[Turtle]

Jay-qu said:

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 ). 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.

[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.

jay-qu said:

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]

cwes99_03 said:

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.

[Jay-qu]

well you could say that the coin has a 4th option - it may quantum tunnel through the earth - and a 5th option... and so on, you can go on to infinity with that point

[C1ay]

Turtle said:

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.

It is important to note however, many lotteries use a new set of balls for each drawing to prevent any of the balls' properties from contributing to any such islands of stability.

[Turtle]

Jay-qu said:

well you could say that the coin has a 4th option - it may quantum tunnel through the earth - and a 5th option... and so on, you can go on to infinity with that point

Yes exactly; that is just the point. Those possibilities really exist. Probability came out of trying to understand the occurence of real events (OK gambling) & despite theoretical work, that is entirely what it is about.
Here is a poser; in the 6/49 Lotto game, is a 6 number combination of all even numbers equally as likely as one of all odd numbers?
I have to refer to this article again as they make some of my points in a different manner:
http://www.cs.brown....WallStreet.html

[CraigD]

Turtle said:

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
…
_______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

Correct. However…

In general, there are m!/(n!*(m-n)!) ways of choosing n of m elements where order isn’t important (where “!” is the factoral unary operators, eg: 4! = 1*2*3*4) [1].

The probability P of drawing a specific n of m elements is its reciprocal, (n!*(m-n)!)/m! [2].

The probability of choosing any 1 of x different choices of n of m elements is x*P [3].

As you’ve correctly calculated, and per [1], the probability P1 of drawing exactly {1,2,3,4,5,6} is (6!*(49-6)!)/49!,
while the probability P2 of drawing any 6 balls numbered with multiples of 5 is (9!*(49-6)!)/(49!*(9-6)!).

Note that P2/P1 = ((9!*(49-6)!)/(49!*(9-6)!)) / ((6!*(49-6)!)/49!)
= (9!*(49-6)!*49!)/(49!*(9-6)!* (6!*(49-6)!))
= 9!/((9-6)!*(6!))
= 84

However the probability of choosing a specific 6 of 49 numbered balls (eg:{5,10,15,20,25,30}) is not the same as choosing any 6 of 49 where each’s number is a multiple of 5 (eg: {5,10,15,20,25,30} or {5,10,15,20,25,35} or {20,25,30,35,40,45}, etc.)

There are 9!/ ((9-6)!*6!) = 84 possible ways to draw 6 of 9 (the number of ) elements. As expected from [3], this is the same as P2/P1.

So, in a fair drawing of 6 of 49 balls, the probability of drawing {1,2,3,4,5,6} is the same as the probability of drawing {5,10,15,20,25,30}, or any other choice of numbers – 1/13983816.

[Turtle]

___I still maintain that is misleading in regard to modeling & predictability. I mean to provoke a response on the significance of modeling any given system - from Brownian motion to insurance rate tables - by equations from chaos theory and not from probability theory. If one is better, i.e. more accurate in prediction - than the other, then using the lesser is illogical.
___I think the evidence is clear, if relatively unknown, that chaos is the better. I only wish to corrupt the youth.

[cwes99_03]

turtle said:

Here is a poser; in the 6/49 Lotto game, is a 6 number combination of all even numbers equally as likely as one of all odd numbers?

No, there are more odd numbers in total. 25 odd, 24 even
24/49,23/48,22/47,21/46,20/45,19/44 = (24!-18!)/(49!-43!)
25/49 24/48 23/47 22/46 21/45 20/44 = (25!-19!)/(49!-43!)
Meaning odds are hehe that the list of odd numbers is more likely to get you to win than the list of even numbers.

[Turtle]

cwes99_03 said:

No, there are more odd numbers in total. 25 odd, 24 even
24/49,23/48,22/47,21/46,20/45,19/44 = (24!-18!)/(49!-43!)
25/49 24/48 23/47 22/46 21/45 20/44 = (25!-19!)/(49!-43!)
Meaning odds are hehe that the list of odd numbers is more likely to get you to win than the list of even numbers.

___Now that...is brotherly conduct.

[Erasmus00]

Turtle said:

___I still maintain that is misleading in regard to modeling & predictability. I mean to provoke a response on the significance of modeling any given system - from Brownian motion to insurance rate tables - by equations from chaos theory and not from probability theory. If one is better, i.e. more accurate in prediction - than the other, then using the lesser is illogical.
___I think the evidence is clear, if relatively unknown, that chaos is the better. I only wish to corrupt the youth.

It depends on the system. In many instances, standard random walk works wonderfully for brownian motion. In the lottery as well, standard probability theory works pretty well (mostly because they do everything possible, from swapping out balls and machines to make the game as fair as they can). Probability theory also has the tremendous advantage of allowing you to calculate things from first principles.

Now, use the same roulette wheel and ball over and over again, and chaos theory is your game. Or with the stock market, where you have loads of past data to stick into models...
-Will

[Turtle]

Erasmus00 said:

Now, use the same roulette wheel and ball over and over again, and chaos theory is your game. Or with the stock market, where you have loads of past data to stick into models...
-Will

Or insurance data, medical data, psychological data, geological data, etc.. In short, everything we've been using standard probability to model - inadequately model. These areas affect real peoples lives in their economic situation, their health, their rights accorded by government & law, & other numerous aspects. I feel that where this new knowledge is not applied, whether by ignorance or deceit, we the people get screwed. Notice the air of secrecy in the article I linked to? Notice this guy was at Los Alamos? Notice his current contract won't allow him to say just how accurate the predictions get? Notice these chaos algorthms have world consequrnces? Follow the money. Not only who is spending it, but on what.
I have more, but I need a fresh bier. Discuss.

[Erasmus00]

Turtle said:

Or insurance data, medical data, psychological data, geological data, etc.. In short, everything we've been using standard probability to model - inadequately model. These areas affect real peoples lives in their economic situation, their health, their rights accorded by government & law, & other numerous aspects. I feel that where this new knowledge is not applied, whether by ignorance or deceit, we the people get screwed. Notice the air of secrecy in the article I linked to? Notice this guy was at Los Alamos? Notice his current contract won't allow him to say just how accurate the predictions get? Notice these chaos algorthms have world consequrnces? Follow the money. Not only who is spending it, but on what.
I have more, but I need a fresh bier. Discuss.

Lots of physicists (even those who haven't left the field) have been applying chaos theory to all the things above. Well, perhaps not psychological or medical data (I fail to understand the connection) but certainly to geological data, insurance data, etc. Scientists and private industry alike are trying to predict the stock market, lightning, turbulent fluid flow, earthquakes, etc.

As to the secrecy, the guy in your article wasn't at a government facility, he worked for a private research company, and his contracts were with private companies who didn't want their golden goose plucked. If everyone suddenly used his methods to predict the stock market, the market would adjust, and the system would change, rendering his predictions useless.
-Will

[Turtle]

Erasmus00 said:

Well, perhaps not psychological or medical data (I fail to understand the connection) but certainly to geological data, insurance data, etc. Scientists and private industry alike are trying to predict the stock market, lightning, turbulent fluid flow, earthquakes, etc. -Will

Why should medical or psychological data get different treatment? When good old Doc says oh, 30% chance to die, or recover, or whatever, isn't that important enough to get the same analysis as my car insurance?

___As to the guys system going useless, that only means you have to put the changed system data back in. You make it sound like it is an artifice somehow Erasmus. Maybe the geologists work is too arcane for me to have read that uses chaos; I don't readily recall reading any.
___Perhaps it is not a problem that it isn't widely used, but rather not widely published. Any links at hand?

Addendum: I only had to look.
http://www.cambridge...isbn=0521567335