It's about when I felt explaining the thread. Polaritie's proof is correct.

A formal proof isn't necessary if you understand what large numbers of trials do to probability. The more trials you have, the more likely it is that you receive a value very close to the expected return.

Say you used option B 20 times. Since Option B is actually less than the average you need to get, the remaining 80 coin flips have to reach a HIGHER average value to meet your minimum.

I asked the poll question in a very biased way. The reason I did so is because people look at elo in a very biased way, they all think they're amazing players. When confronted with something as abstract as 100 coinflips or 100 matchmaking games with 9 other players who leave on both teams, the bias can take over.

A lot of criticisms to the elo system come from the sort of people that would miss this question. There's nothing wrong with criticizing the elo system if you understand statistics and math pretty well, but using anecdotal evidence and bias about your own elo clogs the forums.

Interestingly, option B is VERY analogous to "stat tracking", the suggestion that players repeatedly make asking that stats like kills, assists, and tower destroys be used to determine someone's true elo. Stat tracking is more stable for a sample size of one game, just like option B, but since it's overall inaccurate on anything but carries (and probably still not 100% accurate for carries), it's missing the ideal amount the way option B does. Riot says they use it only for the first few games, very small sample sizes, where it makes sense.

Instead of stat tracking, it's better to allow a large number of random matchmaking games to occur and eventually arrive at an accurate elo.