Lottery Probability

[C1ay]

___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:

6 Even/0 Odd----134596

5 Even/1 Odd----177100

4 Even/2 Odd----212520

3 Even/3 Odd----232760

2 Even/4 Odd----232760

1 Even/5 Odd----212520

0 Even/6 Odd----177100

[Turtle]

6 Even/0 Odd----134596

5 Even/1 Odd----177100

4 Even/2 Odd----212520

3 Even/3 Odd----232760

2 Even/4 Odd----232760

1 Even/5 Odd----212520

0 Even/6 Odd----177100

:friday: :eek: :eek: :eek:

Oh, and ... :eek:

 

___The same type of counts derive from the other features as well, e.g. we may count how many different ways to get couples. We procede for now without further counting, but with its method.

___Consider now the 2-dimensional array constrained on the Table attached in post #71 by just the first 5 games. :doh: I only have 5 entered so far! All the better; consider them. See that in 3 places, 2 occupied cells lay together as do Couples, but side-to-side, not one above another. This feature I call Adjoining. It is a 2-dimensional feature. What others do you 'see':cup:

[CraigD]

Counting is what computers were made for!

 

Here’s a quick program to count even/odd number combination:

K  S M=6,A=49
F N1=0:1:M S A(1)=A+12,A(0)=A2,C(N1)=1 F N=1:1:M S G=N>N1,C(N1)=C(N1)*A(G),A(G)=A(G)-1
S F=1 F N=1:1:M S F=F*N
S C=0 F N1=0:1 W N1," even/",M-N1," odd: ",?16,$J(C(N1)/F,16),! S C=C(N1)+C I N1=M W "total",?16,$J(C/F,16),! Q

It’ll give you this:

0 even/6 odd: 177100

1 even/5 odd: 212520

2 even/4 odd: 232760

3 even/3 odd: 232760

4 even/2 odd: 212520

5 even/1 odd: 177100

6 even/0 odd: 134596

total 1379356

 

Matching C1ay’s numbers, and totaling to the correct 49!/((49-6)!*6!).

 

I can’t see how this can lead anywhere, though – for an effect to emerge from a chaotic system, there has to be some underlying physics. For real Lotto machines, there isn’t – In principle, you could randomly renumber the balls before each drawing, without effecting the machines initial conditions. This would leave the actual balls drawn the same, but alter any relationship between it and the numbers on the balls. Since most state drawing replace the balls with every drawing, this is close to what actually occurs.

 

:friday: Repent, y’all, and turn your arithmetic energies to something productive!

[Turtle]

Counting is what computers were made for!

 

Here’s a quick program to count even/odd number combination:

K S M=6,A=49
F N1=0:1:M S A(1)=A+12,A(0)=A2,C(N1)=1 F N=1:1:M S G=N>N1,C(N1)=C(N1)*A(G),A(G)=A(G)-1
S F=1 F N=1:1:M S F=F*N
S C=0 F N1=0:1 W N1," even/",M-N1," odd: ",?16,$J(C(N1)/F,16),! S C=C(N1)+C I N1=M W "total",?16,$J(C/F,16),! Q

It’ll give you this:

0 even/6 odd: 177100

1 even/5 odd: 212520

2 even/4 odd: 232760

3 even/3 odd: 232760

4 even/2 odd: 212520

5 even/1 odd: 177100

6 even/0 odd: 134596

total 1379356

 

Matching C1ay’s numbers, and totaling to the correct 49!/((49-6)!*6!).

 

I can’t see how this can lead anywhere, though – for an effect to emerge from a chaotic system, there has to be some underlying physics. For real Lotto machines, there isn’t – In principle, you could randomly renumber the balls before each drawing, without effecting the machines initial conditions. This would leave the actual balls drawn the same, but alter any relationship between it and the numbers on the balls. Since most state drawing replace the balls with every drawing, this is close to what actually occurs.

 

:friday: Repent, y’all, and turn your arithmetic energies to something productive!

 

:eek: and :eek: and :doh: and :eek:

 

___Wave for the programming; we'll need it

___Driving; I've got the wheel so you have plenty of freedom to site see (sight see? :doh: )

___Laughing hihi; I mentioned early on that we might change the symbols; however, they don't. Whatever 'they' do, I intend to map it, analyze the map, & show a narrow group of outcomes is more likely than probability belies.

