Christmas

The Christmas period can be really hard on the wallet. How much do you spend on presents, when the average spent by adults is around to 1000-1500$? We are compelled to buy very expensive presents, because the society we live in slowly brainwashed us into thinking that love is proportionally quantified to the gift price. This is a very smart system implanted by the stores and financial institutions.

If you don't believe me, you can check the ads in december. For example, I have beside me a "Gift Guide" from Apple. Yes, the iPad 2 is in it (650$+), and so are the iMac (1200$+) and MacBook Air (1000$+). Who buys presents at that price? Companies say it's ok to spend that much, so people listen to them.

In my family, we have turned our back on such practices. Christmas 2011 will be the second such Christmas. It plays out like this: we have a designated name (chosen at random) beforehand, set a maximum price (we usually go for around 25$), and set how many "small gifts" to prepare (depending on how long you want the evening). That means everyone bring one single "bigger gift", and a number of "small gifts". These "small gifts" should be inexpensive (eg. a special chocolate bar, a tennis ball, a rubik's cube you found in your basement, a few cookies you made...), and are exchanged for fun.

This kind of gift exchange is for a group of adults. Let's admit it - Christmas should be for kids! We buy slightly more expensive presents for each of them - usually, 25-50$ should be enough. No need to break your credit card limit, and no need for a 200$ gift. We all know that children can have more fun with a huge cardboard box than with almost anything.

We usually end up spending less than 150$ each (there are three kids in my family - my sister's). We feel better about ourselves, our wallets thank us, and we can put more emphasis on good food. We can focus more on children, and us all being together. We can have fun, instead of having that nagging feeling in our head that asks you how you're going to pay your credit card debt in January.

I admit - this is very hard to implement and accept. You will all feel cheap, fell that the other person will think you don't love him/her if you don't give the perfect gift. You will look at the neighbors' Christmas tree filled with colorful gifts. But then, you will mature and really understand what Christmas should be about.

Some Mathematics
Every year we have been doing this, we ran into some statistical problems when choosing the gift target at random. We each get a piece of paper with a name on it from a hat. Done manually like that, chances are on one turn, someone will get an invalid name, because you can't have your own name, and we also decided that you can't get your significant other's.

In our case, we have two couples (my parents and my sister+boyfriend, plus myself). Lets get this step by step...

At the simplest, everyone gets someone else's name (the couples don't count), and all pieces of paper are put back in the hat. Everyone has 4 / 5 chances of getting a valid name, which results in ( 4 / 5 ) ^ 5 = 1024 / 3125, or 32.8%.

If the names are not put back in the hat, we fall into a derangement. For 5 people, !n / n! = 44 / 120, or 36.7%.

If the names are put back, but the couples count, we have 4 persons with 3 / 5 chances, and one with 4 / 5 (me). That results in ( 3 / 5 ) ^ 4 × ( 4 / 5 ) = 324 / 3125, or 10.4%.

The calculation gets pretty complicated if the names are kept, and the couples count. Maybe I'll try working out a general equation about this in a future post. Turns out there's only 16 possibilities on 120, or 13.3%. This is why we had to retry again and again (for an average of 120 / 16 = 7.5 times).

Statistics...


Edit: the final statistics should be linked to the Rencontres Numbers, but I don't get exactly the same numbers when I manually calculate the possible permutations.