Post #27
(ISO)
» Fri Feb 23, 2018 5:02 pm
I should really just write a guide to calculating EV and finding optimal strategies. There's a lot of good stuff to be said there.
As for your specific question, the main thing is that it is a lot of tedious work (if the setup is at all complicated), mostly in establishing what the best strategy is in LyLo or near-LyLo situations. Towns (and sometimes Mafia) often have non-obvious ways to increase their EV, and significant changes in small setup EVs carry over to the larger setups.
Other than that, it's all logic and math. If you want to generalize to an arbitrary size, the idea is to set up a recursive relationship to smaller setups (simple example: 2:5 Vanilla can either reduce to 2:3 or 1:4 after a lynch and nightkill, depending on whether you lynch Mafia or Town; to calculate the EV of 2:5, you need to know the EV of 2:3 and 1:4, along with the probabilities of reach both states, and similarly you need the EV of 1:2 to calculate those). In some setups, you can find a pattern and go back and prove the pattern holds via induction (see the Vanilla Variants thread for examples - that complicated mess in the most recent post is just the result of me putting things into a spreadsheet until I found the pattern). Some setups don't have nice non-recursive EV formulas (Vanilla doesn't), but some do (Nightless is (T-M)/(T+M)), and once you know what the answer is it's pretty easy to prove it.
The other thing to remember is that small changes can lead to huge complications. You want to approach EV in an incremental way, understanding the simplest setups first before you add even a minor role ability.