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

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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?

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19 Answers

Anonymous 0 Comments

They are not functionally the same.

Let’s do this instead.

————–

Take a MILLION TICKETS.

Make ONE TICKET A WINNER.

Give a million different people a ticket.

Point at a random ticket receiver. Anyone at all that got one of the tickets..

The odds that they have the winning ticket is one in a million.

————

Now take a MILLION TICKETS

Make NO TICKETS WINNERS.

Distribute and point, exactly as above.

The odds that they have the winning ticket is zero in a million.

It is not possible for anyone there to be a ‘winning ticket holder’.

——————–

**With one in a million, someone can win, or the thing can happen. With ZERO in a million, nobody can win, and there is no way for the thing to happen. Ever.**

It could possibly happen if you said *one in a billion*, or *one in a trillion*, or… keep going. Someone MIGHT hold a winning ticket.

But it CANNOT happen if there are zero winning tickets. This is true regardless of whatever number you put after the phrase “zero in a ???”.

Zero means NO CHANCE. Period.

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