____Hyper laughing; call it 'recreational' math & we can argue the merits of recreation in the social science arena.

___Allllll aboooooard! :eek: :eek:

[Turtle]

Here's something on how the balls work; I have more but lost it. Going back in. BRB

http://www.playuklottery.com/languages/eng/faq.asp#12

:friday:

 

Love the speedy vehicle! Sorry fo the squealing.

http://www.lotterypost.com/threads114548.htm

___This is what I intend to map, whether its 'chaos theory' or not, it is a view. One can never have too many maps! :eek:

[dasraiser]

hi folks

 

i'm not stepping into your number game, I'm just popping in to share my opinion for the probabilities for a 6/49 draw. I have to admit i don't quite understand the underlying math here, as in 49!/6! try it for a 1/4 draw this produces incorrect results! so i'm guessing that the formula is 4!/(4-1)! except when you use 3/4 draw it falls flat on it face. :friday:

 

So to try and answer Iron4ever's original post if you take the formula for the lottery as

 

n/m n=No balls drawn in a m ball lotto, the probabilities for an n ball draw is an

 

m bit number with all combo's of [n bits set to 1 and m-n bits set to 0]. (#1) fact.

 

So to answer your question, 123456 has exactly the same chance as any other combo of 6 numbers (and will probably happen at some point in time, will people see this as a sign of something special i don't know, but given an infinite amount of time/draws anything is possible so i guess no, not really).

 

As for any same number being drawn from one week to the next the odds are quite small ie the first ball from the previous week has a 1:49 chance, then the next a 1:48 etc in fact the odds improve with the total number of balls being drawn, however taken as a whole #1 probabilities still apply over the system.

 

Furthermore even though chaos is the underlying mechanics behind the lotto the probability still holds for #1 and cannot be changed by fudging mathematics to suit (in the case of 'odds' i call this phenomena 'bookies law of mathematic probabilities' (they always win))

 

I could go further to say that taking the total accumulative amount each ball has been drawn and using only balls with the smallest number will give me a better chance of predicting the outcome (as an infinite No of draws should yield all balls having been drawn the same amount of times) , although this looks good chaos will throw this in the bin and it will still have #1 probabilities.

 

So to conclude, the probabilities are fixed when chaos is involved (not in the case of a computer random number generator (just a math formula) unless it's seed can be guaranteed to random, even then it is constrained by the size of it bits). No matter how good you mathematical predicting model is nothing is guaranteed except #1, even if absolutely every piece of information can be gathered, however taking measurements will affect the outcome! so #1 still applies.

 

regards

 

(and please feel free to rip this apart :eek: )

[CraigD]

… as in 49!/6! try it for a 1/4 draw this produces incorrect results! ...

The formula for the number of ways C to select N from a collection of M, where order is not important, is C= M!/((M-N)!*N!). So, for M=49, N=6, C= 49!/(43!*6!) = 49*48*47*46*45*44/(2*3*4*5*6) = 13983816. For M=4,

N=1, C=4!/(3!*1!) = 4.

… (and please feel free to rip this apart :friday: )

Other than the math vagueness, I think you’re pretty right on with the rest of your points.

[Turtle]

hi folks

i'm not stepping into your number game, I'm just popping in to share my opinion ...

 

___This is why I'm driving a bus; the more, the merrier.

___Can't stay long as this isn't my computer & the guy wants on. I remind you that the data in Table is REAL, from a lotto machine with balls. I haven't looked ahead, but if I bought all the tickets EXCEPT those having 6/0 5/1 1/5 & 0/6 even odd combos, will I (we) win game # 6? Foget odds, forget value, forget what is the jackpot. Place your bets ladies & germs. :friday:

[cwes99_03]

So to try and answer Iron4ever's original post if you take the formula for the lottery a

I believe it was answered in post number 2. Thanks.

So to answer your question, 123456 has exactly the same chance as any other combo of 6 numbers

Yep, thats what post 2 said.

Furthermore even though chaos is the underlying mechanics behind the lotto the probability still holds for #1 and cannot be changed by fudging mathematics to suit

Don't know what you call fudging math. Chaos is applied math (i.e. physics).

49! means 49x48x47x46x.... get it?

As for any same number being drawn from one week to the next the odds are quite small ie the first ball from the previous week has a 1:49 chance, then the next a 1:48 etc in fact the odds improve with the total number of balls being drawn, however taken as a whole #1 probabilities still apply over the system.

I don't think you realize what is being asked, but you give the odds for any ball being draw first, and then any ball being draw second (note any means the size of your set is 1) Now we are again talking mathematical probability, and the actual question is what is the odds of a numbered ball being drawn one week, and again the next week. And since you are discussing mathematically, I will say even chances, (since the underlying mathematical rule says that they have to be fair.)

Ok, enough ripping on my part, next contestant step right up.

[Jay-qu]

Ok im here now! Just sat my last english exam EVER (I hope) :friday:

 

I sure missed a lot... :friday: you guys are moving quick

 

so 2 dimensional features:

-looking at each 7th the 1st and 7th both have 6 draws (from 5), the 3rd and 5th have 5 from 5, the 4th has 4 from 5 and the 2nd and 6th have 2 from 5

actually looking really close now down 7th's we have 6-2-5-4-5-2-6 Palindrome! :friday:

 

-looking across collumns (like what you call cousins) some numbers have been drawn up to 3 times some not at all (note that after 5 draws its not yet possible to have drawn each and every number, so I find it curious that some have been drawn thrice at this point)

also there has been no game so far to have one draw in each 7th

 

my game #6 numbers 11-9-23-30-37-45

[dasraiser]

thanks :friday: , i did completely mess up the math i forgot to balance the eq with both the (m-n)! and the *n! , basically an abbreviated form of #1 (should have written eq.1 for clarity sorry).

 

The odds for a ball marked '1' will have a 1 in 49 chance of being drawn 1st or a 1 in 48 chance of being drawn 2nd or a 1 in 47 chance of being drawn 3rd etc, that's my point, quite small odds.

 

Oh i did read all of this thread but forgot this was mentioned when i posted (easy to do with long threads, got side tracked)

 

regards

[Turtle]

Ok im here now! Just sat my last english exam EVER (I hope) :friday:

I sure missed a lot... :hihi: you guys are moving quick

so 2 dimensional features:

-looking at each 7th the 1st and 7th both have 6 draws (from 5), the 3rd and 5th have 5 from 5, the 4th has 4 from 5 and the 2nd and 6th have 2 from 5

actually looking really close now down 7th's we have 6-2-5-4-5-2-6 Palindrome! :friday:

 

-looking across collumns (like what you call cousins) some numbers have been drawn up to 3 times some not at all (note that after 5 draws its not yet possible to have drawn each and every number, so I find it curious that some have been drawn thrice at this point)

also there has been no game so far to have one draw in each 7th

my game #6 numbers 11-9-23-30-37-45

___Numbers actually drawn: 1-6-21-29-45-49

Jayq has one number right, but wins nothing. I don't win the jackpot, I spent around $7 million virtual dollars(2 picks for a dollar then, minus the even/odd tickets I didn't buy)

I did win a lot of virtual dollars back because they have prizes for 5 numbers right, 4 right & 3 right. Still a loss for me; however I said in the beginning you have to expect to lose.

___I mentioned not mentioning value, & in the lottery, timing is everything. Clearly spending $7 million for a $1 million win is short sighted. We fix that by eliminating more combinations by using rules on the feature counts &/or we wait to play until the jackpot at least covers our bet. I don't have the jackpot data to go with this or I would use it for fun.

___On the bolded of JayQ's quote...all good. We make arrays & files to hold our counts for all features. We have 6 records in the Couple count file & 2 records in the 'by groups' of five category files. :friday: Off now it's late; I'll update attached table in post #71 with the new draw.

[Iron4ever]

I don't have the jackpot data to go with this or I would use it for fun.

.

 

Here is a link to some jackpot data for the UK lottery. The UK version has used 8 sets of balls and 12 different machines, since its introduction in 1994. If you click on Download Draw Histories it will give you all the winning numbers, ball sets and machines since the UK lottery began.

 

 

http://www.national-lottery.co.uk/player/p/results/resultsHistory/resultsHistoryAction.do

[Turtle]

Here is a link to some jackpot data for the UK lottery. The UK version has used 8 sets of balls and 12 different machines, since its introduction in 1994. If you click on Download Draw Histories it will give you all the winning numbers, ball sets and machines since the UK lottery began.

 

 

http://www.national-lottery.co.uk/player/p/results/resultsHistory/resultsHistoryAction.do

 

I have a set of drawn numbers, just not what the jackpost was at each drawing; they probably have it archived too. The Jackpost amount isn't necessary to the Tabular Analysis per se, but rather would make it a little more fun seeing how much we (I) loose or win with the method. :friday:

[Turtle]

___I just spent some time looking for the past records I have used from the Official Washington site; seems you have to phone in for data pre-1993. Not. :friday:

___In doing that search, I found no end of contentious this-n-that about the topic we have at hand, & every bit similar to our discussion. In looking back over this thread, I see a lot of 'yes, but...' & 'that's true, however...'; what I haven't seen is the dreaded 'illucid' of the Velvet Hammer.

___Anyway, I have current researches ongoing that need my attention & I simply have to sum up here, velvet hammer or no for efficiency's sake. I have shown you my approach & we agreed on the math, i.e. the counting & isomorphism of the data to the table, the rest seems to be a matter of belief regarding what one can addeuce from that. :friday:

[Jay-qu]

ohhh, so are you saying the ride ends here? we where only just getting started!

[Turtle]

ohhh, so are you saying the ride ends here? we where only just getting started!

___ :friday: Pretty much; at least I'm too tired to drive or ride, so it's off the bus and afoot for me. I pointed 'a' way, not 'the' way; it's all mapped out back there behind us. To me, it is a sapid mapping, but one has to See it for one's self.

 

 

 

:friday: