League of Legends ARAM champion selection math & statistics

[RU] Switch to Russian General information about LoL ARAM [click to expand] Purpose Many players have doubts about ARAM champions distribution. Champions seem to repeat too often, you are getting none of your favorite champions. However the whole process is a bit more complicated than it might intuitively seem. There are multiple cognitive biases that may strongly affect estimations: Specific champion. When you get Katarina 3 times in a row, you can think that this is very unlikely event. But your feelings will not change much if you will get Shaco, Varus or Kai'Sa 3 times in a row. Getting specific champion (like exactly Katarina) is different from getting the same champion. Later one is way more likely. Birthday paradox. Let's say the game has a total pool of 161 champions. Also there are 10 champions that you like to play. Game lobby starts and your team rolls 10 champions to choose from. How likely that there will be at least one champion that you like playing? It's about 48%. This...