Lottery Probability

[cwes99_03]

You might clarify your meaning here. Are you implying i don't understand the subject? Not that I'm offended, but your assumption would be wrong.

[Turtle]

You might clarify your meaning here. Are you implying i don't understand the subject? Not that I'm offended, but your assumption would be wrong.

___No such implication intended. Clealry you have sufficient understanding by evidence of your post. I meant to find clarification of 'confounding', express my difference with you that fairness exists, & stimulate others to investigate the subject. :confused:

[cwes99_03]

I only meant that there are so many techniques that could be used that one would have to know many variables, and that this would confound any simplistic system of odds finding as mentioned above. Thanks for the post.

[Turtle]

That seems to imply that because it is complex it has some less value. The article makes the point that the complexity 'settles' at certain times allowing just a few variables of the many to predominate the near term predictions. I think they also clearly make the point that some 'physical' - or real-world if you wish - system is the source of the data input, not some 'theorized' data set. :confused:

[cwes99_03]

Both pointed out in my post.

If the numbers are based upon improperly shaped balls and a vacuum, then yes history is imporant.

and

this would not preclude the same number from occuring more than once, unless the same balls from the first machine that were not drawn are parsed into the second machine. Then it becomes a statistical analysis of which ball is most likely to be picked up by each machine, and a running statistical analysis of which number would be most likely in the second machine if the first machine picks up number x.

I was noting that some variables are more important than others, but that initial important variables may be different from later important vessels.

 

My post is looking more at all the different ways of doing something. If one person were to try and win a lottery in every state based upon the same statistical analysis of one states method, my post says, would be doomed to failure, because there are many different methods and many different machines. The original post just said lotteries. It did not specify much, therefore I was only pointing out that there are many different types of lotteries, though you've drawn more out of me :confused: . Well, I think I've killed my joy in this post. Thanks all for reading and bearing with me.

 

These nodes in chaos theory I believe are called poincare (sp?) points.

[Turtle]

Both pointed out in my post.

 

and

 

I was noting that some variables are more important than others, but that initial important variables may be different from later important vessels.

 

My post is looking more at all the different ways of doing something. If one person were to try and win a lottery in every state based upon the same statistical analysis of one states method, my post says, would be doomed to failure, because there are many different methods and many different machines. The original post just said lotteries. It did not specify much, therefore I was only pointing out that there are many different types of lotteries, though you've drawn more out of me :edizzy: . Well, I think I've killed my joy in this post. Thanks all for reading and bearing with me.

 

These nodes in chaos theory I believe are called poincare (sp?) points.

 

Still Joy...still joy! :confused: I agree with the different machines, I just took a while to understand your meaning in that regard. Given the tremendous power of predictability in some arbitrary system (machine), it appears to me chaos is a better bet than probability. That is to say it has more real-world utility; it better describes non-linear behavior. In spite of this, one rarely sees chaos in use where probability has reigned so long.

___Finally, again to the point of the thread in answer to its author; all outcomes of the lottery(any lottery, any non-linear system) do not have the same 'probability'. Your intuition may deny that, most your proffessors deny that, the Lottery Commissions deny that & I venture to say 98% of any one you ask denies it as well. :confused: (Devil's Advocate) :confused:

[Boerseun]

The best way to experience the lottery, is to not watch the actual draw on TV.

 

Because, according to quantum theory, and if Schroedinger's cat is anything to go by, you've definitely won it until you find out that you definitely didn't.

 

Probability waves: Surf's up!

 

Duh...

[Jay-qu]

cant you equally say that you have definitly not won it untill you find out you have...

[cwes99_03]

Yes, but you are missing his point. There are two sides to the coin, but according to the theory mentioned, you can believe one side or the other until you actually see the result.

[CraigD]

This thread has taken the question “Is the probability of the numbers ‘1 2 3 4 5 and 6’ being drawn in a 49/6 lottery the same as ‘3 10 11 23 44 and 49’?”, and managed to turn it into discussions of chaos theory and Schrödinger’s cat.

 

This sort of behavior is why I love scienceforums. :confused:

[Turtle]

This thread has taken the question “Is the probability of the numbers ‘1 2 3 4 5 and 6’ being drawn in a 49/6 lottery the same as ‘3 10 11 23 44 and 49’?”, and managed to turn it into discussions of chaos theory and Schrödinger’s cat.

 

This sort of behavior is why I love scienceforums. :confused:

:confused: Ditto.

