Lottery Probability

[Jay-qu]

well I say its not very real at all... you could strip back the balls make them all identical and the probability of drawing of drawing any 6 combinations of those balls (although there would be no way of telling which ball is which) would still be the same

[Turtle]

well I say its not very real at all... you could strip back the balls make them all identical and the probability of drawing of drawing any 6 combinations of those balls (although there would be no way of telling which ball is which) would still be the same

 

___Aha! Exactly! What is a valid 'way of telling' in this discussion. With no markings, the point is moot as you say. But, we have markings, we have numbers on the balls i.e. we DO have 'ways of tellings' , so I want to clarify what 'ways of tellings' we agree have validity.

___I have to laugh a bit :cup: , because I intend to 'just do it' soon enough; nevertheless, there is never too much common ground.

:hihi:

[Turtle]

____Ok, prop ready. A blank cellular array 49 rows by 15 columns. The numbered rows represent the numbers on the balls, the columns represent individual drawings. The number of columns grows by one with each succesive drawing.

___I haven't recovered any real data yet, but if there is a 6/49 game out there someone is following, we can use that data. Technically, we want the first game in the first column, but any starting point is OK as long as it comes from a real game & we don't miss recording each following new drawing data once we start. Initial conditions.

___Ok so far? Isssss everyyy one happyyy? :hihi:

[Turtle]

___We debated the idea of 'confounding' in all this, & if by that we mean not 'impossibe to understand' but 'difficult to follow', then confound it all & on we go.

___I have retrieved real 6/49 Lotto data for the table! These I have entered in the table attached to the previous post, & intend the same procedure for other additions. I made 6 entrys which constitute the actual first 6 drawings of the Washington State Lotto when they started 6/49 to replace the 6/44 game circa. late '80's early 1990's.

___ :hihi:

[Jay-qu]

Even though it is 'oldish' data it will be fine, so I am happy - you may continue...

[Turtle]

Even though it is 'oldish' data it will be fine, so I am happy - you may continue...

:cup: So in the first years of my investigation, I used nothing but paper & pencil; about '89 while recovering from an accident, I took a home-study computer course which included a computer. An 8088 IBM clone with 2 5 1/4" floopy drives & a mono-tone monitor. Ran MS DOS 3.21 if I remember at a whopping 8mhz & included GW Basic. I taught myself the language sufficient to program my analysis of the tables & it was on like Donkey Kong. :cup: It wasn't long before I ran up against the dreaded 64K code barrier of Basic A & GWBasic. The answer...TurboBasic from Borland. Not only did it allow chaining multiple segments of code 64K or less each, it is a compiled Basic & produced an .exe file with a single keystroke. Other amenities, multidimentional arrays, premade function commands, & stuff . :hihi: :cup:

___I never went beyond it to other languages other than in a cursory manner; I still use it. :cup:

___To the table! Yes to the Table! The first column is the first game & there is a filled cell contingent to the row index which coincides with the number of a drawn ball. In the first game the draw is 3 28 32 43 48 49. For our only feature so far, i.e. even/odd, the drawn combination is in the 3 even/3 odd group of the seven possible groups in the feature.

___Pausing for cogitation & comment. :cup:

[cwes99_03]

I don't know if I would bet on the very next game, as the longer you take data the more likely you will be able to predict an outcome. But I see a couple of numbers repeating there. Interested where the next 6 games' numbers wind up.

[Jay-qu]

___To the table! Yes to the Table! The first column is the first game & there is a filled cell contingent to the row index which coincides with the number of a drawn ball. In the first game the draw is 3 28 32 43 48 49. For our only feature so far, i.e. even/odd, the drawn combination is in the 3 even/3 odd group of the seven possible groups in the feature.

___Pausing for cogitation & comment. :cup:

 

well 3 numbers are over 40, 1 single digit number, all the numbers can be made from 5 numbers ie 2,3,4,8,9

 

oh and they are all divisible by 1 :hihi:

[Turtle]

___Just for everyone's clarification, the Table is in post #71 of this thread. I will edit in all our changes there. I overwrote the first jpeg with the second; I better at least save them separately.

But I see a couple of numbers repeating there.

___For clarification, do you refer to 48 & 49 in the first column?

 

well 3 numbers are over 40, 1 single digit number, all the numbers can be made from 5 numbers ie 2,3,4,8,9

oh and they are all divisible by 1

___On the last part first; never underestimate the importance of the trivial. Since divisability by 1 is a 'feature' of the numbers just as even/odd is a feature, then we put it in our list of features & move it to first position. What list you say? Why the new array we made to hold the list of lists, of which we have 2 lists & we make arrays for them as well. The first list is a list of numbers drawn in a single game which divide evenly by 1 & the second list is the list of numbers drawn in a single game which evenly divide by 2. Logically, we go ahead & make arrays to hold lists up to & including numbers drawn which divide evenly by 49.

___I have to post up or lose my signin; I still have to get to the bolded of Jayq's quote. :cup:

 

Continuing: On the bolded, the phrase 'single digit number' is the same as saying one number drawn under 10 & that is also saying it is less than 40 which makes it the same sort of 'feature' as 'over 40'. It is also a feature I intended to introduce; for simplicity sake, we make only one list of this feature type & call it 'Sevenths'. So for our #3 picked & from the table, it is listed in its new feature array as in the 1st seventh, 28 is in the 4th seventh, 32 the 5th seventh, & 43,48, 49 in the 7th seventh. We add the new array to the array list of lists. Pause to catch breath & see I have added some green horizontal lines to the table showing the divisions of the 'feature' Sevenths'. :hihi:

[cwes99_03]

actually i would be referring to 21 and 32, but by extension 48 and 49 and 3.

[Turtle]

actually i would be referring to 21 and 32, but by extension 48 and 49 and 3.

___Excellent. Now to their classification. Note that the features of 'divisiability' &'Sevenths' only reside if you will in a single column, i.e. the data mined is from one game alone. These features I call one-dimensional, as in a one-dimensional cellular automaton. (Not that I mean to say this IS an automaton, just borrowing applicable terms)

___cwes notes features which involve more than one game, these I call two-dimensional features; their names & descriptions are just around the corner.

___Back to JayQ's suggestion:all the numbers can be made from 5 numbers ie 2,3,4,8,9. That is a valid one-dimensional feature that I never thought of! Nice call! You found it Jayq, why don't you name it? Discoverer's rights you know. :cup:

___Just now starting my day, so I'm at least still a pot of coffee away from picking up the pace. :cup: :cup: :cup: :cup: :cup: :cup: :cup: :cup: :cup: :cup: :cup: :hihi:

[Turtle]

actually i would be referring to 21 and 32, but by extension 48 and 49 and 3.

 

___There is a one-dimensional feature invoked by cwes in the above; that is 48 & 49 drawn in the first game, or in other words 2 succesive numbers. I call this feature 'Couples'. I have updated the Table in post #71 & circled in Green the Couple in the first game (first column).

___As I encountered features I named them as I pleased & when I started programming the analysis I just naturally used these names as my variables. To get my programs from 3" floppies I went through an intermediate machine with a #" drive & a CD burning drive & then brought the CD to this machine. I have dozens of program files, some in chains of four or five 64K segments & moreover these programs make their own data files which number in the dozens as well.

___It is gratifying if not surprising that when I start my old TurboBasic on this machine, it opens in a DOS Window & appears to work A OK. Anyway, I seem to have left off the work abruptly & picking through without doing any dmage (i.e. accidently destroy some iiretrievable data) is coming along albeit slowly. I have found I have 'real' drawing data for a little over 200 games; the continuence of the Table in #71. :hihi:

[Jay-qu]

___Back to JayQ's suggestion:all the numbers can be made from 5 numbers ie 2,3,4,8,9. That is a valid one-dimensional feature that I never thought of! Nice call! You found it Jayq, why don't you name it? Discoverer's rights you know. :hihi:

 

call it the Q feature and when there is a draw the amount of single numbers that can make up the draw numbers can be its Q value eg draw 1 has a Q of 5 or 5Q... something like that :cup:

[Turtle]

call it the Q feature and when there is a draw the amount of single numbers that can make up the draw numbers can be its Q value eg draw 1 has a Q of 5 or 5Q... something like that :cup:

 

___Perfect. Q feature it is. Eventually we will take up the counting of how many variations of each feature exist; I have grown a little rusty in the counting techniques & I hope to rely on Craig, Bo, C1ay et. al when we need these calculations.

___Better add something new myself then, so a few more one-dimensional features. I hope I get the names right as I teased this out of some of my code. Just as we called Couples a feature by virtue of 2 cells occupied immediately adjacent in one column, I have called 2 cells separated by 1 empty cell in a column 'Friends', by 2 empty cells "Cousins', & by 3 empty cells "Aliens'. :hihi:

[Turtle]

Holding just a bit before moving to 2-dimensional features, as I want to firm up some counting. Do we agree that the number of ways to pick 6 even balls is 24*23*22*21*20*19? And for 6 odd balls we have 25*24*23*22*21*20 ways to pick them?

 

If so, is it also correct we have 24*23*22*21*20*25 ways to pick out 5 even & 1 odd?

:friday:

[C1ay]

Holding just a bit before moving to 2-dimensional features, as I want to firm up some counting. Do we agree that the number of ways to pick 6 even balls is 24*23*22*21*20*19? And for 6 odd balls we have 25*24*23*22*21*20 ways to pick them?

 

If so, is it also correct we have 24*23*22*21*20*25 ways to pick out 5 even & 1 odd?

:friday:

Those are the total number of permutations of the ball choices you've picked. Total permutations or arrangements does not represent the odds where the order of the set doesn't count though, i.e. 1,2,3,4,5,6 being the same as 6,5,4,3,2,1. To calculate the unique number of possibilities or combinations where order doesn't matter you must divide the total number of permutations by the factorial of the number of balls or 6! in this case, 720.

 

This said the total number of unordered sets of 6 even balls is 134596 and the number for odd sets is 177100. For 5 even and 1 odd in any order it is actually the same as it is for 6 odds since both are actually 25!/(6!(25-6)!).

[Turtle]

Those are the total number of permutations of the ball choices you've picked. Total permutations or arrangements does not represent the odds where the order of the set doesn't count though, i.e. 1,2,3,4,5,6 being the same as 6,5,4,3,2,1. To calculate the unique number of possibilities or combinations where order doesn't matter you must divide the total number of permutations by the factorial of the number of balls or 6! in this case, 720.

 

This said the total number of unordered sets of 6 even balls is 134596 and the number for odd sets is 177100. For 5 even and 1 odd in any order it is actually the same as it is for 6 odds since both are actually 25!/(6!(25-6)!).

 

___Excellent! Combinations of course, because order doesn't matter. The expression oxidised in my caranium. :friday:

___I bolded 'not represent the odds' because odds are just the probability over 1 & the probability is based on the counting. I only mean to get the counting right before we apply it to other features.

___I'll edit in the list of counts here.

6 Even/0 Odd----134596

5 Even/1 Odd----177100

4 Even/2 Odd

3 Even/3 Odd

2 Even/4 Odd

1 Even/5 Odd

0 Even/6 Odd----177100

___Correct so far? :eek: