Everyone should go back and upvote this person, great idea imo.

Why are all these probabilities assuming exactly 1 troll per game across both teams? The chance of a troll team captain is (chance of someone who is not you being a troll) * (chance of someone not you being selected as team captain). So, (chance of someone who is not you being a troll) * 4/5. You need that missing data point. I guess you could also add (chance of you being a troll) * (chance of you being team captain), if you want maximum accuracy.

Because we assume this is a vote kick system, If more than 1 troll on the team, the voting system would not work anyways. Imagine 3 trolls and 2 regular player...

But wait, your math assumes there is a troll in the game, but not necessarily on your team. The 4/9 is the chance that the troll is on your team. If you want to assume that there is a troll in your team, then the probability of him being picked as captain is just 1/5 (20%), not 8.89%.

You need to exclude your self (which we assume it is not a troll)

Not when we are assuming the troll is already on your team. If we assume a troll is on our team, then that troll will have a 1/5 chance of becoming team captain. Now, if we only assume a troll is in the game but not on anywhich team, then the chance of the troll becoming YOUR team captain is 8.89%

You need to calculate the probability of "troll" on your team. Including that, all numbers will change. that's all the previous discussion all about.

I've read all the discussion and analysed it. You are calculating under the impression that there is a troll in the game, but not necessarily on your team. I am looking at it as if the troll is already on your team. We are trying to analyse the effectiveness of the 'Captain-initiate vote kick' system. If the troll is in a different team, then the team without the troll wouldn't matter in regards to the vote-kick (I'm assuming the vote-kick is team based, not dual-team base). So in the event that a troll appears, only the votes of the team with the troll would matter, not the other team, in that case we would not need to analyse if the troll is in your team or not. Now, if we were talking about a vote kick system where both teams vote with the team-captain with the troll initiating the vote, then it would be reasonable to use your 8.89%.

Lets focus on solutions, not hypothetical math problems of troll probability in any given game. Riot, you have a lot of good ideas, come up with some for the issue OP is describing please and give us something to look forward to. I liked the idea of a remake, that sounds like it has a very low chance of abuse and can place an intermediate band-aid on a long term problem.

Shouldn't this thread be about implementing ban lists too? The subjects are interconnected if you think it through (banning people in game, or voting to make it end in a tie so everyone can play again without the troll, both of them doesn't stop the same troll(s) to return in the next game if matchmaking feels like it)

Since the ignore function carries on after the game, why can't this prevent you from being matched with the same players on your team next time?