5,7
2: 1,2,3,4,5,8
....
etc
....
13983813: 43,44,45,46,47,48
13983814: 43,44,45,46,47,49
13983815: 44,45,46,47,48,49
but I can't work out how to obtain the ID of a given combination from this
system. This is the most ideal numbering system for my needs, so I'd prefer
to stick to it.
At the moment I can perform a pretty fast binary search on a file contain
all these combinations, but the file holding them is about 80MB I think, and
I don't want my finished program to have to use a file that large - I'd
rather just shove six numbers in a function and have it return the ID. I'd
also like to mention that I don't need the REVERSE of this function (i.e.
give it an ID and work out the six numbers), although it might be fun to
play with in the future.
Peace,
FakeLake
Ramsay D. Seielstad, KC2GMW <mrh...@worldnet.att.net> wrote in message
news:Z6oQ7oJPM6/U09...@worldnet.att.net...
Robert Perkis
with a problem like this I would break the number universe into
smaller groups. From there you could tag each combination with
a group number and a number within the group. Like the street
address of an apartment building and the units within. RP
Dick Adams
>>> It can be calculated by simple elementary
>>> maths.
Sean is correct.
>> As I have said before, I have a degree in maths,
So you have said before.
>> but as I also said before, I also have a mental block!
Why am I not surprised?
>> Please explain, as you obviously know.
> Drink a 6 pack of beer and stand on your head for a half hour.
> Works every time ;-)
I suggest you drink two six packs of beers and then you won't care.
For your mental block, I recommend medicinal discovery of the 20th
century: Jack Daniels Black Label. Jack Black cures everything
except alcoholism and for that you can go on a maintenance dose.
Dick -- The Wizard of Odds and sometimes Taxes too.
C(5,48)+C(5,47)+C(5,46)+C(5,45) + ....
If that doesn't help you nothing will. :)
Richard McTavish
FakeLake wrote:
> Hmm. I know quite a bit about prime numbers, and as far as I can work out,
> they aren't needed here. In my mind I can see a blurred vision of an altered
> base-49 number system, but again... the mental block... lol
>
> As I said in my original question, I already have a way of numbering them:
>
> 0: 1,2,3,4,5,6
> 1: 1,2,3,4,5,7
> 2: 1,2,3,4,5,8
> ....
> etc
> ....
> 13983813: 43,44,45,46,47,48
> 13983814: 43,44,45,46,47,49
> 13983815: 44,45,46,47,48,49
>
> but I can't work out how to obtain the ID of a given combination from this
> system. This is the most ideal numbering system for my needs, so I'd prefer
> to stick to it.
>
> At the moment I can perform a pretty fast binary search on a file contain
> all these combinations, but the file holding them is about 80MB I think, and
> I don't want my finished program to have to use a file that large - I'd
> rather just shove six numbers in a function and have it return the ID. I'd
> also like to mention that I don't need the REVERSE of this function (i.e.
> give it an ID and work out the six numbers), although it might be fun to
> play with in the future.
>
The numbering system you suggest above sounds good to me.
Whether you start at 1 or zero may be a personal preference.
Instead of searching a file, generate the combinations inside the function.
What you could do is to go sequentially thru all the combinations.
Initialize a count variable to zero at the start.
Increment the count for each combination until you hit the one you want.
The resulting count will be your unique sequential ID.
psuedo-C-code:
no_match=TRUE;
id=0;
while(no_match)
{
/* cycle sequentially thru all combos */
/* check for match */
id++;
}
You could probably optimize the search part of the function to increase the
speed a bit.
Not the fastest or shortest code, but it will probably work.
The /* cycle sequentially thru all combos */ code can be found on the internet,
or I could post my (re-cycled) version of it.
You can always post your problem to other newsgroups and see what contributions
you get .
Try comp.programming or an appropriate math newsgroup.
FakeLake
Peace,
FakeLake.
p.s. I don't drink, but I do smoke a lot of weed. Maybe that doesn't
help.....
Dick Adams <rda...@smarty.smart.net> wrote in message
news:tk7jann...@corp.supernews.com...
FakeLake
second number etc.
Sorry!
Peace,
FakeLake
YanCanDo
Quite frankly, I think the only reason you posted this is to generate
"FILLER" for the group. Man, are you weird. What sensible purpose can
a unique "ID" for each possible drawn/un-drawn combination have?
For one thing, storing this value as a reference doesn't make much
sense, considering that the actual number sequences themselves only
use up a few extra bytes of storage.
If you're indeed serious, and you want to use this huge freakin' table
in an exclusion mechanism as a method of odds reduction, then you're
absolutely and positively NUTS.
If I wanted to use exclusion based on the existence of drawn history I
would start with a complete draw history since inception. A simple and
efficient scan of the 1600+ draws would tell me if the six numbers
were ever drawn.
Anything I DID generate would go into a scratch table with a unique
record ID generated for each new record added.
Hope this clears the smoke,
YanCanNuts
Manfred
Hi all,
I have heard now the 2nd or 3rd time this question and don't know what
it helps to know the line No. of a combination.
Perhaps someone will explain it here.
But the solution is very simple.
You'll need not a large table.
Only store the 6 number combination in ascent order in a QBASIC
program, generate in a loop all combinations and count the lines as
long as the wanted combination is available.
Please note: The first line starts with the number 1 and not zero
because we have no zero lines.
I know, QBASIC needs for generating of all 14 million combinations
about 10 minutes on a 800 MHz computer (if you want to know e.g. the
line number of 43-44-46-47-48-49), but it is better than nothing.
Manfred
8 REM this program from Manfred counts the line No. for any
combination from 6 of 49
9 CLS
10 PRINT "counting the line No. of the following number combination
from 6 of 49:": PRINT
11 INPUT "1st number: ", aa
12 INPUT "2nd number: ", bb
13 IF bb <= aa THEN PRINT "please 2nd number greater than 1st number
!": GOTO 11
14 INPUT "3rd number: ", cc
15 IF cc <= bb THEN PRINT "please 3rd number greater than 2nd number
!": GOTO 11
16 INPUT "4th number: ", dd
17 IF dd <= cc THEN PRINT "please 4th number greater than 3rd number
!": GOTO 11
18 INPUT "5th number: ", ee
19 IF ee <= dd THEN PRINT "please 5th number greater than 4th number
!": GOTO 11
20 INPUT "6th number: ", ff
21 IF ff <= ee THEN PRINT "please 6th number greater than 5th number
!": GOTO 11
22 IF aa > 49 OR bb > 49 OR cc > 49 OR dd > 49 OR ee > 49 OR ff > 49
THEN PRINT "one wrong number !": GOTO 11
23 IF aa < 1 OR bb < 1 OR cc < 1 OR dd < 1 OR ee < 1 OR ff < 1 THEN
PRINT "one wrong number !": GOTO 11
25 PRINT : PRINT "Please wait": PRINT
29 x# = 0
30 FOR a = 1 TO 44
40 FOR b = a + 1 TO 45
50 FOR c = b + 1 TO 46
60 FOR d = c + 1 TO 47
70 FOR e = d + 1 TO 48
80 FOR f = e + 1 TO 49
81 x# = x# + 1
82 IF a = aa AND b = bb AND c = cc AND d = dd AND e = ee AND f = ff
THEN PRINT "it's line No. "; x#: GOTO 130
100 REM PRINT x#, a; b; c; d; e; f
110 REM LPRINT x#, a; b; c; d; e; f
120 NEXT f, e, d, c, b, a
130 PRINT : PRINT x#, a; b; c; d; e; f
170 END
Store the programm code with the Editor e.g. with the name
counter (no more than 8 signs). The file has then the name counter.txt
.
Change the file extension .txt with the explorer to .bas then you'll
have the
file counter.bas, which is executable with QBASIC. Start it in QBASIC.
QBASIC.exe is delivered with all Windows 9x programs and runs under
DOS mode.
If QBASIC.EXE is not installed on your HD, copy it from the Windows CD
on to the HD.
Gerry
>
> Thanks! Sorted ;)
>
> Peace,
> FakeLake.
