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Statistician's help required - odds in gambling.

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    This isn't for studies really, I haven't done statistics for years and I won't actually be covering chance and odds in my course but something got me thinking this morning about the odds of winning the lottery.

    If I put one line of numbers on on Wednesday I have a 1 in 14million chance of winning. If I put the same number on on Saturday I have a 1 in 14 million chance of winning. But I have two chances of my line being picked out. So what are the odds there? 2 in 14 million? 2 in 28 million?

    I was aways under the impression that the more often I play my line the more chance of winning I have, sort of the "law of averages" kind of thing. But how true is it? On one side of my head I can see how I have more chances of winning if I put it on every fortnight for a year but on the other side I argue that every time is just a new 1 in 14 million chance so my odds never actually change.

    HELP MY HEAD PLEASE.
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    The events are completely independent and if a set of numbers comes up one Wednesday, the can also come up the following Saturday too, just like any other of the 14 million combinations.

    So the odds are still 1/14 million. Or there abouts.
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    The probability of winning the lottery is always 1 in 14 million and this will never change since the draws are independent. But, if you are considering the probability of winning the lottery in a certain time period then you'll have an increased chance of winning.

    To work out the probability of winning the lottery once in a given week (playing Wed and Sat), you need to find the probability of winning on Wed and losing on Sat then find the probability of losing on Wed and winning on Sat. Then add these probabilities together.

    People often get mixed up by this kind of thing. E.g. the probability of getting 100 heads when you toss a coin 100 times is extremely low but the probability of getting a head on the 100th toss after getting 99 heads previously is still 1/2.
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    I agree with '-Someone-Like-You-'. Your odds stay the same, but over 7million weeks (betting twice a week) probability says you'd win (the jackpot) once. (Life says you'd probably die first)

    You'd have better odds putting both numbers on one day... or even your whole year of tickets on one day

    (Though, obviously that isn't a good idea. The odds are so small, you'd still just lose a load of money... Its a scam! )
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    The probability of not winning playing twice is:

    \left ( 1 - \frac{1}{14 \times 10^6} \right )^2

    so the probability of winning playing twice is:

    1 - \left ( 1- \frac{1}{14 \times 10^6} \right )^2 = \frac{2}{14 \times 10^6} - \frac{1}{14^2 \times 10^{12}} \approx \frac{2}{14 \times 10^6}
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    Thanks to all for the speedy replies, this has been annoying me since I woke up.

    And thanks notnek, your suggestion actually gives me a little exercise I can do to refresh my memory on some stats. Although I should probably get on with my actual work; procrastination at its finest, here.
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    (Original post by Hearty_Beast)
    I agree with '-Someone-Like-You-'. Your odds stay the same, but over 7million weeks (betting twice a week) probability says you'd win (the jackpot) once. (Life says you'd probably die first)
    Expanding on this, if you play the lottery over 5 million weeks, then you have around an even chance of winning at least once.

    EDIT: SimonM has shown you how to work out the probability of winning at least once in a given week which is probably more useful than finding the probability of winning only once.

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Updated: April 13, 2012
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