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If you consider that you have a coin, head or tails, and let's say tails equals winning the lottery. If I participate in one such event, I may not get tails. It's roughly 50%. But if a hundred people are standing with a coin and I or them get to flip it, my chances of having gotten a tail after these ten attempts, is higher, is it not? Way higher than 50% though I'm not sure how to calculate it.

So why is it different for lotteries? Or is it? I was once told that in a certain lottery, I had a one in 12 million chance of winning. And like the coin toss, each lottery is different with different odds, but would the accumulated odds be way higher if I participate, be it in this same lottery over a thousand times, or this lottery and thousand other lotteries around country, thereby increasing my chances of getting a win, a tail?

I appreciate a response, especially at level of high school or first year university (did not do math past first year university). Thank you.

Arman
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  • In general, the more times you enter, the better the chance you win (but if there are twelve million possibilities and you cover them all you can't get a higher chance of winning than $1$). But you also need to investigate the cost of entering and the amount you win. Suppose a typical lottery returns a quarter of the stake money in prizes - you will lose, on average, three quarters of everything you spend. – Mark Bennet Aug 06 '15 at 07:14
  • I now see that I misread your question. I thought you were asking about participating in separate lotteries, rather than participating multiple times in the the same lottery. In the latter case, your chances of winning do increase, as others have said (though you'll end up spending a lot of money before you have a decent shot at winning).

    Anyway, I withdraw my previous answer. My bad!

     – 727 Aug 06 '15 at 08:29
  • Does this answer your question? Probability of winning the lottery the more you play it? –  Jun 06 '23 at 07:26

3 Answers3

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There are a few similar but different problems here, perhaps that is what is causing confusion.

  • If you are aiming to win the lottery at least once, then the more times you enter, the better your chance of success. It's the same as the coin problem you described.
  • If you are aiming to win the lottery every time you enter, then the more times you enter, the worse your chance of success.
  • If you are aiming to win overall from the financial point of view - that is, you want your winnings to be more than the amount you paid for lottery tickets - then the more times you enter, the worse your chance of success. At least this is true for a "normal" lottery, but if you imagine an "altruistic" lottery where the organisers pay out more than they receive in entry fees, then the reverse would be true. If you hear of an "altruistic" lottery like this, please let me know in the comments ;-)
David
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Your chances of winning the lottery does increase if you participate in more lotteries. Say you particpate in the lottery where you have a 1 in 12 million chance of winning 1000 times. Then the probability that you don't win a single time is $$\biggl(1-\frac{1}{12000000}\biggr)^{1000} \approx 99.992\%$$ So you would still be very unlikely to win a single lottery, but your chances have definitely improved.

ignoramus
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From a probability point there is no difference between lottery and coin toss, but there is when you compute the number. Tossing ten coin you have $\frac{1}{2^{10}}=\frac{1}{1024}$ probability of not winning which is $\frac{1023}{1024}$ probability of winning. If you partecipate in ten lotteries, say that in each of them you have a 1 on a million probability of winning(i think in real lotteries this is lower). Then you have $(\frac{999999}{1000000})^{10}$ probability of losing which is still almost zero probability of winning

karmalu
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