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UK lotto
15-03-2016, 10:26 AM (This post was last modified: 19-04-2016 04:23 PM by Frank.)
Post: #51
RE: UK lotto
Okay Moses,

Before I start let me take you up on this point:-

(21-02-2016 12:15 PM)Moses Wrote:  Please do not come back and say I am wrong, having said all of these I have never seen you on my side to approve what I say is correct but I found you always in favour of Camelot and always been on their defensive side which makes me wonder!

Have a nice day
Moses


I think you will find, I am on the side of TRUTH whatever that may be. I cannot allow statements based on an incorrect understanding of statistics go unchallenged. I am sorry if you find this inconvenient, but the truth has to come out. If you had said the same things about the Knotty Ash treacle mine lottery I would also have tried to correct you. Its NOT about Camelot, I have my own criticisms of them, which you should be aware if if you read this and other forums. Its about Statistics! I'm not against you Moses, I respect you and the hard work you put in to your projects, but you do need to know what I'm about to tell you.

Let me explain why lotteries behave differently to your calculations, in the circumstances of your comaparisons. The reason why is surprisingly simple, but may not be immediately obvious, so I will take it step by step.

For any lottery when you calculate probabilities and odds they apply only to comparisons between ONE ticket and ONE result. Lets take a probability we all know and can agree on. The old match 3 odds in the 6/49 lotto.

Odds of a match 3 prize fr one ticket, one draw are one in 56.7. Lets call these the raw odds. Alternatively the probability is 1/56.7 and thats the raw probability.
If you go out and buy one ticket, they hold one draw, Fine. Those odds apply.

So what if you bought 2 tickets ? Well your chances of matching three when comparing TWO tickets with ONE result are doubled. Can we agree on that ? Implied within that is that your odds are halved. So the true odds are half of the raw odds. Alternatively, you could say that the probability of matches doubles.

So what if you bought 2000 tickets ? You have 2000 chances of matching 2000 tickets to ONE result. Your expected matched tickets goes up by a factor of 2000. Implied within this is that your true probability of match 3 goes up by a factor of 2000.

So lets turn the circumstances on its head now. Suppose in some parallel universe there existed a lottery where you buy ONE ticket, but they hold on the same day 2000 draws. Suppose your ticket is valid for ALL 2000 draws! you can win if your ticket matches 3 balls in any or all of the 2000 Lotteries.

Question :- what is the probability of you winning a match 3 prize that day ?

Well I put it to you that you still have 2000 chances of winning with your ticket so you still stand to match about 35 of those draws .and therefore your true probability = 2000 x (1/56.7)

So the rules are
1. :- the more tickets you hold, the higher the probability of any match when they are compared with ONE draw result. True probability= raw probability x T where T are the number of tickets.

2.:- The more draw results you are allowed to compare your ticket with, the higher the probability of finding matches with ONE ticket. True probability of a match = raw probability x N where N are the number of results you are allowed to match your ticket with.

So what if you were in a position to choose any ONE combination you like from a pool of 2000 pre-set lines of lotto numbers, and once chosen, that temporarily became a pseudo ticket; suppose you were allowed to compare it with 1999 other pre-set combinations to look for matches ? That would be the same as 2 above ? Yes ? so the probability of a match is increased by 2000, or 1999 to be exact..

When you had done that, suppose you were allowed to choose a different combination from the pool and make it your pseudo ticket, and compare that with the rest of the 2000 draws ? And work your way line by line, checking each 'ticket' to 1999 others until you'd got through them all. Each time you would find another set of matches to add to the ones you already found. Basically having multiple tickets as in 1 above. You'd actually have 2000 tickets each checking 1999 results.

What is the probability of finding match 3's ?

Can you see what is happening here? Every time you make a check:- your probability of finding a match to ONE DRAW are increased by 2000! compared with the original raw probability. Your number of matches are increased by 2000 - AND THAT IS FOR EACH DRAW YOU USE TO CHECK AGAINST.
So both of 1 and 2 above apply at the same time. Your number of matches to ONE DRAW increase by 2000 times. Plus you do this 2000 times (using a different 'ticket' each time) so you have about 2000 goes at this, mutiplying your total matches by ANOTHER 2000. so actually the number of matches are increased above the raw probability's rate by a factor of 2000 x 2000 = 4 million! The number of matches is a square law, based on number of draws. However, the matches are counted twice here, in this process so you actually have to halve the matches to get the true value. So its 2 million.


Using probability instead of odds, its easier to follow:-

Note that the true probability of matches = total number of matches / N/2, in this example N is 2000.

true probability = (2000 x x 2000 x raw probability )/(2 x 2000) , note that one of the 2000's cancels out.

therefore true probability= raw probability x 2000 /2. Note that raw probability = (1/56.7) for a match 3.

If were we looking for Matched linked triples in an unsorted 749 lottery then raw probability = 1/110554

Note that true odds = 1/true probability

Alternatively, True odds of a triple match= 110554/(2 xN )where N is the number of draws in your history. ( for linked triple 749).

So we would expect true probability to be 2000 x 1/(2 x110554) , which converts to odds of 110.4 to 1 . So you find about 20 matched triples in your nominated columns. Overall, using 5 linked triples to cover 7 balls the total matches would be 5 x 20 = 100 matches.


So what is the difference between the above scenario, and producing a list of 2000 old Lotto results and forensically comparing them for matches ? Can we not agree that your odds of finding matches between 2000 draws are reduced by a factor of half of 2000? I can tell you right now that any matches you have found, be it pairs or Triples in the UK results are perfectly normal, as predicted. They are similar to a control group of the same number of draws.

That's it in a nutshell, Moses. It does not matter what the type of match is, what its RAW probability is - or whether order is important. when you compare a fixed list of draws with each other and have the luxury of cherry picking which is your ticket and which 2000 others are your lottery result -your odds, I don't care what they are, the fact is that they are reduced by (in this example) 2000/2.

In fact the number of draws you find with your type of match (whatever it may be) is given by this equation:-

M= N x N X P . (number of matches is proportional to the SQUARE of number of draws.)

where M is the number of draws which have the match (each derived from a matched pair of draws)
N is the number of draws you are comparing with each other
P is the raw probability of the match you are considering.


This is confirmed by spreadsheet trials using random numbers. My speadsheets have buttons to sort a results list by whatever triple group e.g BCD etc and SHOW YOU HIGHLIGHTED, where the matches are. Filters allow you count them easily. I counted them all and put them in tables for easy reference. Random sets from Random.org were used in my trials. Anybody can get their own set prepared for use and paste them in and do their own research with them. Full instructions are supplied.
You don't have to take my word for it. Seeing is believing.

Have a nice day.

For those who wish to have a go at finding linked pairs and triples there is a spreadsheet for each. If you want some ready made random numbers the last link has some on a spreadsheet, but you can use your own.

https://www.mediafire.com/?2g1dn8u5ez99ial (linked pairs finder)
https://www.mediafire.com/?mxihbfcv77xiu20 (linked triples finder)
https://www.mediafire.com/?b4jby5fe25wru8b
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15-03-2016, 11:54 AM (This post was last modified: 15-03-2016 11:56 AM by Moses.)
Post: #52
RE: UK lotto
(15-03-2016 10:26 AM)Frank Wrote:  Okay Moses,

Before I start let me take you up on this point:-

(21-02-2016 12:15 PM)Moses Wrote:  Please do not come back and say I am wrong, having said all of these I have never seen you on my side to approve what I say is correct but I found you always in favour of Camelot and always been on their defensive side which makes me wonder!

Have a nice day
Moses


I think you will find, I am on the side of TRUTH whatever that may be. I cannot allow statements based on an incorrect understanding of statistics go unchallenged. I am sorry if you find this inconvenient, but the truth has to come out. If you had said the same things about the Knotty Ash treacle mine lottery I would also have tried to correct you. Its NOT about Camelot, I have my own criticisms of them, which you should be aware if if you read this and other forums. Its about Statistics! I'm not against you Moses, I respect you and the hard work you put in to your projects, but you do need to know what I'm about to tell you.

Let me explain why lotteries behave differently to your calculations, in the circumstances of your comaparisons. The reason why is surprisingly simple, but may not be immediately obvious, so I will take it step by step.

