Patterns in Lottery Numbers 563
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.
Conclusion: (Score:2, Informative)
Re:Sorta related question. (Score:2, Informative)
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.
Re:Lottery vs. poker (Score:3, Informative)
Let's try some simulations shall we? (Score:4, Informative)
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.
Re:Don't play the lottery, play the players... (Score:3, Informative)
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.
Re:Conclusions... (Score:3, Informative)
This is an insult to statistical analysis (Score:2, Informative)
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.
Re:Conclusions... (Score:3, Informative)
So frankly, I think that your comment is incorrect, overrated, and probably designed for karma whoring.
Sample Size (Score:3, Informative)
This is silly (Score:2, Informative)
Re:Conclusions... (Score:5, Informative)
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.
Re:Conclusions... (Score:1, Informative)
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.
Re:Sample Size (Score:1, Informative)
That's why accurate polling of a population of 300+ million people can be done, with a representative sample of only a few thousand individuals.
( http://en.wikipedia.org/wiki/Opinion_poll#Sampling_error [wikipedia.org] )