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Patterns in Lottery Numbers
markmcb writes "Most everyone is familiar with the concept of the lottery, i.e., random numbers are selected and people guess what they will be for a cash prize. But how random are the numbers? Matt Vea has conducted a pattern analysis of the MegaMillions lottery, which recently offered a sum of $370M (USD) to the winner. Matt shows that the lottery isn't as random as it may seem and that there are 'better' choices than others to be made when selecting numbers. From the article, 'A single dollar in MegaMillions purchases a 1 in 175,711,536 chance of landing the jackpot ... a player stands a mildly better chance of winning a partial prize through the selection of weighted numbers.'" Includes some excellent charts of his analysis.
Most lotteries (as opposed to raffles) have less than half the money spent by lottery ticket buyers going into the payout pool.
You're already losing by buying the ticket.
-- Tigger warning: This post may contain tiggers! --
4, 8, 15, 16, 23, 42.
Interesting as these trends may be, they will not assist in making the odds of winning the MegaMillions lottery any better if the system is truly fair and random. However, in the event there is some peculiar factor skewing the ball selection such that any of these trends continue, a player stands a mildly better chance of winning a partial prize through the selection of weighted numbers.
These differences aren't that compelling. To me I would say, "Congratulations, you have found some deviation from equal frequency for all balls. But this would happen in any instance of drawing these balls."
I'm concerned that this has been an exercise in deviation in pseudo random systems. The same could be done with a computer simulation and similar results would be found.
I hate to say it but this study points out to me that the lottery is actually pretty much as close to random as it could get. In fact, the summary of the paper states that if there were some event to skew this, then you could achieve a small bonus: However, in the event there is some peculiar factor skewing the ball selection such that any of these trends continue, a player stands a mildly better chance of winning a partial prize through the selection of weighted numbers. However this peculiar factor can not only be identified but if it exists, it is highly unlikely it is anything even remotely observable.
My work here is dung.
Fl. Lottery used to print which machine would be used for a particular drawing, and old drawing numbers - with machine that was used - in a nice column format (probably real easy to rip out of a web page, etc).
Now I'm not a math guy, but I *know* that all 50whatever balls aren't identical. Should there be some (very) slight preference for a particular ball, or set of balls, over a series of draws over time? I seem to remember an article in a Dragon magazine about dice and using math to find out if yours had a preference for a particular number...
Don't blame me, I voted for Kodos
And if you look up in the night sky, you'll see an archer, a bull, a big and a small dipper.
What's your point?
I wonder how much ANY person would see ghosts if one tried hard enough to find them at the Waverly Hills Sanatorium?
Of course you can't conclude much from this analysis. In any random distribution you're going to see random statistical fluctuations causing some clustering. Some numbers will get picked more than you'd predict by chance, just by chance. And necessarily some numbers will be picked less often than you'd predict by chance. The upside of this is that you can predict the extent of this clustering and compare that to the actual data to see if it's rigged.
Give me Classic Slashdot or give me death!
One of the slogans for the Illinois lottery used to be "you can't win if you don't play", but I figured every time I didn't play, I won $1. Its both stupid and ironic that many of the same people bitching about taxes pay this voluntary tax!
At the astronomical odds against winning, I figure my chances of finding a winning ticket on the ground are only marginally worse than my chances of buying a winning ticket. So rather than give extra money to the government so it will be funnelled to politically connected rich people, I just watch the ground.
-mcgrew
mcgrew's razor: Never attribute to stupidity that which can be explained by greedy self-interest
While you can analyse the numbers that come up, the interesting data isn't usually available to you: namely what numbers people are betting on. For example in the UK lottery it is known that about 10,000 people a week bet on 1, 2, 3, 4, 5, 6. So that automatically is a really bad choice because if that combination came up, you would get £prize / 10,000.
Example: if lots of people bet on (eg.) birthdays, then you'd expect the people to select numbers > 31 less frequently, which means you could try to cover bets with numbers > 31 and have a greater payout. Without the distribution of betting numbers though you can't tell.
Rich.
libguestfs - tools for accessing and modifying virtual machine disk images
Any statistical deviation in the balls is going to be microscopic.
Rather, observe the following. When a progressive jackpot gets large enough, a single winner would have a positive expectation value, but multiple winners have negative value.
Thus what you need to do is not pick something that is "more likely", you need to pick combinations that normal players would NOT choose, as your odds of winning are the same, but your odds of having to share a win go way down.
EG, something like 7 8 9 10 11 12 13
Given the raw stream of what numbers people choose, there are probably lots of such "less likely" patterns you could use.
Test your net with Netalyzr
2) You don't get an edge in the lottery by picking numbers that are more likely to come up; you get it by picking numbers that other players are less likely to choose (e.g. >31), so that you don't have to split your win with as many others.
What I'm listening to now on Pandora...
Let's simulate the history of MegaMillions in a computer, using a hardware random-number-generator that we trust to be completely random with an even distribution.
Examine the results and look for patterns. Odds are, you will see minor variations from "average." After all, if you flip a coin 1000 times, odds are you won't get exactly 500 heads and 500 tails.
Next, let's repeat this 100 times. Odds are you will see such patterns in most of the experimental runs, but the patterns will vary from run to run.
Think of the real-life MegaMillions lottery as a single experimental run.
How do you counter this?
You could slice-and-dice the MegaMillions into 100 "experimental runs" each consisting of a random 10% of actual drawings. While the overall trend of this slice-and-dice will reflect the real history of MegaMillions, the results of the individual "experimental runs" should vary enough to convince people that this is just a statistical fluke, or at least it's flukiness can't be ruled out.
In particular, let's slice MM into 10 time periods with an equal number of drawings. Odds are the most recent time period's statistical anomalies won't match those of earlier times.
The bottom line:
There is nothing to suggest the statistical anomaly of the history of MM so far will continue.
Knowledge is how to play a game, intelligence is how to win, wisdom is knowing what game to play.
What stuck with me though we a couple of ideas:
- What happened in the past has no influence over what will happen in the future. You may have flipped seventy-five heads, but the odds of the next penny landing head or tails is still 50/50.
- The decision whether to make a bet in any game is based on a variety of factors - the size of the bet, the size of the possible prize, and the odds of winning. No one of those three is enough to make a decision, you need to know all three.
In life, as in games, you have to make decisions based on real odds, not of conjecture or media speculation. Where's the bigger risk? A falling meteor, or getting hit by a city bus? Food poisoning or a terrorist attack?Three Squirrels
Rosencrantz: [flips coin which lands as 'heads'] 78 in a row. A new record, I imagine.
...
Guildenstern: Is that what you imagine? A new record?
Rosencrantz: Well...
Guildenstern: No questions? Not a flicker of doubt?
Rosencrantz: I could be wrong.
Guildenstern: Consider: One, probability is a factor which operates *within* natural forces. Two, probability is *not* operating as a factor. Three, we are now held within un-, sub- or super-natural forces. Discuss.
Rosencrantz: What?
Exactly, a couple years back at vegas, the roulette wheel spun black 13 times in a row.
Thats like 1/.48^13th.
Random things.. happen.
Randomly- some poor investing sod out there has made every choice correctly and been hammered by random market events.
Likewise- some lucky fool (that thinks he is brilliant) has picked google or tasr or crox on some non-logical basis and won big.
That's why you use Mutual Funds and ETF's. You get average performance. You lose the home runs, but you also lose the strike-outs.
She was like chocolate when she drank... semi-sweet at first and then increasingly bitter.
Overall, though, the guys that I have known who have done this sort of stuff have won, though. Not tons, maybe an average of a couple hundred dollars per month at best with the risk of losing thousands
It sounds like a classic case where someone is staying just ahead of Gambler's Ruin--so far. If you don't properly model what happens when you run out of money, there are any number of gambling systems that seem like they work in the short-term, but in reality don't if you run them long enough. The simplest one is the Martingale.
To turn those numbers around:
You have to admit that driving to work 5 days a week has less of an impact (good or bad) on someone's lifestyle than getting killed in a car crash does (again, good or bad).
That the odds of ending up terminated on a highway are far higher than getting an "off the charts lifestyle impact" lottery payout doesn't seem to affect anyone's choice in making that daily drive.
Can we get a "-1 Wrong" moderation option?
An intelligent older gentleman told me once that he plays the lotto every week. I thought this was a silly waste of money too, but he explained that he got entertainment value from imagining how he would spend the money. This entertainment he felt was worth far more than he spent on tickets.
