On Nash equilibria and calculating EVs

[callforjudgement]

I suspect, but am not sure, that mathematically WIFOM (i.e. "scum have to sometimes play suboptimally to prevent them obviously being scum") tends to exactly cancel out any advantage scum get from not aiming to help town with their actions. (Or in other words, that calculating the equilibrium situation assuming that town have zero knowledge gives you the same result as "nobody knows what they're doing, not even the scum".)

In the 3p lylo situation, there are 8 possible sets of scumreads that the players can collectively have (e.g. "A scumreads B, B scumreads A, C scumreads A" is one of the 8 possible cases). Only 2 of these cases lead to scum being lynched, so at first you'd think town's chances are 1 in 4. However, there are also 2 cases where nobody can be lynched without a change of stated read (e.g. "A scumreads B, B scumreads C, C scumreads A"). You might consider this a scum win because scum can just change their read to break the cycle. However, if you make people state their reads in advance before placing any votes (ideally on previous days), then this might force the scum to shift their read in an unnatural way; so equilibrium simulations assume that scum have to commit to their previous read in this situation some proportion of the time (to avoid being caught out as being scum as a result), and thus that the case "cancels itself out" for EV calculation purposes. By the way, this case is why town's EV is 50% if scum votes first; once they commit to a read on the townie who doesn't suspect them, a quick "not hammering" by the non-voted townie will get the other townie to change their mind, and the scum will get lynched.

[callforjudgement]

When I'm scum in 3p lylo, I'm normally the scummiest player there. (If I'm not looking scummy I'd typically, although not always, try to win at 5p instead.)