Seeing people talk about yasuo ban rates got me thinking
I just want to say that, in the end, I spent a lot of time but didnt end up with the result. I invite you guys to help me figure this out. If you solve it, and are on NA, I will send you $10 worth of RP.
There are 6 bans per game. Every other game, yasuo is banned. Assuming there is no influence on players for bans, 50% ban rate means that 1 out of every 20 people ban yasuo (6 people with bans) 60% of games you receive a ban. Originally you would have to ban yasuo once every 20 games, but adding the 60% banrate, that becomes every 12 games you have to ban him. Now let's calculate the fact that once one person bans him, nobody can ban him. We assume that 50% of players want to ban him. There's a 50% chance that the first ban goes to yasuo. 25% chance for second ban. 12.5% for the third ban. 6.25 for the fourth ban. 3.125 for fifth. 1.5625 for sixth ban. That totals up to about to 98% of leagues community wanting to ban him. The mistake here is that it totals to 50% so that, in reality, the ban rate of yasuo is less than 50%. We calculate this by performing a function with variable X where x represents the percentage of people who want to ban yasuo. X%+1/2x%+1/4x%+1/8x%+1/16x% +1/32x%=50% (of games) This totals up to 1/32X=50 which means that 1600% people want to ban yasuo, which means that I probably need to use a multiple variables to determine the actual answer. Stick with me. X will remain as the % of people that want to ban yasuo. A new variable Y will be First ban X0.6 should be logical, but if 100% of people want to ban yasuo, that's a 600% banrate. But if 30% of the community wants to ban yasuo, that's a 18% chance that yasuo gets first ban. Which is logical, oddly enough. So we will continue using this Person 2 has x0.6 chance of wanting to ban yasuo. However we must deduct the chance of person 1 already banning yasuo. 100-(x*0.6) Third ban would be {100-[100-(x0.6)]}(x0.6) Fourth would be (100-{100-[100-(x0.6)]})(x0.6) Fifth would be 100-(100-{100-[100-(x*0.6)]}) And finally sixth would be Here we go {100-[100-(100-{100-[100-(x0.6)]})]}(x0.6) So someone please correct my errors and tell me how to solve this.
