I had problems getting to sleep today, because I was thinking about an interesting mathematical problem. My brain isn't going to let me sleep unless I post about it here.
For the past two weeks, Steam (the game distribution platform run by Valve) has been having a sale, as it has been doing every year at this time. This time around, there are also giveaways to encourage people to play the games it has on sale. These take the form of extra achievements for certain games. When you manage to get one of these achievements, you'll get something for your trouble. Prizes come from what Valve calls "The Great Gift Pile", and it includes games and coupons.
However, there's only a 25% chance that you'll actually get something from the GGP (as I'll call it from now on). 75% of the time, you'll receive coal instead. Coal isn't completely useless, though; if you collect 7 coal, you can 'craft' them into a random item from the GGP. In addition, each piece of coal that remains in your inventory at the end of the promotion (which is tomorrow) will count as one entry into the "Epic Holiday Giveaway", which is a big raffle which takes place at the end.
The prizes for this raffle can be seen at the bottom of http://store.steampowered.com/ Since the page is no longer online, the prizes were as follows:
- Grand Prize (1 winner): Every single game on Steam
- First Prize (50 winners): Top 10 items on wishlist
- Second Prize (100 winners): Top 5 items on wishlist
- Third Prize (1,000 winners): Valve Complete Pack
(If you're interested, this is the thread in question. The fun begins at post #9, but remember while reading that X01 deleted their posts, so the quotes are all there is to go on.)
At first, the answer seems really obvious. After all, with 100 coal you're 100 times more likely to win than someone who only has 1 coal... right?
( Think about that for a second and how this relates to the whole, and decide for yourself who's right. Then, if you like, expand the cut to see my take on it. )