Combinatorics and Gaming Dynamic Queues
I decided earlier today to figure out a way to attempt to play the Mid lane more often. Coupled with this desire and time to play with friends, I came up with a scheme to boost the probability of getting a primary role in a group with two or more people. This was largely done in a back of the envelope type fashion for a quick estimate the potential effect of gaming the role assignment from dynamic queues with a friend to weight role assignment in a particular manner.
The principle is simple, find friends who prefer a different lane to your main and share a secondary.
For example with three people, who's preferred roles are listed as follows.
- Primary: ADC, Secondary: MID
- Primary: TOP, Secondary: MID
- Primary: JUN, Secondary: MID
Thus if one of the players gets MID the other must then get their main role. This would imply that, assuming all roles are approximately equally popular, each individual would get their role n/(n+1) percent of the time. Where n is the number of people queuing together.
I am unsure how to approach this given an uneven probability distribution for each role, but I will be giving the the good old college try over the course of this week.
