Eli5: What’s the difference between something with 1 in a million odds and 0 in a million odds?

Question

I was thinking about lottery odds, and how so much of the pitch is, essentially, you miss 100 percent of the shots you don’t take, with the thought that you should at least enter because your odds go up so much with just one ticket. The odds were non existent before, and now they exist even if they’re vanishingly small.

Is the difference between 1 in a million and 0 in a million actually somehow more than the difference between 1 in a million and 2 in a million, or between 492,368 in a million vs 492,369 in a million? Or are all three of these functionally the same?

In: 0

Answer 1

Let’s say there are three raffles you can buy, the 0 in a million raffle, the 1 in a million raffle, and the 2 in a million raffle.

You want to better your chances so you’re looking to buy enough raffles to get you a 10% chance of winning.

For the 2/million one you would need to buy 50.000 raffles.

For the 1/million one you would need to buy 100.000 raffles.

For 0/million, you cannot buy enough raffles or best case assuming its a rounded down 0/million you would need at least over 2.000.000 raffles.

So that means that they are not functionally the same.