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Odds of winning the jackpot in 6/49 lotto is 1 in 13,983,816. So imagine there were 13,983,816 countries and each country had its own lotto 6/49. If you bought one ticket in each country with the same numbers (eg. 1, 2, 3, 4, 5, 6) and all the lotteries made their draw on the same day, what are your odds of winning the jackpot in one of the countries?

The scenario above is hypothetical and the reason I ask is because in my country, we have two 6/49 lotteries (national and regional) that draw on the same day and I would like to know if buying the same combination of numbers for both lotteries on the same day actually improves chances of winning the jackpot in one of the two lotteries?

Please explain what the odds are for the hypothetical question and the odds for the real-life scenario of buying the same combo in the national and regional 6/49.

Thank you

Rodrigo de Azevedo
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Cannon444
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1 Answers1

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If the probability of winning in a single lottery is $p$, and you buy a ticket in $n$ different lotteries, the probability that you win in at least one of them is $1$ minus the probability that you lose in all of them or $$1-(1-p)^n$$ When $n=2$ this gives $$1-(1-p)^2=2p-p^2\approx 2p,$$ since $p^2$ is miniscule. If you but two different tickets in one lottery, the probability that one of them will win is $2p$, effectively the same, but in theory, a tiny bit more.

For $n>2$, the same remark holds. As a practical matter, you do just as well by buying $n$ different tickets in one lottery, but in theory, you do just a tiny bit better.

saulspatz
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