>
> p.s. I don't drink, but I do smoke a lot of weed. Maybe that doesn't
> help.....
You did say you dabble in psychology didn't you.
Time will tell if you have a BS degree in math
or a degree in BS.
Gerry
Robert Perkis
Sean B
Here's a couple of posts from 1999 that were still
in my outbox of my old computer.
=====================================================
Newsgroups: rec.gambling.lottery,alt.lotto.players,
sci.stat.math,alt.sci.math.combinatorics,
alt.sci.math.statistics.prediction,alt.sci.math.probability
Subject: Re: Algorithm wanted on combination
Date: Mon, 31 May 1999 19:14:38 GMT
(Sean B) wrote:
>GFA Basic has a Combin(ation) Function so I knocked up the
>following brief program which will run on the free trial version
>of GFA.
>
-> snip
>
I've slightly tidied up the still crude program so that it will
accept any legitimate set of 6 balls via the keyboard. Must
be in ascending order. I could have added a sort but it would
take up more space.
It should be possible to write a program that will reverse
this calculation. A test would be needed to find the value
of the 6th ball; fairly easy because all starting values after
the increment of the 6th ball equal 0+0+0+0+0+(6th Ball value)
So if we want to find the 6 numbers that are value 120,500 a test
of the combinations of the 6th ball only would give
1-2-3-4-5-25 = 134,597 and 1-2-3-4-5-24 = 100,948 so the 6th ball
must be 24. Quite possibly the other values could be found in a
similar way. The value of the 6th ball having been found would
remain a constant for the rest of the program; so it could probably
be deducted 120,500 - 100,948 = 19,552 The 5th ball now sets
the values from 0+0+0+0+(5th Ball value) to 0+0+0+0+(5th Ball value
+1)
so we would have to find the two 5th ball values that 19,552 lies
between and take the lower on...... then proceed to the 4th ball.
Happy pondering,
Sean B
>
>'//* or ' = REM statement
>
>'===================save as COMBNUMS.LST===================
>
>'Program will run on the 16 bit Windows trial version
>'of GFA Basic (runs OK on W95) runs on the DOS
>'version as well.
>'download from http://www.gfasoft.gfa.net/eng/trials.htm
>'From file menu select new, then merge, then choose COMBNUMS.LST
>'Delete these 6 lines if they cause any problems.
Screen 18 '//* For DOS ver of GFA
Color 7,1 '//* ignored by Windows ver. (this ain't Microsoft)
Titlew #1, " Lottery Combination Calculator v1.01 "
Openw #1,30,30,_x * .9,_y * .9,-1
ClearW #1
Defdbl "A-Z"
'Following algorithm by Don McDonald
'Arranged into ascending order, the lucky numbers were
'3 5 14 22 30 44. The combination sequence number of these
'numbers is :
'2C1 + 4C2 + 13C3 + 21C4 + 29C5 + 43C6 +1 = 6,221,489.
'//* Alter the 6 balls below
A = 1
B = 2
C = 3
D = 5
E = 6
F = 9
'//* If you rem out the PRINT and INPUT lines below
'//* the values given above will be used instead of the
'//* keyboard entry
Print '//* rough and ready input routine follows.
Print "Enter Six Sorted Lottery numbers, press enter after each one "
Print
Input A,B,C,D,E,F
'//* reduce all by 1
A = A - 1
B = B - 1
C = C - 1
D = D - 1
E = E - 1
F = F - 1
If A >= 1
AC = Combin(A,1)
Else
AC = 0
EndIf
Print
Print
Print " 1st Combination Total = ";AC
If B >= 2
BC = Combin(B,2)
Else
BC = 0
EndIf
Print " 2nd Combination Total = ";BC
If C >= 3
CC = Combin(C,3)
Else
CC = 0
EndIf
Print " 3rd Combination Total = ";CC
If D >= 4
DC = Combin(D,4)
Else
DC = 0
EndIf
Print " 4th Combination Total = ";DC
If E >= 5
EC = Combin(E,5)
Else
EC = 0
EndIf
Print " 5th Combination Total = ";EC
If F >= 6
FC = Combin(F,6)
Else
FC = 0
EndIf
Print " 6th Combination Total = ";FC
X = AC + BC + CC + DC + EC + FC + 1
Print
Print " Lottery Line = ";
Print A + 1,B + 1,C + 1,D + 1,E + 1,F + 1
Print
Print " Combination Number = ";
Print Using"###,###,###",X
Print
Print
Print
Print " Any Key to finish"
Keyget w
CloseW #1
Sean B
2nd file (re-post of 2 from 1999)
Worth noting that of all the groups the original
poster, posted to only rgl was able to help.
Sean B
===============================================================
Newsgroups: rec.gambling.lottery,alt.lotto.players,sci.stat.math,
alt.sci.math.combinatorics,alt.sci.math.statistics.prediction,
alt.sci.math.probability
Subject: Re: Algorithm wanted on combination
Date: Wed, 02 Jun 1999 05:54:38 GMT
adi...@hartco.com (Alain Dionne) wrote:
>On Sun, 30 May 1999 23:42:51 -0400, Paul <NOSP...@idirect.com>
>wrote:
-> snip
>>
>>Appreciate the post. I understand how this algorithm works and the basic
>>logic behind it. Unfortunately, it doesn't always give the correct
>>answer.
>>>
>>> 01-02-03-04-05-06 = Sequence Number 1 Correct
>>> 01-02-03-04-05-07 = Sequence Number 2 Correct
>>
>>> 01-02-03-04-06-07 = Sequence Number 3
>>Why the jump here? Wouldn't the next sequence be 1-2-3-4-5-8?
>>
>>> 01-02-03-05-06-07 = Sequence Number 4
>>Why the jump here? We haven't yet finished cycling through the number 4
>>in the 4th position
>>...
>>Skip<
>
>
>Base on "Varying Highest Possible Ball" from Dick Adams
>
>If I perform a loop on the highest number in this VB Code:
>
-> snip
>
>
>I Get
>
>1-2-3-4-5-6 = 1
>1-2-3-4-5-7 = 2
>1-2-3-4-5-8 = 3
>1-2-3-4-5-9 = 4
>1-2-3-4-5-10 = 5
>1-2-3-4-5-11 = 6
>... (Skip) ...
>43-44-45-46-47-48 = 13,983,814
>43-44-45-46-47-49 = 13,983,815
>44-45-46-47-48-49 = 13,983,816
>
>
>So, why to loop on the lowest number. As Paul wrote, you haven't
>completed the cycle for the highest number???
>
Dons algorithm is a better way of doing it because:
a): Some calculations are possible; we do not have to go
through a program loop to find the numbers or reverse
them.
b): Each set of 6 numbers have the same unique combination
number irrespective of Lottery size so 1-3-6-16-28-39 will have
the same combination number in say a 6/40 ball lottery as it
would have in a 6/49 ball Lottery.
c): It has potential of being taken much further and as Don has
demonstrated is of great use in statistical analysis.
There is nothing wrong with using the loop that you posted. It is
however of use only for the Lottery size that it was written for
and reversing the combination number means running through
the full loop again. With Dons we can find fairly quickly find the
value of the last (6th ball) by calculation and then solve the others
in a similar manner or via a mini loop. In fact a look up table for
the 6th ball would only be 49 lines long as probably would be
a look up table for the 5th (48 to be precise).
Hope this helps.
Sean B
Royce Penny
Dick Adams wrote:
>
> I suggest you drink two six packs of beers and then you won't care.
>
> For your mental block, I recommend medicinal discovery of the 20th
> century: Jack Daniels Black Label. Jack Black cures everything
> except alcoholism and for that you can go on a maintenance dose.
>
> Dick -- The Wizard of Odds and sometimes Taxes too.
>
> C(5,48)+C(5,47)+C(5,46)+C(5,45) + ....
>
> If that doesn't help you nothing will. :)
------------------
Dick - Johnny Walker Black Label works much better.
Do you think that I should tell him also that the formula would be:
CSN = C(n1-1,1)+C(n2-1,2)+C(n3-1,3)+C(n4-1,4)+C(n5-1,5)+C(n6-1,6)+1
where CSN is the Combination Ssequence Number?
Or, should I keep it to myself??
john Latala
> Do you think that I should tell him also that the formula would be:
>
> CSN = C(n1-1,1)+C(n2-1,2)+C(n3-1,3)+C(n4-1,4)+C(n5-1,5)+C(n6-1,6)+1
>
> where CSN is the Combination Ssequence Number?
>
> Or, should I keep it to myself??
Unless my math is totally shot you might want to keep it to yourself
because it deosn't work.
For {1 2 3 4 5 6} we should get 1:
C(1-1,1)+C(2-1,2)+C(3-1,3)+C(4-1,4)+C(5-1,5)+C(6-1,6)+1
C( 0,1)+C( 0,2)+C( 0,3)+C( 0,4)+C( 0,5)+C( 0,6)+1
0+ 0+ 0+ 0+ 0+ 0+1
1
Which makes sense. For the case {1 2 3 4 5 7} the last term becomes
C(7-1,6) or C(6,6) which is one so we end up with 2 which again makes
sense.
Now for {1 2 3 4 5 6 8} nothing changes again except the last term whihc
is C(8-1,6) or C(7,6) which gives 7 for a CSN of 8. I expected 3.
Am I doing something wrong or is your formula wrong?
--
john R. Latala
jrla...@golden.net
Sean B
>On Fri, 6 Jul 2001, Royce Penny wrote:
>
>> Do you think that I should tell him also that the formula would be:
>>
>> CSN = C(n1-1,1)+C(n2-1,2)+C(n3-1,3)+C(n4-1,4)+C(n5-1,5)+C(n6-1,6)+1
>>
>> where CSN is the Combination Ssequence Number?
>>
>> Or, should I keep it to myself??
>
>Unless my math is totally shot you might want to keep it to yourself
>because it deosn't work.
>
See below:
>For {1 2 3 4 5 6} we should get 1:
>
> C(1-1,1)+C(2-1,2)+C(3-1,3)+C(4-1,4)+C(5-1,5)+C(6-1,6)+1
> C( 0,1)+C( 0,2)+C( 0,3)+C( 0,4)+C( 0,5)+C( 0,6)+1
> 0+ 0+ 0+ 0+ 0+ 0+1
> 1
>
>Which makes sense. For the case {1 2 3 4 5 7} the last term becomes
>C(7-1,6) or C(6,6) which is one so we end up with 2 which again makes
>sense.
>
>Now for {1 2 3 4 5 6 8} nothing changes again except the last term whihc
>is C(8-1,6) or C(7,6) which gives 7 for a CSN of 8. I expected 3.
>
>Am I doing something wrong or is your formula wrong?
The sequence is :
1). 6 5 4 3 2 1
2). 7 5 4 3 2 1
3). 7 6 4 3 2 1
4). 7 6 5 3 2 1
5). 7 6 5 4 2 1
6). 7 6 5 4 3 1
7). 7 6 5 4 3 2
8). 8 5 4 3 2 1
9). 8 6 4 3 2 1
10). 8 6 5 3 2 1
etc.
Anyone fancy writing the pseudo basic code
loop to generate the numbers in this order
instead of:
1 2 3 4 5 6
1 2 3 4 5 7 etc.
One of the many things I never quite got
round to ;-(
Dick Adams
> Dick Adams wrote:
>> I suggest you drink two six packs of beers and then you won't care.
>>
>> For your mental block, I recommend medicinal discovery of the 20th
>> century: Jack Daniels Black Label. Jack Black cures everything
>> except alcoholism and for that you can go on a maintenance dose.
>>
>> Dick -- The Wizard of Odds and sometimes Taxes too.
>>
>> C(5,48)+C(5,47)+C(5,46)+C(5,45) + ....
>>
>> If that doesn't help you nothing will. :)
> Dick - Johnny Walker Black Label works much better.
I prefer Chevis to JW Black. But reasonable people can disagree.
> Do you think that I should tell him also that the formula would be:
>
> CSN = C(n1-1,1)+C(n2-1,2)+C(n3-1,3)+C(n4-1,4)+C(n5-1,5)+C(n6-1,6)+1
>
> where CSN is the Combination Ssequence Number?
>
> Or, should I keep it to myself??
If he tries that, he'll go blind before he solves it.
I have code (Quick Basic) for translating both ways. When I find it,
I'll post it.
Dick Adams
Using Royce's method, 3 is {1 2 3 4 6 7) or C(6-1,5) + C(7-1,6) + 1 = 3.
I prefer the sequencing method you were using because it is more logical
to me and thus easier to code.
Dick Adams
> "FakeLake" <nos...@me.com> wrote:
>> [snipped]
> Quite frankly, I think the only reason you posted this is to generate
> "FILLER" for the group. Man, are you weird.
Absolute agreement.
> What sensible purpose can a unique "ID" for each possible drawn/un-drawn
> combination have?
Give some thought to the following methodology:
Take the ID's of the last four draws and sort them into numerical order.
Then place them between zero and C(49,6)+1, calculate the average ID for
each interval, convert those ID's back to draws, and buy the tickets.
Clarification:
0 IDa IDb IDc IDe C(49,6)+1
(0 + IDa)/2; (IDa + IDb)/2; ....
Given the possibility of odd sums, you'll get five to ten draws every
time you do it.
It's no worse than hot-n-cold numbers, longitude-latitude, numerology, or
Psychic-Hotline. It also makes sense: by averaging these draws you are
simply relying upon "Regression to the Mean" to hit the jackpot. AND if
you really want a sophisticated marketing term to use for soliciting
people to fund your play, call it "Morphing into Predictability".
Royce Penny
john Latala wrote:
> On Fri, 6 Jul 2001, Royce Penny wrote:
>
> > Do you think that I should tell him also that the formula would be:
> >
> > CSN = C(n1-1,1)+C(n2-1,2)+C(n3-1,3)+C(n4-1,4)+C(n5-1,5)+C(n6-1,6)+1
> >
> > where CSN is the Combination Sequence Number?
> >
> > Or, should I keep it to myself??
>
> Unless my math is totally shot you might want to keep it to yourself
> because it deosn't work.
>
> (...snip for brevity...)
It works 100% - but only if you know how to use it. Obviously, you do not.
I think Sean clarified this for you in his post.
FakeLake
Dick Adams
FakeLake
Dick Adams <rda...@smarty.smart.net> wrote in message
news:tkg9hme...@corp.supernews.com...
^ No need for a capital T in taxes ;) lol
Peace,
FakeLake
John Smith
strange as it apparently seems to some I too use the "ID" in my lotto
programs. In my attempts to produce a 46,6,3,3,759 wheel (please tell me
someone has it on the net somewhere and put me out of misery !!), I
calculate the
ID for any 3 number combination and that helps keep track of which
combinations I have already covered. Using this technique and other
programming "shortcuts" I have a program which can start producing
26,6,3,3,130 wheels in about an hour. I am not a mathematician and
so I derived the logic for the code by just studying the data. It does
however rely a short loop and that means processing power. So the
purpose of this email is to ask you to please explain the formulas
mentioned as I don't understand the symbolism C(...) etc.
Again my math is very very basic ... :)
Thanks.
Royce Penny <lottoking....@yahoo.com> wrote in message
news:3B45BDE5...@yahoo.com...
Robert Perkis
how to make the wheel. If you just want to generate it
grab a free copy of CoverMaster there is a link to it on
my page http://www.lotto-logix.com/wheellinks.html John
is a nice guy, you might even ask how he does it. When
it comes to 2if2 and 3if3 it appears to be a straight
forward build, nothing fancy so it runs much faster than
a 3if6 build. You can visit one of Nick's pages off my
page as well. Stick with it and good luck. Robert Perkis
Ion Saliu
> >
> > C(5,48)+C(5,47)+C(5,46)+C(5,45) + ....
> >
> > If that doesn't help you nothing will. :)
>
> ------------------
>
> Dick - Johnny Walker Black Label works much better.
