[OLD] The Balance Quiz

[Thok]

Had to include 4:7 Nightless, since I've noticed a rather common misconception about the Town's chances in Nightless games. 3:9 Treestump has also been run before, and 2:5 PairedLovers has at least been suggested (has it been run?). 3:32 Vanilla again demonstrates how many Townies you need to get a 50-50 balance in a Vanilla game... I think most would argue, however (and I'd agree) that the Town would be favored in such a game realistically.

Given my intuition, this suggests that town benefits from the lack of nightkills in games like 4:8 Nightless and 3:9 Tree Stump (and the continuing participation of dead players in actual Tree Stump.) Basically, if a couple people can convince the town that they are townies and that they shouldn't be lynched, there's nothing scum can do about that.

Of course, that's "real life" which this doesn't quite model accurately.

[Thok]

I was surprised these two were as close as they are... PairedLovers looks roughly linear, like Nightless, with a slightly different ratio. Want to investigate this a bit further.

Having thought about that, it's not that surprising. Think of it in terms of the number of lynches town needs to win.

In Nightless, town needs 10 correct lynches, each townie lynch costs 1 mislynch and 1 townie, and each scum lynch gains back a town mislynch and kills 1 scum.

In Paired Lovers, town needs 5 correct lynches, each townie lynch costs 1 mislynch and 2 townies, and each scum lynch gains back a mislynch, kills two scum and loses 1 townie. You can sort of kind of think of 10 scum Paired Lovers as a double version of 5 scum Nightless if you look at it funny.

In general, I think there's a theorem floating around that says that if a scum lynch in a vanilla variant gives town a nonzero number of extra mislynches, then the number of townies needed for balance is linear. If town earns back 0 mislynches for a scum lynch, than the number of townies needed should be quadratic in scum.

I suspect that properly phrasing that theorem is harder than actually proving it.

[Thok]

The trick to polylovers is to squeeze out as much information as you can before voting. You don't have to find all of the scum: you just need to find one of the weakest scum in the scum group and force him to crack under pressure.

[Thok]

Results?

Mith posted them on page 1 already.