ELI5: The almost surely probability concept

Think about throwing a dart with an infinitely small point at a map of the world, which you can scale down to any size. If you throw the dart, it's going to stick somewhere on the planet. It may very well stick right on the border between Canada and the USA.

But there's the problem: there is no point in which the dart can hit that exact spot, because that exact spot is infinitely small. (In practical terms, it doesn't have any area for the dart to stick into.) However, it still exists. There is a border between the USA and Canada -- there has to be, because some points are the USA and some points are Canada and there's no gradient between the two -- so in theory the dart could stick there, in that exact spot. It's within the bounds of the possible. It can also never happen, because the area is zero. The dart sticking there is no less likely than it sticking in any other random spot... but there are also no spots in which you could consider that part of a 'win' condition.

That's what probability theory would call call 'almost surely'. It means that there's zero chance of something happening (not just that it's super unlikely, like randomly shuffling two decks of cards of having them come out identically, but actually zero chance) -- but that's still within the other rules of the game.

/r/explainlikeimfive Thread