Mafiascum.net

What would be the proper distribution for mountainous multi ball, starting at around eleven?

Finally put together a script to do this for higher counts. These are the results with the 1:1:2, 1:1:3, and 2:2:2 improvements included (I'm including the first setup with EV > 1/3, the closest setups to EV = 2/5 and EV = 3/7, and the last setup with EV < 1/2):

2:2:9 (33.6%)
2:2:15 (40.2%)
2:2:18 (42.9%)
2:2:28 (49.5%)

3:3:20 (33.8%)
3:3:30 (40.0%)
3:3:36 (42.9%)
3:3:56 (50.0%)

4:4:32 (33.7%)
4:4:48 (39.9%)
4:4:57 (42.7%)
4:4:88 (49.9%)

5:5:46 (33.5%)
5:5:69 (40.1%)
5:5:82 (42.9%)
5:5:125 (49.9%)

I think my next run of the script is going to be something like Jungle Republic - multiball setups where each group plays with "Vanilla Variant" rules but not necessarily the same rule.

One interesting thing I found generating the above numbers is that for a general setup X:Y:Z where 0<=Y<=X, town EV is not necessarily maximized at Y=0 or Y=X. For example:

2:0:9 - 0.3520923521
2:1:9 - 0.3790586343
2:2:9 - 0.3362550955

This isn't universally the case though:

2:0:28 - 0.5730082052
2:1:28 - 0.5546413745
2:2:28 - 0.4952180666

Hey mith, any chance you can hand over the script or perhaps run it yourself over the variations of this setup? http://forum.mafiascum.net/viewtopic.php?f=115&t=67712

Just posting here so I have it in my "view my posts" section.

Posting to answer shos' old question:

I may make my script available at some point (I haven't looked at it in a while, and would want to make it more user-friendly). It is only useful for setups with no role abilities, or with very limited (both in number and in options) role abilities. For example here is an example of caluclating EVs with a single Vigilante with the Innocent Child modifier (to avoid fake/counter claiming strategies); a subsequent post allows fake claims but makes some assumptions about both Mafia and Town strategy in the process.

The more significant improvements in EV calculation come with the really small setups that the script isn't useful for anyway (such as 2 Mafia, 1 Vigilante, 2 Townies). It's hard to prove that a particular claim/lynch strategy is optimal, but improvements affect larger setups that can reduce to the small setup.

In post 4, mith wrote:Town EV 1/2(2+m+w); Mafia EV w/(2+m+w) + 3/4(2+m+w) = (3+4w)/4(2+m+w); Werewolf EV (3+4m)/4(2+m+w)

That means if we were always going to lynch, m->0 and w->0, as expected.

I understand everything up until this point.. No idea where 1/2 and 3/4 come in...

I think the confusion here is from me being lazy with brackets and order of operations.

In the 1:1:2 setup:

If scum is lynched first (which has probability of w/(2+m+w) or m/(2+m+w), where m and w are the likelihood that Mafia and Werewolf would offer themselves as the lynch), the other scum wins (EV 0 for town, EV 1 for that scum group).
If town is lynched first (which has a probability of 2/(2+m+w), where m and w are the likelihood that Mafia and Werewolf would offer themselves as the lynch), town's EV is 1/4 (it's a 1:1:1 Night with unknown alignments, and town only wins if Mafia and Werewolf shoot each other). Mafia and Werewolf each win 3/8 of the time (counting the both-shoot-town as a draw and EV 1/2). So town EV is 1/4 * 2/(2+m+w) = 1/(2(2+m+w)), since this is the only way they can win.

Mafia EV is 1 * w/(2+m+w) + 3/8 * 2/(2+m+w), with the first part coming from Werewolf lynch and the second from town lynch, this reduces to (3+4w)/(4(2+m+w)). Similarly for the Werewolf EV.

In post 33, mith wrote:I think the confusion here is from me being lazy with brackets and order of operations.

In the 1:1:2 setup:

If scum is lynched first (which has probability of w/(2+m+w) or m/(2+m+w), where m and w are the likelihood that Mafia and Werewolf would offer themselves as the lynch), the other scum wins (EV 0 for town, EV 1 for that scum group).
If town is lynched first (which has a probability of 2/(2+m+w), where m and w are the likelihood that Mafia and Werewolf would offer themselves as the lynch), town's EV is 1/4 (it's a 1:1:1 Night with unknown alignments, and town only wins if Mafia and Werewolf shoot each other). Mafia and Werewolf each win 3/8 of the time (counting the both-shoot-town as a draw and EV 1/2). So town EV is 1/4 * 2/(2+m+w) = 1/(2(2+m+w)), since this is the only way they can win.

Mafia EV is 1 * w/(2+m+w) + 3/8 * 2/(2+m+w), with the first part coming from Werewolf lynch and the second from town lynch, this reduces to (3+4w)/(4(2+m+w)). Similarly for the Werewolf EV.

Thanks for explaining that.

In post 31, mith wrote:Posting to answer shos' old question:

I may make my script available at some point (I haven't looked at it in a while, and would want to make it more user-friendly). It is only useful for setups with no role abilities, or with very limited (both in number and in options) role abilities. For example here is an example of caluclating EVs with a single Vigilante with the Innocent Child modifier (to avoid fake/counter claiming strategies); a subsequent post allows fake claims but makes some assumptions about both Mafia and Town strategy in the process.

The more significant improvements in EV calculation come with the really small setups that the script isn't useful for anyway (such as 2 Mafia, 1 Vigilante, 2 Townies). It's hard to prove that a particular claim/lynch strategy is optimal, but improvements affect larger setups that can reduce to the small setup.

Cool, never thought I'd get an answer eventually lol ^_^

Since this question came up, I ran ~5 variations of this setup to form the first (?) micro multiball which seemed actually balanced. A few runs were needed to perfect it. Those games were fun to mod!