Not quite the same thing, but last year I ran a version (off-site) where the mafia had a (single-shot) ability which let them (secretly) nominate a (town) player at the start of the game who would never be allowed to become the gunbearer. If this player were shot by the gunbearer, they wouldIn post 6746, Leafsnail wrote:Also, I was thinking of running a version where the mafia get to choose the next gunbearer after they're shot (kindof like a vengekill). Has anyone ever run a setup like that, or alternatively, does anyone have any tips for calculating win probabilities more easily for such a game?
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die and the mafia would get to choose the next gunbearer from the remaining townies. (Obviously?) the nominated player wasn't told that he was the nominated player until after
he was shot...I spent quite a bit of time working out EVs for that. At some point I wondered if I should have made the scum's ability multi-shot instead of 1-shot. In that case, there's a nice(ish) closed expression for the odds of a town win: with S scum and T townies town wins 1/(2S) of the time if T=S+1 and town wins (T-S)/(T+S) of the time if T>S+1. So if you start with 4 scum and eight townies, town wins a third of all games with random voting. I have no similar nice expression for the town's chances when the ability is single-shot, but it's obviously more than that and less than the (T-S)/T of standard popcorn mafia (with 8 townies and 4 scum, town wins 39.7% of all games, for instance).
I also thought briefly about a version where the mafia had venge-kills whenever they died (but the current gunbearer was bulletproof). This is even harder for town than the "multi-shot ability" version above (with 8 townies and 4 scum, town win only 30.5% of games), though again I couldn't work out a nice close expression (or if I did, I never posted it in the game's dead thread).
... actually, I think this last variant is very close to your idea, isn't it? (From the random-voting perspective, having the gunbearer die when he shoots mafia and letting the mafia pick a new (town) player to become gunbearer seems to be equivalent to having the current gunbearer live and letting the mafia kill a different town player.) "Balanced" set-ups might be 7 townies against 3 scum (town wins 43.8% of games) or 10 townies against 4 scum (town wins 43.0% of games). Not thinking about it too hard right now, but I think the numbers stay the same even when the mafia can pick themselves as gunbearer (simply because it's suboptimal for the mafia to ever actually pick themselves like this; S scum always do better against T townies than (S-1) scum do against (T-1) townies.)
Will see if I can dig up my original notes for this in the next couple of days. At the very least I should have the spreadsheets where all the above numbers came from lying about somewhere.
