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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Unless you picked the same numbers, your coworker is wrong. Since every combination of numbers has an equal chance of winning, every subsequent entry multiplies the likelihood that you’ll win.
To see this in action, just do some simulations with very small numbers.
If you have a pool of 5 numbers and only need to match 2 of them, you’ll see that every combination has a (1/5)(1/4), or .05, chance of winning. This is true whether you choose 1 and 2, 1 and 3, 1 and 4, 1 and 5, 2 and 3, 2 and 4, and so on.
If you buy two unique entries, your chances become 2(1/5)(1/4) or .1, which is double the odds of one entry. This is true even if one of the numbers on the second ticket is the same as one number on the first ticket because, as mentioned earlier, every combination has an equal chance of winning.
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