For any lottery when you calculate probabilities and odds they apply only to comparisons between ONE ticket and ONE result. Lets take a probability we all know and can agree on. The old match 3 odds in the 6/49 lotto.

Odds of a match 3 prize fr one ticket, one draw are one in 56.7. Lets call these the raw odds. Alternatively the probability is 1/56.7 and thats the raw probability.
If you go out and buy one ticket, they hold one draw, Fine. Those odds apply.

So what if you bought 2 tickets ? Well your chances of matching three when comparing TWO tickets with ONE result are doubled. Can we agree on that ? Implied within that is that your odds are halved. So the true odds are half of the raw odds. Alternatively, you could say that the probability of matches doubles.

So what if you bought 2000 tickets ? You have 2000 chances of matching 2000 tickets to ONE result. Your expected matched tickets goes up by a factor of 2000. Implied within this is that your true probability of match 3 goes up by a factor of 2000.

So lets turn the circumstances on its head now. Suppose in some parallel universe there existed a lottery where you buy ONE ticket, but they hold on the same day 2000 draws. Suppose your ticket is valid for ALL 2000 draws! you can win if your ticket matches 3 balls in any or all of the 2000 Lotteries.

Question :- what is the probability of you winning a match 3 prize that day ?

Well I put it to you that you still have 2000 chances of winning with your ticket so you still stand to match about 35 of those draws .and therefore your true probability = 2000 x (1/56.7)

So the rules are
1. :- the more tickets you hold, the higher the probability of any match when they are compared with ONE draw result. True probability= raw probability x T where T are the number of tickets.

2.:- The more draw results you are allowed to compare your ticket with, the higher the probability of finding matches with ONE ticket. True probability of a match = raw probability x N where N are the number of results you are allowed to match your ticket with.

So what if you were in a position to choose any ONE combination you like from a pool of 2000 pre-set lines of lotto numbers, and once chosen, that temporarily became a pseudo ticket; suppose you were allowed to compare it with 1999 other pre-set combinations to look for matches ? That would be the same as 2 above ? Yes ? so the probability of a match is increased by 2000, or 1999 to be exact..

When you had done that, suppose you were allowed to choose a different combination from the pool and make it your pseudo ticket, and compare that with the rest of the 2000 draws ? And work your way line by line, checking each 'ticket' to 1999 others until you'd got through them all. Each time you would find another set of matches to add to the ones you already found. Basically having multiple tickets as in 1 above. You'd actually have 2000 tickets each checking 1999 results.

What is the probability of finding match 3's ?

Can you see what is happening here? Every time you make a check:- your probability of finding a match to ONE DRAW are increased by 2000! compared with the original raw probability. Your number of matches are increased by 2000 - AND THAT IS FOR EACH DRAW YOU USE TO CHECK AGAINST.
So both of 1 and 2 above apply at the same time. Your number of matches to ONE DRAW increase by 2000 times. Plus you do this 2000 times (using a different 'ticket' each time) so you have about 2000 goes at this, mutiplying your total matches by ANOTHER 2000. so actually the number of matches are increased above the raw probability's rate by a factor of 2000 x 2000 = 4 million! The number of matches is a square law, based on number of draws.


Using probability instead of odds, its easier to follow:-

Note that the true probability of matches = total number of matches / N, in this example N is 2000.

true probability = (2000 x x 2000 x raw probability )/ 2000 , note that one of the 2000's cancels out.

therefore true probability= raw probability x 2000. Note that raw probability = (1/56.7) for a match 3

If were we looking for Matched linked triples in an unsorted 749 lottery then raw probability = 1/110554

Note that true odds = 1/true probability

Alternatively, True odds of a triple match= 110554/N where N is the number of draws in your history. ( for linked triple 749).

So we would expect true probability to be 2000 x 1/110554 , which converts to odds of 55.2 to 1 . So you find about 40 matched triples in your nominated columns. Overall, using 5 linked triples to cover 7 balls the total matches would be 5 x 40 = 200 matches.


So what is the difference between the above scenario, and producing a list of 2000 old Lotto results and forensically comparing them for matches ? Can we not agree that your odds of finding matches between 2000 draws are reduced by a factor of 2000? I can tell you right now that any matches you have found, be it pairs or Triples in the UK results are perfectly normal, as predicted. They are similar to a control group of the same number of draws.

