Date: 2012-01-02 07:18 Security: Public xpost http://soph.livejournal.com/228251.html Tags: big posts, math, steam Subject: Musings on a math problem before sleep

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/holidaysale/details . 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

The Steam forums have had an interesting discussion going on about this last raffle. One person (whose name was "X01" on the forums) casually mentioned how having 100 coal would hardly increase your chances to win, and that you wouldn't be 100 times more likely to win. Another person replied to say that 100/<number of entries> is 100 times bigger than 1/<number of entries>, so yes, you would be 100 times more likely to win. From there, there was a big argument between X01 insisting they were correct, and most of the other people on the forum saying that, c'mon, this is basic math. It eventually ended up with X01 deleting their comments in anger and disappearing from the thread.

(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. )

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