Originally Posted by
Ziggurat
You actually need to be more specific about your setup. The latter has a slightly higher chance of never winning. But it also has a very small chance of winning more than once. So if winning twice is twice as good as winning once, then the two are equivalent, but if winning twice isn't twice as good, then the former is better than the latter.
This.
Given most lottos split the winnings between multiple winners, winning 2x or more in the second lotto gains you nothing. You're just splitting in half the exact same pot you'd win with 1 winning ticket anyway.
Hence you are slightly better off with the one bet on the first lotto.
The math isn't all that hard, either. To calculate it, you invert the calculation.
Consider two lotteries, one with 1/1000 and the other, 1/10,000 odds.
The chance of winning is 1 minus the chance of not winning.
In the first case, the chance of not winning is 999/1000. In the second, it's 9999/10,000, but that's with just 1 ticket.
Now why calculate the inverse? Because in the second case, you are buying 10 tickets. And the chance of winning at least once is one minus the chance of winning none at all.
And the chance of winning none at all is the chance of not winning on the first time, 9999/10,000, times the chance of not winning with the second ticket, 9999/10,000, and so on.
That's 9999/10,000 to the 10th power, or 0.99900044988002099748020998800045, which is a whisker above the 0.999 chance of the 1 ticket lottery. So you're slightly more likely to not win anything with the 10 ticket lottery, the first number.