by David Malki !
What is the chance that the piece would actually be the piece we need?
@Amber – That's a really great question. It depends, of course, on whether or not certain pieces are more likely to be lost than others, and I can't find any studies with data on either side of that.
My guess is that since edge pieces are usually assembled first, they're slightly less likely to be lost (less likely to be hanging around the table loose). And pieces that are likely to go into the puzzle last (i.e. pieces with very subtle coloration, or with a pattern that is very common in the puzzle) are loose longer, which means they may be more likely to be lost.
But since that varies from puzzle to puzzle, and in every case those percentages will fluctuate from puzzler to puzzler with respect to storage practices, kids in the house, etc., I think the best we can do is take a rough average and say, out of a 1000 piece puzzle (which can sometimes have up to 1036 pieces), the odds of losing a particular piece are about 1/1000, or 0.1%.
We can probably assume similar odds for the piece you will be getting, unless the puzzle has a mirrored die, meaning that there are really two pieces of every given shape in the puzzle (top left and bottom right are the same piece, and so on). I've seen this be the case but I don't know how common it is, so for the sake of being conservative I'll say that's also 0.1% (1/1000 chance of getting any particular piece).
So, if we accept these numbers, the chance of you losing a certain piece, and having that particular piece to replace it, are roughly 1/1000000 or 0.0001%. It truly is..."one in a million!" :) Hope that helps!!
Soo... Still better than the odds of winning the lottery! And, if I happen to lose 2 pieces - 'cause if I've lost one, I'll probably lose another - I've just doubled my chances! Yes!
Everyone who read Terry Pratchett's "Guards! Guards!" knows that when the odds are exactly 1:1.000.000 that means the event has a very high chance of happening ;)
Of course, if we could come up with some way to precisely characterize the shape of a piece, we could set up some kind of exchange amongst the whole Wondermark puzzle community, so that folks can post needed piece/available piece and exchange through the mails, and very slightly improve chances...