;)
Just because you probably won't win doesn't make it worthless. Try buying a ticket. Go on, you won't get addicted to gambling, but you might have fun
Does this guy know there are multiple ball sets in these big games, that are "randomly" selected before each drawing?
Looking at statistical weighting of ball frequency in a huge aggregate is fine. But I'm guessing (but not betting) you can't translate it directly into predictions in the short term, because of this random set issue. Now, if you want to make multiple analyses based on the specific historical performance of each set, then you have something more practical. But then you need to buy multiple sets of tickets based on the multiple predictions you get. I don't think his data source will tell him what ball set was used.
(Early on, when Lotto Texas was new, I used to guess 2 or 3 of the numbers based on simple frequency analysis, in every single drawing. But they kept adding ball sets. And Texas did tell people which ball set they used. After the fact, of course. And then I think they changed the number of balls picked. So I gave up my paper trials.)
I'm just saying. I don't care about $5/month, but if those guys win, and I'm still at this $@#%ing desk, that'll be bad.
It's not gambling, it's "gloating ex-co-worker insurance."
ceci n'est pas un sig.
Back in the early 20th century, the mob used to run a kind of informal lottery. It was called a "numbers game". There were places (like barbershops) where people could pick a number from 1 to 1000, and if their number came up, they won. The mob typically paid out between 800-to-1 and 600-to-1. This meant that the mob paid out 60-80% (and kept 20-40%) of the money people initially paid. On the other hand, most state lotteries only pay out about 50% of earnings, making them a worse bet than going with the mob.
http://en.wikipedia.org/wiki/Numbers_game
http://marketplace.publicradio.org/features/underground/1114undergroundpm.html
Thats like 1/48^13.
Random things.. happen.
And guess what? Last night in Vegas, the roulette wheel spun this:
Red, Black, Black, Red, Black, Red, Red, Black, Red, Red, Red, Black, Red.
That's like 1/.48^13th.
A lot of people would be better off in understanding "randomness" if they would just realize that these two situations have exactly the same probability. Humans just assign more "meaning" to certain sequences than others.
So you're saying that if I buy just 80 tickets a day, I'll have above even chances of winning over 40 years!
...is that the patterns of stars, planets, and constellations you see in the night sky is not random at all, but rather are arranged by a very intricate system of mathematical functions which describe all the interactions of all those objects and include their wildly varying velocity vectors, sizes, densities, masses, and distances from one another and they are not contained in a fixed size and shape container where frequent collisions will affect their positions as seen by a viewer here on this planet.
The lotto balls are much more matched in size, shape, mass and density to each other, and they are contained in a relatively small, fixed size container respective in ratio of the volume of all the balls to the volume insode the container, where extremely frequent collisions between the balls will profoundly affect the probability of which ones will get picked by the picking mechanism.
Spock!
You're rambling again.
But your example has 8 reds and 5 blacks. The other example had 13 blacks. As far as the probability of any particular SEQUENCE, yes, these probabilities are the same. But there are MANY possibilities where there were 8 reds and 5 blacks, but only ONE possibility with all 13 being black. So the two situations, if you look at it purely in terms of how many reds and blacks were hit, are very different.
Or to put it another way, the chances of getting 13 blacks in a row are 1/48^13. The chances of getting 8 reds and 5 blacks, in SOME order, is far higher than that.
But sequences are useless in roulette because the results of one test do not affect the next. My chances of winning by picking black, red, black, red are just as poor as picking black, black, black, black.
"I only speak the truth"
Karma: null(Mostly affected by an unassigned variable)
I was quite amused when I first heard of it. I d onot know if it has ever actually been done, however.
Pick some random stock, send email to 2*10 suckers that it will go up, and to an equal number of suckers that it will go down.
Whichever direction it moves, divide that batch of suckers in two, pick some other random stock, send half email taht it will go up and half email that it goes down.
Repeat until you have only a few suckers left. They will see you as a genius who has correctly predicted the last {n} stock moves correctly. It may be the final sucker, or the last 2, or 4, etc.
Now tout a stock you have just bought and make some money!
Infuriate left and right
In other words, if I flip a coin 10 times and see Heads 10 times, that's not a guarantee that the 11th time will be heads; in fact, the probability of getting 11 heads is so small that you'd be better off betting on tails.