That's it in a nutshell, Moses. It does not matter what the type of match is, what its RAW probability is - or whether order is important. when you compare a fixed list of draws with each other and have the luxury of cherry picking which is your ticket and which 2000 others are your lottery result -your odds, I don't care what they are, the fact is that they are reduced by (in this example) 2000.

In fact the number of draws you find with your type of match (whatever it may be) is given by this equation:-

M= N x N X P . (number of matches is proportional to the SQUARE of number of draws.)

where M is the number of draws which have the match (each derived from a matched pair of draws)
N is the number of draws you are comparing with each other
P is the raw probability of the match you are considering.


This is confirmed by spreadsheet trials using random numbers. My speadsheets have buttons to sort a results list by whatever triple group e.g BCD etc and SHOW YOU HIGHLIGHTED, where the matches are. Filters allow you count them easily. I counted them all and put them in tables for easy reference. Random sets from Random.org were used in my trials. Anybody can get their own set prepared for use and paste them in and do their own research with them. Full instructions are supplied.
You don't have to take my word for it. Seeing is believing.

Have a nice day.

For those who wish to have a go at finding linked pairs and triples there is a spreadsheet for each. If you want some ready made random numbers the last link has some on a spreadsheet, but you can use your own.

https://www.mediafire.com/?2g1dn8u5ez99ial (linked pairs finder)
https://www.mediafire.com/?mxihbfcv77xiu20 (linked triples finder)
https://www.mediafire.com/?b4jby5fe25wru8b

After all the time you had then you came up with this?
I just asked you to correct me on these following

Let’s find your Error

Any 6 from 49 has 13,983,816 right?
Any 6 numbers has 21 wheels, we agree that much, yeah? Short example below

A – B – C – D – E – F – G

A – B
A – C
A – D
A – E
A – F
A – G etc

But and big BUT

A can only make linked -pair with B and not to others that’s what we call LINKED-PAIR
Therefore for A and B to be linked at all time there can only cover 7 possible positions

A – B
X – A – B
X – X – A – B
X – X – X – A – B
X – X – X – X – A – B
X – X – X – X – X – A – B
X – X – X – X – X – X – A – B

So, there are only 7 possible positions available to be covered therefore 3422/7 = 488.8 to 1 which means in every 488 draws (almost 1/5 of the total current draws) we should witness one linked-pair to be repeated in one of the 7 possible positions.
BUT if the linked-pair are drawn in exact location or the same position then 3422/1 = 3422 to 1

Now the same calculation applies for linked-triples and if they are repeated in exact location then that triple are standing chance (from field of 49 numbers) 110544 to 1



Just highlight my error please on my above statement and tell me where I am wrong
Can you make another LINKED-PAIR between A and B apart from what I have showed you above?

One chain of 7 numbers has 5040 different settings, out of 5040 settings in how many lines A and B can be linked?

Thanks
Moses
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15-03-2016, 12:28 PM (This post was last modified: 15-03-2016 01:32 PM by Frank.)
Post: #53
RE: UK lotto
(21-02-2016 12:15 PM)Moses Wrote:  Some examples of triples from reverse wheels from UK lotto results

07/11/2007, 02,06,36,13,17,09,04 ---------- 05/05/2010, 03,08,47,10,36,06,02
22/07/1995, 03,21,22,02,23,40,24 ---------- 01/02/2012, 07,39,38,17,22,21,03
04/08/1999, 03,31,36,04,29,09,41 -----------28/09/1996, 19,26,23,39,36,31,03
21/01/2009, 03,32,25,45,28,29,48 ---------- 27/10/1999, 09,04,13,22,25,32,03
10/04/2013, 03,36,27,33,16,42,12 ---------- 01/06/2002, 13,41,19,44,27,36,03
19/03/2014, 04,27,25,21,31,49,26 ---------- 08/02/2014, 08,44,39,36,25,27,04
06/08/2003, 08,45,01,36,13,22,21 ---------- 25/03/1998, 25,10,06,31,01,45,08
28/01/2012, 10,25,31,40,28,12,01 ---------- 10/12/2005, 30,20,23,48,31,25,10
03/11/2007, 10,49,03,22,31,25,04 ---------- 28/07/1999, 14,32,30,46,03,49,10
07/04/2010, 11,08,20,47,33,43,49 ---------- 25/08/1999, 22,01,48,36,20,08,11