>
> Do you think that I should tell him also that the formula would be:
>
> CSN = C(n1-1,1)+C(n2-1,2)+C(n3-1,3)+C(n4-1,4)+C(n5-1,5)+C(n6-1,6)+1
>
> where CSN is the Combination Ssequence Number?
>
> Or, should I keep it to myself??
> --
> Royce Penny
> Royce Penny's Money Machine
> http://www.geocities.com/lottoking.geo
>
>
• Dear Mr. Vice-President Dick “Quincy” Adams:
• Your Majesty Lotto-King:
With all due respect, Your formulae are utterly incorrect.
Let’s think of a simple combination, such as 1-2-3-4-5-8. What is its CSN? An
absurd result, for there is no C(0,1), C(1,2), C(2,3), C(3,4), C(4,5); there can
be only C(7,6).
Also importantly, the correct formula should take into consideration differences
in games formats. One fundamental element of a lotto game format is its largest
number. Thus, in a lotto 49/6 game, the CSN for combination 6-7-16-20-28-47 is
6,991,908 (exactly the mid-point in the combination set). The same combination
6-7-16-20-28-47 has an index (CSN) of 45,148,858 in a lotto 69/6 game (PA
lottery). Your formulae do not lead to these results, the only correct results.
Although not a general-purpose formula, the algorithm I presented a few days ago
represents the easiest way to calculate the indexes of any lotto combinations.
The algorithm is for the BASIC language, but it can be converted to any
programming language. I compiled NTHINDEX.EXE with PowerBasic, especially
because of increased speed of execution.
In article <9ifhhr$mum$1...@usenet.otenet.gr>, John Smith says...
Return to Socrates
http://www.saliu.com/
Nothing stronger than Reason.
Royce Penny
Ion Saliu wrote:
> > > Dick -- The Wizard of Odds and sometimes Taxes too.
> > >
> > > C(5,48)+C(5,47)+C(5,46)+C(5,45) + ....
> > >
> > > If that doesn't help you nothing will. :)
> >
> > ------------------
> >
> > Dick - Johnny Walker Black Label works much better.
> >
> > Do you think that I should tell him also that the formula would be:
> >
> > CSN = C(n1-1,1)+C(n2-1,2)+C(n3-1,3)+C(n4-1,4)+C(n5-1,5)+C(n6-1,6)+1
> >
> > where CSN is the Combination Sequence Number?
> >
> > Or, should I keep it to myself??
> > --
> > Royce Penny
> > Royce Penny's Money Machine
> > http://www.geocities.com/lottoking.geo
> >
> >
>
> • Dear Mr. Vice-President Dick “Quincy” Adams:
> • Your Majesty Lotto-King:
>
> With all due respect, Your formulae are utterly incorrect.
> Let’s think of a simple combination, such as 1-2-3-4-5-8. What is its CSN? An
> absurd result, for there is no C(0,1), C(1,2), C(2,3), C(3,4), C(4,5); there can
> be only C(7,6).
> (...snip,snip...snipe below)
> Return to Socrates
> http://www.saliu.com/
> Nothing stronger than Reason.
---------------------
Ion - As per your sig above, there is "...nothing stronger than reason...".
So...the number of sets of 1 number when you have 0 is 0, the number of sets of 2
numbers when you have 1 is 0, the number of sets of 3 numbers when you only have 2
is again 0, the number of sets of 4 numbers with only 3 available is 0, the number
of sets of five numbers with only 4 on the table is also zero.
It is really that simple, unless you have a mental block, which, according to Dick,
can be cured instantly with Jack Daniel's Black Label.
--
Royce Penny (Your Majesty Lotto-King)
Royce Penny
John Smith wrote:
(...snip for brevity...)
> ...please explain the formulasmentioned as I don't understand the symbolism
> C(...) etc.
> Again my math is very very basic ... :)
>
> Thanks.
---------------------
John - "C" is simply the number of combinations of numbers available within a
specified range of numbers when the numbers cannot repeat themselves within
each set. Thus, C(49,6) is the number of combinations of 6 numbers available
within 49 numbers.
The generic formula is C(N,x) = N!/((N-x)!*x!), which in the case of C(10,3)
would calculate to be (10*9*8)/(3*2*1) = 120 ways that three numbers can be
grouped with 10 available.
Ion Saliu
> Let’s think of a simple combination, such as 1-2-3-4-5-8. What is its CSN? An
> absurd result, for there is no C(0,1), C(1,2), C(2,3), C(3,4), C(4,5); there can
> be only C(7,6).
> (...snip,snip...snipe below)
> Return to Socrates
> http://www.saliu.com/
> Nothing stronger than Reason.
---------------------
Ion - As per your sig above, there is "...nothing stronger than reason...".
So...the number of sets of 1 number when you have 0 is 0, the number of sets of
2
numbers when you have 1 is 0, the number of sets of 3 numbers when you only have
2
is again 0, the number of sets of 4 numbers with only 3 available is 0, the
number
of sets of five numbers with only 4 on the table is also zero.
It is really that simple, unless you have a mental block, which, according to
Dick,
can be cured instantly with Jack Daniel's Black Label.
--
Royce Penny (Your Majesty Lotto-King)
Royce Penny's Money Machine
http://www.geocities.com/lottoking.geo
-------------------------
• To His Majesty The King of Lotto:
There are kingdoms in this world where the pupils are taught the combinatorial
mathematics. The very first rule they learn is this: “In combinations of N
elements taken M at a time, M must be less than or equal to N. For it is absurd
to try combining 2 elements taken them 3 at a time, or 0 elements 6 at a time.”
If one has only 2 elements, how can one combine them 3 at a time? One particular
value that M can take is 0. “The number of combinations of any N elements taken
0 at a time is 1.” But “0 elements taken N at a time is an absurdity.”
I don’t know if you still keep your school textbooks. I don’t! I would like to
refer you, however, to a book recognized in all kingdoms. It just deals with
numbers. It compiled mathematical knowledge from various times and “kingdoms”.
The book is Warren Weaver’s “Lady Luck”. It presents combinatorial analyses
starting at page 92.
On the other hand, everybody has the right to set new knowledge, including new
mathematics. You have a right to design a combinatorial algorithm with the
following premise: “If N is less than M, then the number of combinations is set
to 0.” I quote you again:
“So...the number of sets of 1 number when you have 0 is 0, the number of sets of
2 numbers when you have 1 is 0, the number of sets of 3 numbers when you only
have 2 is again 0, the number of sets of 4 numbers with only 3 available is 0,
the number of sets of five numbers with only 4 on the table is also zero.”
Your indexing formula, however, is still wrong:
CSN = C(n1-1,1)+C(n2-1,2)+C(n3-1,3)+C(n4-1,4)+C(n5-1,5)+C(n6-1,6)+1
What is CSN for combination 1-2-3-4-5-8?
According to your formula, CSN = 0+0+0+0+0+C(7,6)+1 = 7+1 = 8.
In reality, CSN is 3:
1-2-3-4-5-6
1-2-3-4-5-7
1-2-3-4-5-8
I am afraid whisky in summer time in North America is a no-no. I consider also
the divine wine to be a no-no in the hot season. May I recommend Cinzano on ice,
with club soda and lemon? Here is my recipe: one empty, clean glass; add two
cubes of ice; add Cinzano to the half level; add club soda (sometimes tonic
water); add a slice of lemon. Enjoy! Nothing beats it in summer time in North
America!
Ion Saliu
John Smith
would be easy and it wouldn't help my cause much (making my 46,6,3,3,759
wheel program run faster). So I'll stick with the QBASIC code I wrote some
time ago to calculate the ID of any 3 different numbers between 1 and
Max.Numbers (which is 46 for me). Maybe some of the helpful "math-heads" on
this list can understand it ... :)) I derived it just by studying the data
and testing and refining the formula. It probably boils down to something
similar to what is being discussed.
Again, if anyone has or can produce a 46,6,3,3,759 wheel please let me know.
It would be great !!! I am convinced it's "THE dream wheel". I could then
turn my PC off at nights .... :) and actually start playing lotto again and
I hereby agree to pay 5% of any 6 number win I have, to the person who first
provides the 46,6,3,3,759 wheel I win by :))
Don't know what help this is to anyone .... but you can copy/paste it into
QBASIC and try it. If it helps you win a 6 number win (your conscience will
know and forever remind you ;)) you must hereby pay me 5% !
T1,T2,T3 are the 3 numbers, Max.Numbers is the "pool", Threeno is the ID
===========================================
EA000.Calc.Three.Number:
Threeno = 1
LC = 0
VL = Max.Numbers - 1
WHILE LC < T1 - 1
Threeno = Threeno + (((VL - 1) * VL) / 2)
VL = VL - 1
LC = LC + 1
WEND
LC = 0
VL = Max.Numbers - 1
WHILE LC < T2 - T1 - 1
Threeno = Threeno + (VL - T1)
VL = VL - 1
LC = LC + 1
WEND
Threeno = Threeno + T3 - T2 - 1
EA999:
RETURN
=============================================
John Smith
Athens, Greece
Royce Penny <lottoking....@yahoo.com> wrote in message
news:3B4C5DB5...@yahoo.com...
Dick Adams
> strange as it apparently seems to some I too use the "ID"
> in my lotto programs. In my attempts to produce a
> 46,6,3,3,759 wheel (please tell me someone has it on the
> net somewhere and put me out of misery !!) .....
OK -- explain 46,6,3,3,759.
THEN -- explain the significance of 759
ADD -- what Lotto are you playing.
I calculate the ID for any 3 number combination and that helps
keep track of which combinations I have already covered. Using
this technique and other programming "shortcuts", I have a program
which can start producing 26,6,3,3,130 wheels in about an hour.
I am not a mathematician and so I derived the logic for the code
by just studying the data. It does however rely a short loop and
that means processing power.
An hour?? What mhz is your machine?
> So the purpose of this email is to ask you to please explain
> the formulas mentioned as I don't understand the symbolism
> C(...) etc. Again my math is very very basic ... :)
Have no fear. We only eviserate people who claim they know
more than we do.
C(a,b) = a! / ((a-b)! * b!)
where a! = 1 * 2 * 3 * 4 * 5 ......* a
Gerry
>
> Have no fear. We only eviserate people who claim they know
> more than we do.
>
> C(a,b) = a! / ((a-b)! * b!)
> where a! = 1 * 2 * 3 * 4 * 5 ......* a
>
> Dick -- The Wizard of Odds and sometimes Taxes too.
Said another way in street language if you (third person )
stay in your box and don't make any wild assed claims the
predators will leave you alone.
r.g.l. survival 101
Gerry
Robert Perkis
Dick Adams wrote:
>
> "John Smith" <so...@toomuchspam.already> writes:
>
> > strange as it apparently seems to some I too use the "ID"
> > in my lotto programs. In my attempts to produce a
> > 46,6,3,3,759 wheel (please tell me someone has it on the
> > net somewhere and put me out of misery !!) .....
>
> OK -- explain 46,6,3,3,759.
> THEN -- explain the significance of 759
> ADD -- what Lotto are you playing.
That looks like how you would enter a wheel request into CoverMaster.
Pool-46, Pick-6, Match-3, Hits-3 Which means you'd be building a
3if3in46number Pick-6 wheel.
When I type into my odds calculator . . .
Lotto Game Size: 46 (Total Balls in the lotto machine)
Drawing Size: 3 (Numbers Drawn without Bonus Numbers)
Lotto Bet Size: 6 (Numbers Required for a single Chance)
I get
3 of 3 1 in 759.00
2 of 3 1 in 25.30
1 of 2 1 in 3.24
When I try to generate this wheel in 759 combinations I get
about 87% coverage. Maybe this is a case of trying to match
odds rather than a true count of 3# sub combinations, like
when people ask for the 64 combinations that will guarantee
the 1 in 64 odds of a 3if6in49 of a 3# prize the lottery
prints on the back of their tickets? Which we know isn't
possible because those are only odds of occurrence within that
range and not a guarantee. At least that's what I think and
I could be right. ^_~ Robert Perkis
Dick Adams
>> Ion Saliu wrote:
>>> Royce Penny wrote:
>>>> Dick Adams wrote:
>>> C(5,48)+C(5,47)+C(5,46)+C(5,45) + ....
>>>
>>> If that doesn't help you nothing will. :)
>>>
>>> For mental blocks, I suggest Jack Daniels Black
>>> Label. It cures everything except alcoholism,
>>> and for that you can go on a maintenance dose.
>> Dick - Johnny Walker Black Label works much better.
>>
>> Do you think that I should tell him also that the formula would be:
>>
>> CSN = C(n1-1,1)+C(n2-1,2)+C(n3-1,3)+C(n4-1,4)+C(n5-1,5)+C(n6-1,6)+1
>>
>> where CSN is the Combination Sequence Number?
>>
>> Or, should I keep it to myself??
>> Dear Mr. Vice-President Dick "Quincy" Adams:
>> Your Majesty Lotto-King:
There is no need for sarcasm.
>> With all due respect, Your formulae are utterly incorrect.
>> Let's think of a simple combination, such as 1-2-3-4-5-8.
>> What is its CSN? An absurd result, for there is no C(0,1),
>> C(1,2), C(2,3), C(3,4), C(4,5); there can be only C(7,6).
>> (...snip,snip...snipe below)
Ah ha, you confused Royce's formulae with mine which I did
not provide in full and was situation specific to an example
provided by the original poster of this thread, FakeLake.
It is often difficult when you come into the middle of a
thread. So I understand your confusion.
>> Return to Socrates
>> http://www.saliu.com/
>> Nothing stronger than Reason.
> Ion - As per your sig above, there is "...nothing stronger
> than reason...". So...the number of sets of 1 number when
> you have 0 is 0, the number of sets of 2 numbers when you have
> 1 is 0, the number of sets of 3 numbers when you only have 2 is
> again 0, the number of sets of 4 numbers with only 3 available
> is 0, the number of sets of five numbers with only 4 on the
> table is also zero.
>
> It is really that simple, unless you have a mental block,
> which, according to Dick, can be cured instantly with
> Jack Daniel's Black Label.
Royce: The cure is not instant.
Dick Adams
> Dick Adams wrote:
>> Have no fear. We only eviserate people who claim they know
>> more than we do.
>>
>> C(a,b) = a! / ((a-b)! * b!)
>> where a! = 1 * 2 * 3 * 4 * 5 ......* a
>>
>> Dick -- The Wizard of Odds and sometimes Taxes too.
> Said another way in street language if you (third person)
> stay in your box and don't make any wild assed claims, the
> predators will leave you alone.
>
> r.g.l. survival 101
Gerry's comments should be in the FAQ.
Philippe
I took a look at your excel workbook, downloaded it and try it with some
examples.
So far so good but yesterday I try to find the combination for a pool of 20
out of 70.
It work for sometimes with lower ID3 then when I try to enter the ID# for
the middle pool the answer was "run-time error '6' : overflow".
COMBIN(70,20)/2 = 80,942,301,831,328,900 this is the ID# I entered.
When I enter a ID# 46,252,743,903,616,300 then the answer was
70 20 ==> 4.62527439036163E+16 = : 1 49 52 53 54 55 56 57 58 61 62 63 64
65 66 67 68 69 70 72
which should not be in a select Lotto Size 70, Select Pool Size 20.
Then if you try to modify the ID# by just 1 increment like ........,300
become ......,301 or ....,302
then the worksheet does not take it and keep rounding down to .....,300.
Any ideas.
Philippe
"Nick Koutras" <tl...@hotmail.com> wrote in message
news:3B433A50...@hotmail.com...
> Hi all,
>
> This has come up a few times.
>
> So I created an Excel worksheet that will do that.
>
> You can download the sheet here:
>
> http://groups.yahoo.com/group/LottoDesigner/files/Excel%20Downloads/
>
>
>
> The algorithm I used can be found below.
>
> http://www.netlib.org/toms/
>
>
> file 515
> keywords combinations
> gams B,C1
> title COMB
> for generates a vector from a lexicographical index
> , That is, let C1, C2, ... Cm be the set of
> , combinations of n items taken p at a time arranged in
lexographical
> , order. Given an integer i, this routine finds Ci
> by B.P. Buckles and M. Lybanon
> ref ACM TOMS 3 (1977) 180-182
>
>
> Regards,
>
> Nick Koutras
>
> "Greek by Design"
>
>
>
> FakeLake wrote:
>
> > Hey there everyone.
> >
> > I've struck a bit of a mathematical problem.
> >
> > I'm in the process of writing a lottery number analysis program, and as
one
> > aspect to my research towards it, I have made a file containing all
possible
> > 6/49 combinations. They are stored in a very orderly manner:
> >
> > 1,2,3,4,5,6
> > 1,2,3,4,5,7
> > 1,2,3,4,5,8
> > ...
> > etc
> > ...
> > 43,44,45,46,47,48
> > 43,44,45,46,47,49
> > 44,45,46,47,48,49
> >
> > The reason I did this is to try and work out a system of giving all
> > combinations and ID number from 1 to 13983816. My problem is that I
can't!
> > I've hit a stumbling block and my mind has gone blank!
> >
> > Can anyone see how I can work out the ID number from a given
combination,
> > i.e. what is the ID number of 5,24,26,31,44,47 ?
> >
> > I've been wracking my brains for hours but my mind has gone blank!
> >
> > Any help would be much appreciated!
> >
> > Peace,
> > FakeLake.
>
>
Ion Saliu
Some users tried to run NTHINDEX.EXE for Keno games. The odds in a game like
Keno 80/20 are so huge, they leave me speechless. We are talking about 18-figure
numbers! Billions of billions?
I made changes to the program so that it accommodates Keno games. The data types
were pushed probably to the maximum limits of today’s PCs.
The option ‘Find combination for a given index’ for Keno is as fast as for
standard lotto games.
The other option, ‘Find the index of a given combination’ for Keno with 20
numbers per line can be extremely slow! Billions of billions of loop iterations!
(To stop the program, press Ctrl+Break.) At this point, I can’t see an easy way
around it. Just hope that somebody will find an easy way around it and publish
the algorithm in the public domain.
Since Keno 20 is very, very slow, Keno with 10 numbers per combination is
recommended. Besides, the winning Keno combinations have a maximum of 10
numbers. The combination of the mid-point index (CSN) can be further improved.
You can add to each number two of its neighbors, both lower and higher. For
example, in the lotto 48/6 the mid-point combination is 5-25-28-31-32-40. An
extended normal group would be:
3,4,5,6,7 – 23,24,25,26,27 – 26,27,28,29,30 – 29,30,31,32,33 – 30,31,32,33,34 –
38,39,40,41,42.
Ion Saliu
PS
The same download link: http://www.saliu.com/infodown.html
In article <iFD37.464$JS2....@newsread1.prod.itd.earthlink.net>, Philippe
says...
John Smith
news:3B4DF2B4...@gate.net...
>
>
> Dick Adams wrote:
> >
> > "John Smith" <so...@toomuchspam.already> writes:
> >
> > > strange as it apparently seems to some I too use the "ID"
> > > in my lotto programs. In my attempts to produce a
> > > 46,6,3,3,759 wheel (please tell me someone has it on the
> > > net somewhere and put me out of misery !!) .....
> >
> > OK -- explain 46,6,3,3,759.
> > THEN -- explain the significance of 759
> > ADD -- what Lotto are you playing.
>
> That looks like how you would enter a wheel request into CoverMaster.
> Pool-46, Pick-6, Match-3, Hits-3 Which means you'd be building a
> 3if3in46number Pick-6 wheel.
>
Yes that's what I mean. I thought that it was "standard" to describe the
wheel that way. The Lotto here in Greece is 49 numbers but a 46 number wheel
would be a great test !!
> When I type into my odds calculator . . .
>
> Lotto Game Size: 46 (Total Balls in the lotto machine)
> Drawing Size: 3 (Numbers Drawn without Bonus Numbers)
> Lotto Bet Size: 6 (Numbers Required for a single Chance)
>
> I get
>
> 3 of 3 1 in 759.00
> 2 of 3 1 in 25.30
> 1 of 2 1 in 3.24
>
> When I try to generate this wheel in 759 combinations I get
> about 87% coverage. Maybe this is a case of trying to match
> odds rather than a true count of 3# sub combinations, like
> when people ask for the 64 combinations that will guarantee
> the 1 in 64 odds of a 3if6in49 of a 3# prize the lottery
> prints on the back of their tickets? Which we know isn't
> possible because those are only odds of occurrence within that
> range and not a guarantee. At least that's what I think and
> I could be right. ^_~ Robert Perkis
Well, again, not sure I understand all you are saying, but for me the
efficiency of a 100% coverage wheel is the target. It has to be at least
until I actually try it and find it doesn't work.
> >
> > I calculate the ID for any 3 number combination and that helps
> > keep track of which combinations I have already covered. Using
> > this technique and other programming "shortcuts", I have a program
> > which can start producing 26,6,3,3,130 wheels in about an hour.
> > I am not a mathematician and so I derived the logic for the code
> > by just studying the data. It does however rely a short loop and
> > that means processing power.
> >
> > An hour?? What mhz is your machine?
Yes an hour is what I remembered from the last time I ran it quite some time
ago. But I ran it and timed it and it actually hits the first 26,6,3,3,130
wheel in about 20 minutes. I use an AMD 200Mhz I put together back in 1997.
> >
> > > So the purpose of this email is to ask you to please explain
> > > the formulas mentioned as I don't understand the symbolism
> > > C(...) etc. Again my math is very very basic ... :)
> >
> > Have no fear. We only eviserate people who claim they know
> > more than we do.
> >
> > C(a,b) = a! / ((a-b)! * b!)
> > where a! = 1 * 2 * 3 * 4 * 5 ......* a
> >
> > Dick -- The Wizard of Odds and sometimes Taxes too.
I had to look up eviserate. You've spelt it wrong. According to my
dictionary
it's "eviscerate" :))
I've been messing with Lotto and writing all sorts of little programs for
it since it first appeared in Greece. Earlier this year when I finally felt
I was
actually running out of steam and ideas I thought I'd check the newsgroups.
Lo and behold rec.gambling.lottery with no end of helpful folk with web
sites and pointers and programs and ready made wheels ... including 'my'
26,6,3,3,130 ! I was astonished to discover that the wheel it had taken me
probably a couple of years of program tweaking and tuning to produce was
already on the net ... ! That what is it for me. Talk about reinventing the
wheel !!From now on it has to be a
group effort and I'd like the target to be a 46,6,3,3,759 wheel.
John Smith,
Athens-Greece
John Smith
Adams. Dick, your surprise at my claiming 1 hour to produce a 26,6,3,3,130
wheel was justified!! To make things worse I replied to another post by
Robert Perkis and claimed the program does it in 20 minutes !!! I was
obviously wrong. I had not run the program for quite some time now. Provoked
by your surprise I decided to time it. Yesterday I started the program and
noted the time 17:48 and left. I didn't check my PC again until the next day
by which time my program had finished and printed the time on the screen. It
read 6:05 and so I quickly figured it started at 12 minutes to 6 and it
finished at 5 past 6 so that's about 20 minutes ... wishful thinking, an
honest mistake and an embarrassing claim. Subtracting the two times
correctly I realize the program needs about 12 hours !!!
Still if anyone has a machine which is 12 times faster than an AMD K6 200
... then it would only take an hour :))
Again apologies all around.
John Smith,
Athens-Greece
Gerry
>
>
> I had to look up eviserate. You've spelt it wrong. According to my
> dictionary
> it's "eviscerate" :))
I don't know the correct spelling and only know
that Dick Adams has never claimed to be a
Wizard of spelling. That's not a flame John,just
poking a little humor or is that humour ??
Gerry
Philippe
more than 15 numbers then I look for myself in Excel help ( which I should
have done before asking my question...but I was so sure that Excel could
handle anything ) and he is right, Excel cannot handle more than 15 digits
and all digits after the fifteenth turn to "0".
So when I enter "COMBIN(70,20)" then the answer was wrong as well ( for the
last 4 digits only), and for sure Nick's worksheet could not give me either
the right combination for an ID# above 15 digits but still works great when
staying within 15 digits.
Now I would like to know if any of you guys knows a spreadsheet program that
can accurately handle at least 20 digits and have the same capabilities of
Excel for functions, formulas and VBA programming or is there a way to trick
Excel and increase its capability in handling more than 15 digits.
I am already using NthIndex from Ion Saliu that I thank again for his great
program (but there is also a limitation in handling ID# above 15 digits) and
between Ion and Nick I can work a lot more with lotto and keno ID#,
but this is good only for one by one ID or combination and under 15 digits
ID#.
And in Excel my own basic formulae give me, as I know it now, 15 digits ID#
max but I can past it all along my columns to know their ID# and work from
there.
If anyone would help me in finding that dream program, it will be very much
appreciated.
Thank you
Philippe
"Philippe" <phil...@earthlink.net> wrote in message
news:iFD37.464$JS2....@newsread1.prod.itd.earthlink.net...
Gerry
>
>
> Well, again, not sure I understand all you are saying, but for me the
> efficiency of a 100% coverage wheel is the target. It has to be at least
> until I actually try it and find it doesn't work.
Hi John,
A 100% coverage wheel isn't really all that effecient.
For instance on a 6/49 lottery the following is pretty
easy.
50% coverage in about 31 lines
75% coverage in about 55 lines
95% coverage in about 100 lines
As we get deeper into the coverage the cost will
begin to skyrocket to get to 100% closure and it
really isn't worth all the time and effort to
gain so little.
The current record is 163 lines for 100% and is
it really worth it to buy 63 more lines to gain
5% ??
It's fun stuff to do but is it really worth it ??
Gerry
Dick Adams
> especially Dick Adams. Dick, your surprise at my claiming
> 1 hour to produce a 26,6,3,3,130 wheel was justified!!
> To make things worse I replied to another post by Robert Perkis
> obviously wrong. I had not run the program for quite some
> time now. Provoked by your surprise I decided to time it.
> Yesterday I started the program and noted the time 17:48 and
> left. I didn't check my PC again until the next day by which
> time my program had finished and printed the time on the screen.
> It read 6:05 and so I quickly figured it started at 12 minutes
> to 6 and it finished at 5 past 6 so that's about 20 minutes ...
> wishful thinking, an honest mistake and an embarrassing claim.
> Subtracting the two times correctly I realize the program needs
> about 12 hours !!!
>
> Still if anyone has a machine which is 12 times faster than an
> AMD K6 200 ... then it would only take an hour :))
>
> Again apologies all around.
No apologies are necessary for wishful thinking or an honest
mistake. Also I see no embarrassment here.
If you are using Pascal, interpretive or compiled, it is fairly
slow. If you want to do number crunching, get a very high mhz
machine with a very large bus bar.
I once had a program that tied up a PC for 36 hours. I put it
on another computer and it finished before I returned from
making a sandwich.
Dick Adams
> John Smith wrote:
>> I had to look up eviserate. You've spelt it wrong.
>> According to my dictionary, it's "eviscerate" :))
> I don't know the correct spelling and only know that
> Dick Adams has never claimed to be a Wizard of Spelling.
> That's not a flame John, just poking a little humor or
> is that humour ??
It's funny no matter how you spell it.
Robert Perkis
I don't think he's looking for 3if6, he's looking for
3if3of6 and when you look at the multiple 3# prize
coverage of the 3if3in22n77c wheel we use for the first
half of the 163 wheel you see why. More like making a
wheel in lotwin32 http://www.lotwin32.com/ set for 5
or more 3# prizes for maximum return, though I don't
think it's going to happen in 759 tickets for 46 numbers
but it would be interesting to play with in some game
where tickets cost cents to the dollar. Saw some free
lotto game paying off in Indian Rupees, was like 1,000
to ten dollars. Wonder how many Rupees their lottery
tickets over there might go for. RP
Robert Perkis
Hate to reply to my own posts, but I really screwed this
one up. Here's what you should do John. While lotwin32
is the name of the software and the 32 bit program is at
http://www.lotwin.com/ not lotwin32.com, you need to go
here http://www.futuresoft.co.uk/lottery/ and get the 16
bit LotwinPick6 free version. You can test it to see
what coverage you get before you go through the free
registration process to see the actual results of your
attempt. Anyway, once you download and install Lotwin6
open the program, click [finished] on the auto box and
open the Greek 6/49 from the first pulldown menu. (If
you want to try working with all 49 numbers you have
to open a larger lottery like 6/51.)
Click on the left column "Number Sets" and a window will
open with columns, click the first 46 of them and then
[OK]. Now click on "Build Lines" and when that finishes
click on "Reduce". When that box opens, click on wins 5
prize 3#'s Maximum return leave the other settings and
go. The build will take a long time, perhaps overnight
but you can stop it at anytime once it gives you numbers.
When you stop it you can see the overall coverage of the
wheel for winning something in one of the prize tiers.
The above settings for 22 numbers gave me 100% overall
coverage in 73 combinations with a good chance of 1-5 4#
wins and 10-21 3# wins in an either or situation. Until
you register the copy it will put ?? in place of a number
in every one of the combinations, but you can still see
what kind of coverage you could get.
Send me an email if you get really stuck, try making some
smaller wheels first, they will build a lot faster. RP
Gerry
My advice is to not try this on a 200 MHZ machine
and Lotwin 6. It will probabbly take over your computer
for a few days. Tonight I will start a reduction with
Lotwin 32 and let it run overnight and see what comes out.
Sorry for the misunderstanding on what you're looking for
Gerry
Nick Koutras
Philippe wrote:
> Ok, Tom Ogilvy gave me an answer in Excel NG that Excel do not recognize
> more than 15 numbers then I look for myself in Excel help ( which I should
> have done before asking my question...but I was so sure that Excel could
> handle anything ) and he is right, Excel cannot handle more than 15 digits
> and all digits after the fifteenth turn to "0".
That is not correct
Excel can handle
Calculation specifications
Feature Maximum limit
Number precision 15 digits
Largest allowed positive number 9.99999999999999E307
Smallest allowed negative number -9.99999999999999E307
To display your set ID use string indicator (single quote)
>
> So when I enter "COMBIN(70,20)" then the answer was wrong as well ( for the
> last 4 digits only), and for sure Nick's worksheet could not give me either
> the right combination for an ID# above 15 digits but still works great when
> staying within 15 digits.
That is not correct
The error was in the subroutine which I converted very quickly to VBA
Enter the following statment below:
101 C(I) = C(I) + 1
If (V - C(I)) < 0 Then GoTo 201 '<= new line to add
This will correct the overflow error and will give you the correct set ID
>
> Now I would like to know if any of you guys knows a spreadsheet program that
> can accurately handle at least 20 digits and have the same capabilities of
> Excel for functions, formulas and VBA programming or is there a way to trick
> Excel and increase its capability in handling more than 15 digits.
Display the set ID as string!
>
> I am already using NthIndex from Ion Saliu that I thank again for his great
> program (but there is also a limitation in handling ID# above 15 digits) and
> between Ion and Nick I can work a lot more with lotto and keno ID#,
> but this is good only for one by one ID or combination and under 15 digits
> ID#.
> And in Excel my own basic formulae give me, as I know it now, 15 digits ID#
> max but I can past it all along my columns to know their ID# and work from
> there.
If you indend to make many calls to the same parameters V,K then
you shall use a dynamic programming table of the binomial table
which is what this program does. That way you will increase the speed to 100
fold
If you want more help on this please contact me privetly
Nick
Nick Koutras
John Smith wrote:
> Hello Royce and Dick,
>
> strange as it apparently seems to some I too use the "ID" in my lotto
> programs. In my attempts to produce a 46,6,3,3,759 wheel (please tell me
> someone has it on the net somewhere and put me out of misery !!),
You can not generate this Steiner system with 759 blocks
The reason is that V mod 6 is not 1 or 3
which is one of the conditions for such designs
For more info see Steiner systems
http://www.google.com/search?num=100&hl=en&safe=off&q=steiner+triple+systems&btnG=Google+Search
Ion Saliu
says...
