Secret Santa - Holiday Exchange 2012

The thing about probability is that it is not that straightforward. Even the very big names in Math who were at its birth were oftentimes confused about the right ways to do stuff. For example for a long time they believed that when you flip 2 coins the chance of getting one heads and one tails was 33% and couldn't understand why it didn't work in practice (the correct answer is 50%).

There's a classic question in probability about a length of a chord obtained by drawing a random straight line across a circle. The thing is that the answer differs and depends on how you define drawing a random line!

There's a (totally natural and totally making sense) way to randomly draw Secret Santa assignments with 0% chance of a participant having to gift oneself.

About 39% of reciprocal draw - highly doubtful. First, it depends on the number of participants.
It goes from 100% chance with only two participants, who have to exchange gifts to 0% with three (because if A and B swap gifts C is stuck with himself, and this scenario should be eliminated).
But it is 50% with 4 people, 33% with 5, and it goes down from there. It's going to be significantly low with over 100 participants ...

You might've miscounted something here
With 4 people, there are 9 possible assignments, of which 3 involve a reciprocal draw; so the chance is 1/3, or about 33%.
With 5 people, there are 44 possible assignments, of which 20 involve a reciprocal draw; so the chance is 5/11, or about 45%.
With 6 people, there are 265 possible assignments, of which 105 involve a reciprocal draw; so the chance is 21/53, or about 40%.
It gets a little complicated here... with 7 people, there are apparently 1854 possible assignments, of which, if I counted correctly, 714 involve a reciprocal draw; so the chance is 119/309, or about 38.5%.

...I don't know how exactly that sort of stuff works, but this looks a lot like a sequence that converges to something slightly over 39% to me. The theoretical limit for a completely random draw is 1-exp(-1/2)=0.393469... (a number I rounded off to 39%); and it seems now that it's the same when we exclude assignments with 1-cycles (I wasn't originally sure of that - thought it would be slightly higher).

How early can we send our gifts? I already have my assignment!

May I offer a different approach to choosing the coin for your recipient? Rather than trying to figure out what she/he likes, you should send something 'different'. If you are from different countries then send a coin from your country. If you collect different types of coins send one that you like.

I'm thinking that this may help to broaden everyone's areas of interest. OK, just my opinion...

Good idea, after spending a hour or two this afternoon looking through 35 pages of threads that my recipient posted in I found one coin that he said he needed but that was 4 months ago. No need to stress out over this, just enjoy it.

To january1may:

OK, I concede! I found a flaw in my handling four people ( I thought it would be 3*2*1, but now I see where the extra 3 options come from). And I don't even want to venture into figuring out more people ... I'll agree with your numbers!

Now, back to the current topic: it is eventually totally up to you what you choose to send. If you find out that your recipient collects wheat cents (and probably has tons of them) will you send him/her yet another one?

My gift to my secret recipient has been sent. I'm sure I'll be notified when it is received. I hope you wait until Christmas morning for the bountiful booty yee shall receive.

And one more thing. My recipient just so happens to be on this page of this thread.

Not even a slight chance this will happen on my end!