___Allow me to behave probabilitisticly. Keep the 1 2 3 4 5 6 & choose 5 10 15 20 25 30 for comparison, or more precisely any 6 number combination where all elements are multiples of 5. As the 6 balls are drawn independantly without replacement, the probability of any experiment of drawing 6 balls is the product of the probability of all the independant events.

___For 1 2 3 4 5 6: Probability of drawing 1 of these on the first draw is 6/49; probability of drawing a second 1 of these is 5/48; then 4/47; 3/46; 2/45; 1/44

___For 6 numbers that are multiples of 5: Probability of 1 multiple of 5 drawn is 9/49; then 8/48; then 7/47 to draw a third multiple of 5; then 6/46; then 5/45; then 4/44.

 

_______For 1 2 3 4 5 6: Probability is 6/49*5/48*4/47*3/46*2/45*1/44

___For 6 multiples of 5: Probability is 9/49*8/48* 7/47*6/46*5/45*4/44

 

____Clearly these 2 combinations don't have the same probability.QED

[Jay-qu]

because they have unequivilent boundary conditions placed on them. Any six numbers picked without any conditions that have or have not previously been drawn, in my opinion, are equally likely to be drawn

[Erasmus00]

:confused: Ditto.

___Allow me to behave probabilitisticly. Keep the 1 2 3 4 5 6 & choose 5 10 15 20 25 30 for comparison, or more precisely any 6 number combination where all elements are multiples of 5. As the 6 balls are drawn independantly without replacement, the probability of any experiment of drawing 6 balls is the product of the probability of all the independant events.

___For 1 2 3 4 5 6: Probability of drawing 1 of these on the first draw is 6/49; probability of drawing a second 1 of these is 5/48; then 4/47; 3/46; 2/45; 1/44

___For 6 numbers that are multiples of 5: Probability of 1 multiple of 5 drawn is 9/49; then 8/48; then 7/47 to draw a third multiple of 5; then 6/46; then 5/45; then 4/44.

 

_______For 1 2 3 4 5 6: Probability is 6/49*5/48*4/47*3/46*2/45*1/44

___For 6 multiples of 5: Probability is 9/49*8/48* 7/47*6/46*5/45*4/44

 

____Clearly these 2 combinations don't have the same probability.QED

 

Its because the set of multiples of 5 is larger then the set of 1,2,3,4,5,6. You specified, in the second case, only that the balls be multiple of 5, not a specific 6 multiples of 5.

-Will

[Turtle]

because they have unequivilent boundary conditions placed on them. Any six numbers picked without any conditions that have or have not previously been drawn, in my opinion, are equally likely to be drawn

 

___While Erasmus is technically correct, JayQ gets more to the point of why I invoked chaos theory (much to Craig's delight :confused: ). The standard probability works well with equivalent boundary condition, i.e. linear, but falls apart when trying to accomodate all the different boundary conditions. Nevertheless, the qualities (boundary conditions) of number do apply to those ping pong balls just as stricktly as do the minor variations in the physical makeup of the balls & the machine that chooses them. Mark the balls with some other symbols & find different boundary conditions.

___Our problem here is at the core, whether or not we can predict the outcome of a particular drawing. Standard probability says the game is fair & further says you can't predict short term, i.e. the next drawing. Chaos says the game isn't fair because you can predict short term by analyzing the past performance of a system & looking for islands of stability - attractors if you will - that have relatively predictable short term patterns.

___The Lottery is not fair; nothing is fair. Nothing is equally likely to anything else. :confused:

[cwes99_03]

Yep, a large set does not mean that you have a higher probability of winning. It only means that you have to buy more tickets(to cover the set), and the purchase of more tickets always increases your probability.

 

because they have unequivilent boundary conditions placed on them. Any six numbers picked without any conditions that have or have not previously been drawn, in my opinion, are equally likely to be drawn

 

Correct until you consider some of the above postings that point out unequality in the ways the number are physically drawn for the system. Purely mathematically (and I'm not referring to someone's code that picks a random number, i'm referring to the mathematical analysis of a completely fair drawing where all possibilities have equal chance of occurance) you are correct.

[cwes99_03]

that's the word i was looking for last night. Attractors.

Thanks.

[Turtle]

Yes, but you are missing his point. There are two sides to the coin, but according to the theory mentioned, you can believe one side or the other until you actually see the result.

___Actually there are 3 sides to a coin; 2 faces and an edge. What is the probability of a nickel landing on its edge when tossed? How did you calculate that? I have seen it happen at least once.

___The Cat also has a third possibility; disapearing from the box. :confused: