UK Lotto 6/49 Formulas to calculate Average appearances of Pairs

S

Sammy

Member
Hi All,

UK 6/49 Lotto.

Using Excel can anyone provide me with formulas to calculate:


1) the average number of times any pair of numbers can appear together.

2) the average number of times any pair of numbers can appear together from a pool of 10 numbers from the 49.

3) the average number of times two specific numbers can appear together.

4) the average number of times two specific numbers can appear together from a pool of 10 numbers from the 49.


Thank you,
Sammy
 
CMF

CMF

Member
Using the Combin function in Excel

An integer can be expected on average to appear 1 in 49/6 or 1 in 8 draws. The reality is this is just a guide as the integer 32 did not appear for 85 draws in the Washington 6/49 game.

The number of CombTwos in a 6/49 game is given by the Excel Combin worksheet function ie Combin(49,2) to give 1176. Similarly, the CombTwos for a Pool of 10 is Combin(10,2) to give 45. Also Combin(6,2) is 15.

Over 100 draws we have 600 integers with of course uneven repetition. The CombTwos will also have uneven representation. Theoretically, over 100 draws we have 1500 CombTwos so it is possible but unlikely to have all the 1176 CombTwos represented ie 1500/1176 = 1.27. Proportionately, 45 of the 1176 CombTwos from Pool 10 could appear once as they all have equal opportunity to be represented albeit unevenly.

It appears to me you are looking for certainty to the extent where it will give you an advantage but it doesn't exist. Implicit in your post is the assumption that the particular Lotto game's history of draws is more relevant than any other 6/49 history and that there is a limit to the absence of an integer or subset such as a CombTwo (which is not paid on).

If you are after a rational analysis I suggest you look at:
Lotto History Absence and Occurrence Myths Exposed
http://lottoposter.com/forum_posts.asp?TID=650

ANALYSIS OF LOTTO DRAW HISTORY - THE FINAL WORD
http://lottoposter.com/forum_posts.asp?TID=638&FID=46&PR=3

Colin Fairbrother
 
blitzed

blitzed

Member
CMF said:
An integer can be expected on average to appear 1 in 49/6 or 1 in 8 draws. The reality is this is just a guide as the integer 32 did not appear for 85 draws in the Washington 6/49 game.
Colin Fairbrother
Click to expand...

Many people likely got burned chasing that #32, a skip of 85 draws is way out on the fringes of probability. I do not know if Excel has Binomial Distribution function...but I mucked around in OpenOffice Calc, at 75draws there is .01% probability of a number skipping that long, anything beyond that is 0%.
=B(75, 6/49, 0)

here is a chart from one of my spreadsheets...showing probabilities at 28draws of 6/49:
Times a Number is Drawn | Probability
0x 2.58%
1x 10.08%
2x 18.99%
3x 22.96%
4x 20.03%
5x 13.41%
6x 7.17%
7x 3.15%
8x 1.15%
9x 0.36%
10x 0.09%
11x 0.02%
12x 0.00%

Sometimes people can get lucky using probabilities as a guide...I usually rule out say the upper & lower 5% of probability.

Colin, I checked out the links...you are absolutely right, best to construct a set of picks which utilizes the entire playfield. Otherwise it is easy to get clobbered by a monkeywrench such as the #32 example you cited.

cheers!
blitzed:thumb:
 
C

chilibill

Member
Draw History usage foolish?

Blitzed,
I read Colin Fairbrother's link on the foolishness of using Draw History to predict future results. Do you agree with him ? If so, what to do? I have Gail Howard's software and books, and have been looking at Pick3Stat. If using Draw History to predict is foolish, what would you suggest in it's place?
chilibill
 
S

Sammy

Member
Hi Colin,

Thanks for reply and information.

Hope you can shed some light on calculation of "any pairs" as opposed to a "specific pair". Is there a difference in calculation?

CMF said:
An integer can be expected on average to appear 1 in 49/6 or 1 in 8 draws. The reality is this is just a guide as the integer 32 did not appear for 85 draws in the Washington 6/49 game.

The number of CombTwos in a 6/49 game is given by the Excel Combin worksheet function ie Combin(49,2) to give 1176. Similarly, the CombTwos for a Pool of 10 is Combin(10,2) to give 45. Also Combin(6,2) is 15.

Over 100 draws we have 600 integers with of course uneven repetition. The CombTwos will also have uneven representation. Theoretically, over 100 draws we have 1500 CombTwos so it is possible but unlikely to have all the 1176 CombTwos represented ie 1500/1176 = 1.27. Proportionately, 45 of the 1176 CombTwos from Pool 10 could appear once as they all have equal opportunity to be represented albeit unevenly.

It appears to me you are looking for certainty to the extent where it will give you an advantage but it doesn't exist. Implicit in your post is the assumption that the particular Lotto game's history of draws is more relevant than any other 6/49 history and that there is a limit to the absence of an integer or subset such as a CombTwo (which is not paid on).
Click to expand...

I'm not looking for certainty but a formula that can calculate the average appearances of pairs. I mention the Lotto merely to inform which Lotto I'm looking at.
CMF said:
If you are after a rational analysis I suggest you look at:
Lotto History Absence and Occurrence Myths Exposed
http://lottoposter.com/forum_posts.asp?TID=650

ANALYSIS OF LOTTO DRAW HISTORY - THE FINAL WORD
http://lottoposter.com/forum_posts.asp?TID=638&FID=46&PR=3
Colin Fairbrother
Click to expand...

Could you let me know if there is a difference in the calculation of "any pair" as opposed to a "specific pair". How is the following calculated:

3) the average number of times two specific numbers can appear together.

4) the average number of times two specific numbers can appear together from a pool of 10 numbers from the 49.

Thank you,
Sammy
 
blitzed

blitzed

Member
chilibill said:
Blitzed,
I read Colin Fairbrother's link on the foolishness of using Draw History to predict future results. Do you agree with him ? If so, what to do? I have Gail Howard's software and books, and have been looking at Pick3Stat. If using Draw History to predict is foolish, what would you suggest in it's place?
chilibill
Click to expand...

hiya chilibill, I think best bet on big lottery is to play the entire number-field, using a minimal set of picks.
http://crazynuts.hollosite.com/649_lottery_picks/#spectrum_set

however, I am not adamant about ruling out Draw History...sometimes probability indicators can prove to be lucky.

also, many times I can not resist betting against patterns...tonight's 5/39 draw was: 35 36 32 04 37 so if I was to play tomorrow I would likely limit picks to only one number in the 30's range if any. #37 hit three times in the last 5draws, which is on the fringes of probability as .25%.

as for pick3 lottery, I usually bet small box wheels, mostly comprised of the probable digits and pick one digit from the last draw which I suspect would be the most likely to possibly repeat...for example, lastnight's draw was 880, so I would have chased the 0, and tonight's draw was 409...likewise I would have shot for unmatched tonight since previous two draws were doubles. I usually weight my set of picks according to how certain I am of the draw falling doubles or unmatched.

cheers!
blitzed:thumb:
 
CMF

CMF

Member
Occurrence of CombTwos in UK 6/49 Lotto game

Sammy

As previously pointed out the Excel Combin function can be used to ascertain the possible CombTwos for a 6/49 Lotto game ie Combin(49,2) gives 1176.

For the period 19/11/94 to 12/1/2011 we have 1572 draws in the UK 649 game. Each of the possible CombTwos are represented and as expected some appear more than others. Theoretically we would expect for 1572 x 15 = 23580 CombTwos divided by 1176 for each to appear about 20 times. However, some appear 35 times others just 7. The measurement that is usually used to show the extent of fluctuation from the average is Standard Deviation. Check it out at the MathsIsFun site.

Here is a truncated sample for some of the pairs -
02 23 35x
25 32 35x
09 27 34x
19 44 34x
35 39 33x
38 46 33x
01 38 33x
.
.
.
01 21 8x
07 08 8x
21 26 8x
07 36 7x
05 36 7x

Just doing a quick average on these 12 extremes gives about 23.

If you use Excel then you have MSQuery and I think you will find that is a better choice for working out aggregates than using Excel formulas. To get you started see
Enumerating Combinations or Permutations
http://lottoposter.com/forum_posts.asp?TID=649

Colin Fairbrother
 
CMF

CMF

Member
Grouping of Occurrence Counts for CombTwos UK 5/49 Lotto

Sammy said:
Hi Colin,

Thank you very much for your assistance and suggestions: much appreciated.

Sammy
Click to expand...

You're welcome.

