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Yes you do, assuming you select different numbers. Consider a lottery with only ten possible outcomes - a ticket has just one digit. You buy a ticket, say with the number 3, and I buy two tickets with say 5 and 7. Now we pull a random number out of the hat. Who has a better chance of winning?

To a certain extent, you're right, but the odds are still so small that one ticket or a hundred, you're extremely, infinitesimally unlikely to win. This question was answered by none other than Marilyn Vos Savant, famous for having the Guinness Book of World Record highest IQ.

Q: Say the chances of winning a lottery are 1 in 50 million. A friend claims that if you buy two tickets, your chances improve to 1 in 25 million. Likewise, if you buy ten tickets, your chances go up to 1 in 5 million. I think he must be wrong. While ten tickets would improve your chances, they wouldn't go as high as 1 in 5 million. Who is right?

Marilyn responds:

Your friend is correct. One ticket = 1/50 million; two tickets = 2/50 million; and ten tickets = 10/50 million.

***

In other words, 1 in 50 million or 10 in 50 million, your odds are still so slim that buying nine more tickets won't help much--if at all.

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