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LucasSloan comments on The Prediction Hierarchy - Less Wrong
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Your odds of winning once go up as you increase the number of tickets you buy (# of tickets purchased * Chance of winning per ticket). The expected value of a given ticket remains the same. All you are doing is focusing more money away from other possibilities. If you buy 5 tickets a week for your entire life, and the odds of winning are 1 in 100 million, then you have a 0.000169 chance of winning the lottery, but you could have spent your 16 thousand on a new TV or a vacation.
It comes out to about the right number in this case, but your math is wrong. The expected number of times you win in n trials at probability p equals np, but the probability of winning at least once is slightly less at 1-(1-p)^n.
Yes, thanks for the correction.