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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.
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.
For this problem, you think about your chances of not winning:
One ticket: chance of not winning = 1/2
Two tickets: chance of not winning = (1/2)^2 = 1/4
N tickets: chance of not winning = (1/2)^N
So, even with 100 tickets, you still have a (1/2)^100, or about a one in a thousand billion billion billion, chance to still not win.
Yo dawg, I heard you like the Ackermann function, so OH GOD OH GOD OH GOD
I think the reason is pretty obvious. The state keeps half the money people spend on lottery tickets (more than half according to another comment above--I don't actually know the exact percentage), whereas the private poker house doesn't give anything to the state. So yeah, you're right it's the states' desire to keep their stanglehold on gambling. Note that in Nevada, where gambling is legal, the stanglehold is just as strong. You didn't think the casinos kept all that money did you? Funny thing, it just goes to show how dumb it is to gamble--casinos rip people off of enough money to pay a huge chumk of it to the state and still have plenty left over to build build frilly over-the-top gold palaces and pay their executives millions.
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.
Unfortunately, the jackpot is probably still not large enough, even if you do not have to share it. You lose 30-35% on taxes + the lottery only pays it out over many years (or you can take a much smaller lump sum) which devalues the jackpot at the rate of inflation.
You would be lucky to take 1/3 of the value of the jackpot even if you are the sole winner. In that case
the expected payoff is no longer in your favor.
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"
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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.
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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.
I am trying to point out that a sequence of 13 black is more SURPRISING (from both informal and formal standpoints) than a sequence of 8 black and 5 red.
Sure, because you're comparing completely different things: a single very specific sequence (b,b,b,b,b,b,b,b,b,b,b,b,b) with a whole family of sequences (8b/5r in any combination), whereas the OP was (correctly) comparing (b,b,b,b,b,b,b,b,b,b,b,b,b) with an equally specific sequence: (Red, Black, Black, Red, Black, Red, Red, Black, Red, Red, Red, Black, Red). And the OP is absolutely correct that both sequences have exactly the same probability. It is only when you start comparing classes of sequences that some become more surprising than others.