For the 1572 draws in the UK 6/49 Lotto here is a breakdown on the Occurrence Counts: -
Count Count of Count
19 117
20 104
21 101
22 96
17 91
18 89
23 83
24 67
15 62
25 61
14 53
16 52
26 39
27 32
13 32
12 27
29 14
30 9
28 8
11 7
31 7
32 5
10 5
8 3
34 3
33 3
9 2
35 2
7 2

Colin Fairbrother
 
bloubul

bloubul

Member
Davinci Matrix for Lotto

Hi All

Can any one please help me with info on how to compile this matrix.

Thanks in Advance

BlouBul : cool:
 
Frank

Frank

Member
CMF said:
You're welcome.

For the 1572 draws in the UK 6/49 Lotto here is a breakdown on the Occurrence Counts: -
Count Count of Count
19 117
20 104
21 101
22 96
17 91
18 89
23 83
24 67
15 62
25 61
14 53
16 52
26 39
27 32
13 32
12 27
29 14
30 9
28 8
11 7
31 7
32 5
10 5
8 3
34 3
33 3
9 2
35 2
7 2

Colin Fairbrother
Click to expand...

Colin , I find your table of counts very interesting since it differs from mine over the same number of UK draws. Both our checksums work out OK, 1176 and 23580 (pairs drawn over 1572 draws).

mine is..
19 117
20 108
22 99
21 96
17 90
18 89
23 83
24 65
15 58
25 62
14 53
16 54
26 39
13 34
27 31
12 26
29 14
30 9
28 9
11 8
31 7
32 5
10 5
9 3
34 3
33 3
7 2
35 2
8 2

I can only conclude that we are analysing different versions of the same lottery. Might I ask what source you used for your results ?
I use http://lottery.merseyworld.com/Winning_index.html

Perhaps I might check my spreadsheet against your Lotto results.
Thanks.
 
CMF

CMF

Member
Frank

Scroll down and you will see an advertisement for LottoPro which gives you a well formatted DBase database of UK Lotto results compared to the poorly formatted source you mention.

Colin
 
Frank

Frank

Member
Just to follow up on that Colin, I looked at the site you suggest and could not find any readily downloadable results files for non users of that software as a password is required. I have no desire to download that software.

I therefore went on the other tack of verifying that the Merseyworld source I mentioned was an accurate source. I requested from Camelot ( The operator of the UK lottery) a spreadsheet of all the past results. This took a few days for them to provide, but I can now confirm that my usual source given above has an accurate database of past results.
As for it being a poorly formatted source, I must beg to differ. It has available CSV formatted files which can be imported into spreadsheets and be in use in the correct cells within 2 minutes of downloading. Perfect for spreadsheet users. But more importantly it is accurate.

Frank
 
CMF

CMF

Member
ID 178 and 179 numbers are the same ie 20 22 26 36 40 41. I pointed out this and other errors to John Lake, the author of LottoPro, years ago when combining various 6/49 games into my AllWorld database and assumed he had done the corrections his end

Colin Fairbrother
 
Frank

Frank

Member
CMF said:
Frank
Correct where necessary: -
http://lottoposter.com/forum_posts.asp?TID=662&PID=1252#1252
Colin
Click to expand...

Hi Colin,

You will be pleased to hear that all the results you published above are correct ! They match the Camelot database file.

The interesting thing about draw 178 was that it was not drawn on its normal draw day, Saturday 6th Sept 1997 as a mark of respect on the day of Princess Dianas funeral. It was drawn on Sunday 7th Sept 1997 .

There were 6 additional special, or bonus draws at various dates in Lotto history which are never included as qualifying Lotto draws fror statistical purposes as these draws did not draw a bonus ball.

In view of both our data sources being correct, this does raise the question of why our pairs count of counts differed. I can only look into other checking systems to see whether my analysis is incorrect.
Thanks for your help Colin.

Frank
 
CMF

CMF

Member
Don't worry Frank I updated the 6/49 results so that the duplicate entry 20 22 26 36 40 41 was removed and to make up the 1572 draws, entry 07 08 21 24 33 34 was included and my count of the counts of the CombTwos agrees with yours.

Of course to an outsider it's all gobbledygook but it keeps the brain ticking over.

For anyone using the MerseyWorld results you can combine the date parts into the more usual Date format by using the CDate function as in CDate([DD] & "/" & [MMM] & "/" & [YYYY]).

Colin Fairbrother
 
You must log in or register to reply here.

Sidebar

Top