• Have you checked out the latest NTHINDEX.EXE?
It handles now extended-precision numbers in the IEEE standard. The maximum is
18 to 19 digits. The range is between +-3.4 x 10^-4932 to +-1.2 x 10^4932. There
is nothing larger in the PC world!
An extreme game such as Keno 80/20 has a total of:
3.53531614221217E+18 combinations. As you can see, it is an 18-digit number.
The game you are interested in, Keno 70/20 has a total of 1.61884603662658E+17
combinations. The mid-point is combination #8.09423018313289E+16; the
combination is:
3-4-5-9-10-17-18-20-30-31-33-36-41-42-49-58-60-62-67-68.
Wouldn’t it be great to determine the CSN as fast as calculating the combination
for a given index? I don’t have enough time now to devise a specific algorithm.
The much-debated CSN formula is wrong because it does not take into account the
largest number in a lotto game. Somebody can have a head start, though. Take
first the lotto-6 game. Find a relation for simple combinations that can be
generated manually. For example, in the lotto 49/6 game, the combination
1-2-3-4-5-49 has a CSN=44. In the same game, the combination 1-2-3-4-6-7 has a
CSN=45. The same combination (1-2-3-4-6-7) has the following IDs:
CSN=46 in a 50/6 game;
CSN=47 in a 51/6 game, etc.
How about you trying a formula, Philippe? Hopefully, you’ll publish it in the
public domain. It serves science.
Ion Saliu
Nick Koutras
John Smith wrote:
> Hello Royce and Dick,
>
> strange as it apparently seems to some I too use the "ID" in my lotto
> programs. In my attempts to produce a 46,6,3,3,759 wheel (please tell me
> someone has it on the net somewhere and put me out of misery !!), I
> calculate the
> ID for any 3 number combination and that helps keep track of which
> combinations I have already covered. Using this technique and other
> programming "shortcuts" I have a program which can start producing
> 26,6,3,3,130 wheels in about an hour. I am not a mathematician and
> so I derived the logic for the code by just studying the data. It does
> however rely a short loop and that means processing power. So the
> purpose of this email is to ask you to please explain the formulas
> mentioned as I don't understand the symbolism C(...) etc.
> Again my math is very very basic ... :)
For a Tech Paper complete with a Genetic Algorithm to do such designs you can
find
here:
http://www.mcs.drexel.edu/~shartley/MCS770/index.html
Regards,
Nick
John Smith
My home 200 Mhz PC is always running a lotto program, 24/7. So did the
previous one. So does one at work which is an 850 or so Mhz PC. So did the
one before that. I'd say a Lotto program of one sort or another has been
running every day on a PC for the past few YEARS! The target has evolved
from the 12,6,5,5,132 wheel to the "dream" wheel of 46 numbers out of 49,
where 6 are picked and it has a 100% 3 win, if 3 are matched and all this in
759 games (46,6,3,3,759). Again, the apeal of the wheel is not the
guaranteed number of 3 number wins, but the efficiency of the design. I will
check for your response to the group ... !!
If all else fails, one of you people who seem to form the "core" of the
"interesting" activity on this list, could maybe organize a number crunching
project where a number of PCs (our PCs) each run a specific portion of the
total number of possible combinations (truly astronomical numbers). Just an
idea.
John Smith,
Athens-Greece
Gerry <tul...@earthlink.net> wrote in message
news:3B5068AD...@earthlink.net...
John Smith
I wouldn't be too surprised if it isn't possible. It would explain why no
one has been able to produce it !!
I started to look through all the Steiner system sites (again after first
trying them when I was pointed to them from the list when I first approached
the list), but they are just too theoretical for me ... This is how I figure
it (and thanks to Manfred Stampe for reminding me) :
759 games x 6 numbers each = 4554 total number occurrences / 46 different
numbers = 99 occurrences of each number.
759 games x 15 couples each (2 number combination) = 11385 total couples /
1035 couples possible from 46 number = 11 occurrences of each couple
759 games x 20 triples each3 = 15180 total triples / 15180 triples possible
from 46 numbers = 1 occurrence of each triple
So in these 759 games, each of the 15180 3number combinations which can be
produced from 46 numbers will occur exactly once, each of the 1035 3number
combinations which can be produced from 46 numbers will occur 11 times and
each of the 46 numbers will occur 99 times.
This logic can be applied for all other "dream" wheels which already exist
and also suggests a few wheels which don't. The 46,6,3,3,759 being among
them.
That's about as simple as I can explain it and for the purpose of furthering
this conversation any replies must be at least as simple ... :))
John Smith,
Athens-Greece
Nick Koutras <tl...@hotmail.com> wrote in message
news:3B506D48...@hotmail.com...
a3a38222
>
> > Hello Royce and Dick,
> >
> > strange as it apparently seems to some I too use the "ID" in my lotto
> > programs. In my attempts to produce a 46,6,3,3,759 wheel (please tell me
> > someone has it on the net somewhere and put me out of misery !!),
>
> You can not generate this Steiner system with 759 blocks
> The reason is that V mod 6 is not 1 or 3
Nick, this is a condition for the existence of Steiner TRIPLE systems,
not for Steiner systems in general. A Steiner system 46,6,3,3 in 759 blocks
is possible, because 46.45.44/6.5.4 is 759, an integer (showing the number
of blocks); also,
6/46 of 759 is 99, an integer (showing the number of times
each number participates in the 759 blocks);
5/45 of 99 is 11, an integer (showing the number of times
each pair of numbers participates in the 759 blocks);
4/44 of 11 is 1, an integer (showing the number of times
each triple of numbers participates in the 759 blocks).
This explanation somewhat duplicates the one given by J.Smith.
One can repeat the computations for 26,6,3,3 in 130 to see how it works.
Mathead
Gerry
>
> Gerry,
>
> My home 200 Mhz PC is always running a lotto program, 24/7. So did the
> previous one. So does one at work which is an 850 or so Mhz PC. So did the
> one before that. I'd say a Lotto program of one sort or another has been
> running every day on a PC for the past few YEARS! The target has evolved
> from the 12,6,5,5,132 wheel to the "dream" wheel of 46 numbers out of 49,
> where 6 are picked and it has a 100% 3 win, if 3 are matched and all this in
> 759 games (46,6,3,3,759). Again, the apeal of the wheel is not the
> guaranteed number of 3 number wins, but the efficiency of the design. I will
> check for your response to the group ... !!
>
> If all else fails, one of you people who seem to form the "core" of the
> "interesting" activity on this list, could maybe organize a number crunching
> project where a number of PCs (our PCs) each run a specific portion of the
> total number of possible combinations (truly astronomical numbers). Just an
> idea.
>
> John Smith,
> Athens-Greece
>
Seems to me anyone who runs ther home and work computers
24/7 for years might be a little preoccupied.
Good luck to you in finding your "dream wheel"
Gerry
Philippe
I will try all suggestions.
Thank you again.
Philippe
"Nick Koutras" <tl...@hotmail.com> wrote in message
news:3B506AAE...@hotmail.com...
Philippe
I do appreciate very much your comments as well as from all of you.
I did took already your update of NthIndex.
I am evaluating a formula and will publish my finding as soon as I am sure
that it is correct for any case.
Philippe
"Ion Saliu" <i...@nospam.saliu.com> wrote in message
news:Ll_37.19338$Kf3.2...@www.newsranger.com...
> . Have you checked out the latest NTHINDEX.EXE?
Philippe
I took 2 times the NthIndex believing that the second time was the updated
version.
There was my mistake...I thank you for your email.
I need to be a bit more careful before saying anything and I truly apologize
for my mistake to all of you and I hope I did not offended you too much...I
did not mean it.
Philippe
"Ion Saliu" <i...@nospam.saliu.com> wrote in message
news:Ll_37.19338$Kf3.2...@www.newsranger.com...
> . Have you checked out the latest NTHINDEX.EXE?