math question:
so today I was bored and was trying to figure out the odds of a slightly subpar NFL team's chances of going 16-0. The reason I say 'slightly subpar' is because if all goes well in Cleveland (we are due), I would say the Browns are a slightly subpar team. If things don't go well, we are terrible, but we're due so that won't happen. Proof: see the Cavs.
Anyway, my slightly educated guess was 1/million. I'm going to make the horribly flawed assumption that we have the same chance of winning every game, based on the assumption that every game is an independent event and we have a 1/million chance of going 16-0.
So I started off with 50% chance of winning a game, 2^16, 65536. Number should be familiar to people who used to multiply by 2 in their head starting since they were a little kid (2, 4, 8, 16, 32, 64, 128, etc). Way low. 3^16 was way high, > 4m. 2.5^16, still too high. After doing this for 5 minutes or so, I finally came up with 2.3713737057^16 = 1x10^6, or 1m. Very cool.
Now how do I do this without doing trial and error? I know I learned it in high school and I'm sure I could find the answer in about 30 seconds of googling, but I ask the great people of FTR instead. I don't know why.