15/09/1999, 32,09,27,14,49,30,03
25/10/2014, 43,15,11,17,49,30,03

29/06/2013, 45,34,07,13,31,25,04
03/11/2007, 10,49,03,22,31,25,04

29/08/2009, 09,18,39,34,47,37,05
05/02/2011, 40,34,33,41,47,37,05

28/04/2012, 46,03,01,09,23,37,06
18/06/2014, 26,10,11,18,23,37,06

12/06/2010, 01,19,16,33,34,17,09
11/05/2011, 33,38,30,48,34,17,09

25/01/1997, 35,31,47,01,28,24,09
05/07/2014, 15,34,08,23,28,24,09

13/09/2003, 08,30,32,09,03,04,12
12/03/1997, 05,22,25,16,03,04,12 ---------- 18/03/2009, 39,02,41,05,22,25,27

16/05/1998, 34,04,44,10,02,06,21
02/01/2002, 20,24,29,32,02,06,21 ---------- 16/12/1998, 11,19,40,20,24,29,09

18/08/2007, 26,02,32,37,47,12,22 ---------- 11/10/2014, 26,02,32,23,08,05,18
11/07/2007, 09,46,10,43,47,12,22

14/12/2011, 03,43,30,28,10,25,31
28/09/2013, 14,12,48,46,10,25,31

10/06/2009, 30,08,23,21,46,03,26
04/07/2007, 44,32,13,22,46,03,26

27/01/1996, 16,41,38,17,43,42,28
14/07/2012, 13,27,46,29,43,42,28

05/06/2010, 23,24,22,05,29,26,31 ---------- 25/06/2008, 36,23,24,22,11,12,26
29/06/2005, 12,44,07,23,29,26,31

01/03/2000, 04,12,15,30,10,08,34
08/09/1999, 38,22,17,36,10,08,34

16/10/2013, 24,35,15,26,31,12,36
06/11/2010, 39,34,22,30,31,12,36

03/05/2003, 07,03,49,46,06,29,37
10/03/2010, 23,01,34,13,06,29,37

05/11/2003, 47,22,18,10,20,12,38
08/05/2013, 31,15,40,33,20,12,38

03/06/1998, 17,41,23,18,01,33,42
18/10/2014, 30,47,40,22,01,33,42

07/06/2008, 14,44,37,05,09,38,42
01/06/2011, 18,02,07,45,09,38,42

26/08/1998, 43,26,27,03,30,20,45
13/08/2014, 11,05,23,09,30,20,45

17/09/2003, 15,29,21,09,16,03,46
10/05/2014, 10,05,08,17,16,03,46

18/04/2007, 30,41,17,08,11,32,47
11/04/2007, 08,42,35,21,11,32,47

.................................
What amazes me is, you and others have not said one word about the identical repeated triples which I highlighted it in my earlier post which statistically impossible to be draw in such a way or even from the latest two draws two linked numbers 15,59 to be drawn in two draws on the row so what is the probability of that?
17/02/2016, 05,15,59,51,33,47,07
13/02/2016, 48,23,16,39,15,59,36

Isn’t it true the probability is 59x58 = 3422 but it occurred in two consecutive draws?????
Then repeated triples probability from 49 numbers lottery is 49x48x47 = 110544 but it is happening within 2000 draws over and over again??????????


Moses

Moses my only reason for posting in this thread at all is in reponse to the above. I quoted this at the time.

I come up with "this " as you call it to explain the matches you can make and the spurious deductions you made from your assumption that such matches in a set of results were impossible. You clearly don't want to know what I have told you because you choose to ignore it, and you don't want to look at spreadsheets, you don't want to look at control groups. I wonder why ?

Instead of being grateful,you put up a smokescreen, making the issue about something else. The issue I have covered changes the odds of everything in a results list ( being compared) by a factor of thousands and you don't want to know ?
Hopefully other people will be interested in what I have to say and can make an informed decision about statements like the one you made above and draw their own conclusions.
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