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
Depends on how many times the experiment is run. On a single cycle, they’re basically the same but whenever you go from 0-1 out of a million, when running it many times the odds increase dramatically
Imagine a room with 1 million atoms of air and you are one them. There’s a machine that makes 2 atoms bump into other. Even though there’s a lot of atoms the chance of you as the atom being picked is tiny. 0 in a million is like you’re not even in the room
Something with “One in a million” odds is definitely going to happen, something with a chance of zero in any number of iterations is definitely not going to happen.
They are not functionally the same.
Let’s do this instead.
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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.
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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’.
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**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.
Zero isn’t the same as not zero.
The idea is that in some situations it’s worth giving yourself a chance that isn’t zero, even if it’s small. If you’re playing a sport, a low percentage shot is better than not shooting at all, because eventually one will go in.
The lottery is a negative expected return, which means that in the long term you will lose money on average. So that’s not a rational shot to take. However, if you buy a single ticket every week, then you get to spend the whole week dreaming about what you’ll do with the money, because your chance of winning is no longer zero. And that’s probably the best return you’ll ever get from spending a dollar or two on entertainment.
So that’s the benefit of making your chances not zero.
Odds such as these can be generally thought of in two ways: proportional, or absolute.
Yes, absolutely speaking, 1 in a million is functionally the same as 0 in a million. While there is a distinct difference between the two, especially since it actually *could* happen in the 1 case, you’re *very* unlikely to notice any difference in a practical sense.
Proportionally, going from 1 in a million to 0 in a million is a decrease of 100%. It is *infinitely* less likely comparatively. Meanwhile stepping up to 2 in a million is an increase of 100%. 3 in a million is 200% increase from 1, and a 50% increase from 2.
Your frame of reference matters a lot, as does what the odds are being applied to.
The difference is something that is possible compared to something that is impossible.
If this answer gets removed then the question is indeed as daft as I think it is.
Another way to look at it: 1 in a million odds is INFINITELY more probable than 0 in a million, but 2 in a million is 2x more likely.
As a practical matter, there’s no real difference TO YOU if you purchase a lottery ticket with 1 in a million versus 0 in a million odds. You are for all practical purposes equally unlikely to win either of those lotteries. It does make a big difference to the lottery holder though, since in one instance there’s a good chance they’ll pay out if lots of tickets are sold where while in the other, they’ll never pay out.
Pretty much the same thing from your perspective for all your other examples. And there’s no practical difference from the lottery holder’s perspective for your other examples – an additional 1 in a million (whether it’s 1 v 2, or 492,368 v 492,369) doesn’t change their payout odds significantly.
For all intents and purposes, you have about the same chance of finding a winning Powerball ticket on the street as you do purchasing one.
Imagine a worldwide pandemic that has a 1 in a million chance of killing you. In the US, 330 would die from it. Globally, 8,000 people would die. If the odds were 2 in a million, the death rates would be 660 and 16,000, respectively.
If a pandemic had a 0 in a million chance of killing you, no one would die, either in the US or globally.
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