I mentioned to a colleague that I’d bought two lottery tickets for last weeks Euromillions draw instead of my usual 1 to double my chance at winning. He said “Yeah, that’s not how it works.” I’m sure he is right – but why?
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Imagine that instead of millions of numbers, the lottery just had you pick from 3: 1, 2, and 3. If you bought a ticket with the number 1, you chances would be 1/3. If you bought 1 and 2, you’d have two out of the three, so your odds are 2/3; that’s double 1/3 and you’ve doubled your chances of winning.
But that’s too easy to win, so they add a fourth number. You buy 1, and your chances are 1/4; buy 2, and your chances are 2/4. 2/4 is still 2 times 1/4, so your odds of winning are doubled are by getting 2 tickets, even if your overall off are lower (2/4 instead of 2/3).
In fact, you can increase the size to any number of possibilities, N, and 2/N will always be twice as big as 1/N.
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