Lottery Probability

[Turtle]

Farmers scheme is much like predicting the resting place of a baseball thrown in an empty, not smooth but not-too-lumpy field. By knowing something of the physics of the bouncing ball, and making a reasonably measurement of the position from which and speed and angle with which it thrown, one can predict of where it will come to rest within +- some reasonable error margin. This is roughly analogous (though easier) to what Farmer’s team did with their purchased 2nd-hand roulette wheel. It’s impressive that they were able to judge the initial wheel and ball speeds and position well enough for the scheme to work – I’d suspect that many human perception distractions could confuse an the observer from doing this – though, really, the data for how well it actually worked is very anecdotal – a few paragraphs in books like Kelly’s ”Out of Control” (whole book available via link!) or Gleik’s excellent ”Chaos:Making a New Science” (which I know of only in paper).

 

A major point Farmer makes in even these brief passages is that, to circumvent the randomizing effects of chaos, it’s futile to try to look too far ahead. In the roulette scheme, they considered only the immediate data for one spin/launch of the wheel/ball in their (computer concealed in a shoe!) calculations. Past history of the wheel – its previous numbers - are not considered at all. This is markedly different than the approach most “win the lottery” analysis schemes approach prediction Lotto machine outcomes.

The knowing something of the physics is the past history. They took a real wheel & threw the ball over & over & observed & recorded the results, then worked back to the intital conditions at release. I maintain that recording the outcomes of a real lottery machine provides a data set that belies the physical nuances of that machine. Unlike the roulette wheel however, one has several days after a drawing to access the systems state & place a block of bets. You may have to buy half the tickets available _ but a certain half - & also be prepared to loose several times before winning. If it is possible to handicap these dynamic systems, whether Lottery or stocks etc., then some flaw exists in a probalistic model that says they are euqally likely. At best, they are conditionally equally likely. :confused: :confused:

[Turtle]

OK, Gedanken time. Once upon a time, before the Age of Katabataks, I made a considerable study & analysis of just the 6/49 lottery we have under discussion (actually, it was 6/44 when I started the investigation). I threw out all my notes apparently pursuing the minimalist dog, but it's all in my head anyway. :hihi: So, call this another of Turtle's explorations in pure math.

 

Here's the setup: Our data set is the historical record of a particular Lotto game, from the time it started to present. For the sake of argument, we say the machine is fair, that is the authorities have measured the balls & otherwise limited physical variences.

___My first step is to map the data on a square celled matrix that is 49 rows X # of games past columns. In each column, a cell is colored - occupied - if the number of its row is drawn in that game. Each column is a game & has 6 occupied cells.

___Gedanken this over & get back to me. :cup:

[CraigD]

The knowing something of the physics is the past history. They took a real wheel & threw the ball over & over & observed & recorded the results, then worked back to the intital conditions at release.

True. They did this only to build a general model of “how the ball bounces”, analogous to my example of knowing something of how a ball bounces on a general sort of field. They didn’t do it to make a model of a specific wheel, such as the one they actually played. Once they had their model, they discarded the data used to build it. The model could then predict, roughly +- 1/16 the circumference of the wheel, where the ball would settle. If a particular wheel has a peculiar history (eg: always landed on a particular number when the cheating croupier switched on a hidden electromagnet), their system didn’t detect and take advantage of this data.

Unlike the roulette wheel however, one has several days after a drawing to access the systems state & place a block of bets. You may have to buy half the tickets available _ but a certain half - & also be prepared to loose several times before winning.

Or, you could wait until the jackpot gets high, then buy one of every number combination. An Australian investing syndicate (the brainchild of Peter Smith and Stefan Mandel) did exactly this with the 2/15/1992 Virginia, USA Lotto (and a couple other, smaller ones), making a cool $28M on a $7M investment. All they were gambling on was that no more than 4 other people picked the winning number (none did), none of their hired team of ticket purchasers screwed up and failed to buy their assigned block of tickets (some did – they only got 5.5M of the intended 7M tickets, but got lucky), or that lottery officials didn’t refuse to give them the money (initially, they did, but, unable to find an legal prohibition, had to relent). The VA legislature promptly passed a law banning any future schemes of this kind.

 

This just goes to show that you need neither a good grasp of probability, Physics, or chaos theory to beat the Lottery, just good entrepreneurial skills.