Classic Gambler's Fallacy. How on earth could previous coin flips influence the probability of the current flip? Try brushing up on your own statistics, instead. There are plenty of GOOD criticisms of this guy's work -- yours isn't one of them.
I didn't win the green suit, M-16 rifle, and two-year all-expenses-paid vacation to exciting tropical Vietnam, or the grand prize magic bullet with my name on it, and since my number was high enough to get classified as 1-H, I didn't even win the third-prize government-health-care physical exam. Haven't bought another ticket from those bastards since then.
Bill Stewart
New Fast-Compression-only CPR http://preview.tinyurl.com/dy575ks
Its not too hard.
:)
One method is to take each pair in the sequence as coordinates in a plane and plot them.
Eg, you have a dripping tap. You take the time between drips as your number. Then two successive intervals get plotted on a plane and you can start finding a resulting pattern.
I once did this with pseudo-random number generators as provided with various libraries.
The results were interesting.
Each different PRNG would produce a distinct pattern and the same pattern every single time regardless of whether you initiated with a different seed value. Its like a fingerprint; you look at the resulting pattern and you can say which PRNG produced it.
This was in the '90s and the Borland 'turbo pascal' PRNG produced a pattern that looked a LOT like a space-shuttle
In the free world the media isn't government run; the government is media run.
Drawing trend lines like what is done in this article shows that the author has no idea of the underlying theory. The fact that the balls are numbered does not mean that it reveals any useful information by charting as done in the article.
Charting how many times each ball has been drawn against with the corresponding ball number, and then add some kind of trend lines (of #draws against #ball) is misleading and will not reveal any information about future outcomes of the lottery. All the ball labels are interchangeable and since it is very unlikely that they are all drawn an equal number of times, it is most likely that you'll be able to show trends that show higher chances of getting drawn as ball number increases (or decreases or whatever).
Just to explain the point, lets go back to the day where all the balls were labeled. At that time, there was 50 identical balls with no labels and 50 labels with numbers 1 thru 50. At that time, the balls could have been assigned different numbers that - by accident turned out to place the highest label (50) on the most frequent ball, 49 on the second most frequent ball, and so forth. The result would be a much steeper trend line, telling us that we were "lucky" when the labels were assigned, given the results to date. Any future results will still be evenly distributed.
One might argue that this analysis could tell if the balls are not equally likely to be drawn (due to physical defects), but in that case it is necessary to do a plain multivariate test with the hypothesis that all balls are from the same distribution.
If you had read my post to the end, you'd have seen where I said you can do that. And if you read TFA, you'd know that the author didn't p-values or alpha levels or anything. That's why I said we can't conclude much from this "analysis" instead of we can't conclude much from this data.
So frankly, I think that your comment is incorrect, overrated, and probably designed for karma whoring.
Give me Classic Slashdot or give me death!
They took 1078 combinations and used them to look for patterns in something with over 175 million combinations. It's been a while since I took statistics, but isn't that sample size way way WAY too small?
He should not be looking at winning numbers but at every drawing. This only seems to point out that people have a tendency to pick certain numbers more than other.
Can you win at roulette by betting there will be "only 8 reds in the next 13 spins"? No, you have to say *which* spins will be red of those 13. In other words, you're arguing here that order doesn't matter...but it clearly does.
but have you considered the following argument: shut up.
Lisa: Oh, the Broncos won?
Homer: Why didn't I bet on them like Professor Pigskin told me to?
Lisa: Who's Professor Pigskin?
Homer: (Holding Professor Pignskin pamplet) He's a pig who can predict football winners in advance!
Lisa: How is that possible?
Homer: Because he's got something no gambler's ever had: a system! I've gotten the pamphlet four weeks in a row, and every time, the pick-of-the-week has been right on the money.
Lisa: Ah... I get it. Every week, they send out two pamphlets, half picking one team and half picking the other. Eventually, there's a small group of people who only receive the correct predictions and think Professor Pigskin is always right. That's when they ask for your money.
Homer: I have money!
Lisa: Dad, it's a scam!
Homer: A scam?! Not according to Eddie F. From Tucson, or Football Millionaire in Beloit, Michigan.
TO START
PRESS ANY KEY
Where's the 'ANY' key? I see Esk, Kitarl, and Pig-Up...