[Turtle]

True. ....Or, you could wait until the jackpot gets high, then buy one of every number combination. An Australian investing syndicate (the brainchild of Peter Smith and Stefan Mandel) did exactly this with the 2/15/1992 Virginia, USA Lotto (and a couple other, smaller ones), making a cool $28M on a $7M investment. All they were gambling on was that no more than 4 other people picked the winning number (none did), none of their hired team of ticket purchasers screwed up and failed to buy their assigned block of tickets (some did – they only got 5.5M of the intended 7M tickets, but got lucky), or that lottery officials didn’t refuse to give them the money (initially, they did, but, unable to find an legal prohibition, had to relent). The VA legislature promptly passed a law banning any future schemes of this kind.

 

This just goes to show that you need neither a good grasp of probability, Physics, or chaos theory to beat the Lottery, just good entrepreneurial skills.

 

:hihi: First, I have to laugh because I see 'true' & I figure I just got the nod. :cup: Your good at that Craig & I do actually read the qualifications that follow. I will of course continue on & describe my particular method of analysis for your entertainment.

___The prospect you mention in regard to the logistics of buying all those tickets did not enter the picture for me until my analysis reached its apex; in fact, the analysis demonstrated that one needed to buy about half the tickets for at least 3 drawings before winning. Well, that killed my interest. Fortunately, Hypography has brought it back to life! :cup:

___Prepare your Gedanken graph paper as above while I review the thread for pertinent components. :cup:

[Erasmus00]

___As to the guys system going useless, that only means you have to put the changed system data back in.

 

The reason such methords work is because the market isn't fair. Traditional economic theory says that any unfairness in the market becomes exploited, this exploitation causes the market to correct, and the market becomes fair again. So, in this case, if everyone used chaos theory to predict the market, the equations that govern the market would change, and suddenly you have fairness again.

-Will

[Turtle]

The reason such methords work is because the market isn't fair. Traditional economic theory says that any unfairness in the market becomes exploited, this exploitation causes the market to correct, and the market becomes fair again. So, in this case, if everyone used chaos theory to predict the market, the equations that govern the market would change, and suddenly you have fairness again.

-Will

___Taking up after Craig eh Erasmus? :hihi: :cup: Like Craigs TRUE... I see you start with 'such methods work' & I figure I got the nod from you too. :cup:

___So you then build a new model for the new market. Makes it all sound a bit more ominous that not only are they predicting the short term, that prediction changes the long term.

___Back to my method (which is not 'their' method I'll wager). We have our lotto history mapped out on a square matrix as I described above. While I will use lotto data, any data you can plot as filled/empty cells is susceptible to this analysis. We talked about certain qualities, or boundaries, earlier; I call these "features". One of the features we discuseed is the quality of even & odd. We now go through the entire data set & classify every drawing in terms how many even/odd numbers each drawing produced.

___Pause for comment: :cup:

[goku]

to have the best chance, always play the same number :hihi:

[Turtle]

to have the best chance, always play the same number :cup:

 

___In regard to my analysis, the answer to that is no. The numbers you play to win, depend on the past history of the game & most importantly the most immediate past history. I fully plan to elucidate. :hihi: ( Or is that plan to fully elucidater? :cup: )

[cwes99_03]

There is only one caution, call it brotherly, for you Turtle. That is to re-evaluate your statement that we will assume that the game is completely fair (i.e. that no physical traits of any part of the drawing play any influence on which ball will be drawn.)

 

By saying such, it appears that you have limited yourself. Now math and physics would say that there is no predicting the next drawing based upon history. So I'm interested in your theoretical.

 

Sorry if this blows the fun of your point. :hihi:

[Turtle]

There is only one caution, call it brotherly, for you Turtle. That is to re-evaluate your statement that we will assume that the game is completely fair (i.e. that no physical traits of any part of the drawing play any influence on which ball will be drawn.)

By saying such, it appears that you have limited yourself. Now math and physics would say that there is no predicting the next drawing based upon history. So I'm interested in your theoretical.

 

Sorry if this blows the fun of your point. :hihi:

 

___I only tossed that in because it is the first principle of probability; inspite of all that I have said, I intend to employ some of these principles in my discourse. I fully apprehend that probability is logically sound within its limits; I intend to stretch them.

___I actually believe all the immeasurable (uncountable) sublteties(sp) of the physical characteristics of the balls, the machine, & their environs make all the difference. Since those parameters constitute a 'lottery drawing' , I intend to map them & use that map to predict a future state of a lottery drawing. :cup:

 

PS Still fun.

[cwes99_03]

Just as I figured you would. I await with bated breath.

[Turtle]

Just as I figured you would. I await with bated breath.

:lol: Well, you better breathe. Your fun is in the looking, but mine is in the showing; this stuff can get very dry sometimes & the show is in 3 acts. :cup:

___Prologue: A collection of comments from the thread; popcorn to make you thirsty.

 

#36 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.

 

# 40 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.

 

#47 The most likely scenario for any 6 numbers is that an equal number of them will be even and odd, or 4 will be odd and 2 even.

 

25/49*24/48*24/47*23/46*23/45*22/44

 

Notice that after the first ball being an odd, the next could be an odd or even, the one thereafter would be most likely the opposite of whatever the second was and so on and so forth. then the 6th ball picked has equal chances of being odd or even. If it is even then there are 3 odd and 3even. If it is odd there are 4 odd 2 even. These two possibilites have the same probability.

 

Post Prologue: I originally started this 20 years ago & left it off 10 years ago. I checked my 2 remaining small folders of math papers & I most assuredly threw out the paperwork. I have however found some software I wrote & one of the files may actually have a real list of over 200 games. Mind you, some of it's nearly 15 years old & I have a hard time remebering what I was thinking 15 minutes ago.

Post Post Prologue: Enjoy some refreshments while I hurry & make up some props. :cup: :hihi:

[cwes99_03]

You shouldn't smoke while working around those old papers, might lose more than you want. O and it's bad for your health. :hihi:

[Iron4ever]

Excellent stuff!!! Thanks guys, having posted the original question, which incidentally started off as an argument down the pub, I have now a much better knowledge to throw into the discussion, after reading the last 60 posts!!

[Turtle]

Excellent stuff!!! Thanks guys, having posted the original question, which incidentally started off as an argument down the pub, I have now a much better knowledge to throw into the discussion, after reading the last 60 posts!!

___Let's hope the next 60 prove just as fruitful. :hihi: Our pleasure, right guys? :lol:

 

___I still haven't made my prop, but we don't need it right off. The prop I refer to is just some graph paper with rows numbered 1 to 49, & columns labled 1 to ?. I called this layout a matrix earlier, & as that has so many conotations in math - e.g. in linear programming - let's call it a 'cellular array' or 'table'.

___Now in mulling this through the night, I came up with my own questions about some assumptions we have all already made. As no one put the halt on the even & odd question, I presume we all agree that the calculations involving that feature which I posted for review a couple posts back.

___We all have accepted the idea that even/oddnes is a 'real' feature in a lottery drawing. By extension, we accepted that divisibility by five is a 'real' feature too. Now since I intend to mine the 'table' for features of similar quality, I thought I better explore the validity of our assumptions first.

___Suppose we marked the balls with upper & lower case letters of the alphabet? Now there is no even or odd feature. Same balls, same machine, same match 6 picks to win. Does this in anyway invalidate even/oddness as a feature when we use number labels? :cup:

[Jay-qu]

___We all have accepted the idea that even/oddnes is a 'real' feature in a lottery drawing. By extension, we accepted that divisibility by five is a 'real' feature too. Now since I intend to mine the 'table' for features of similar quality, I thought I better explore the validity of our assumptions first.

 

Im not sure what you mean by 'real' feature, if you count multiples of five then why not also multiples of 2 - hell why not just use multiples of one and include all the numbers :hihi: I think im missing something...

[Turtle]

Im not sure what you mean by 'real' feature, if you count multiples of five then why not also multiples of 2 - hell why not just use multiples of one and include all the numbers :hihi: I think im missing something...

___The table IS just the list you propose.

___I mean to get at perhaps a philosophical question; because we may arbitrarily label the same 49 balls, with numbers, letters, colors, magical symbols, etc., how 'real' are the qualities of these symbols we(I?) intend to count? Since it is a first principle of sorts to what I intend to exposit, I'd like to settle any argument with it before I advance. :cup: