[EV] Vanilla Multiball
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- mith
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mith Godfather
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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%)- mith
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mith Godfather
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mith Godfather
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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- shos
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shos Survivor
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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=67712In post 836, Lucky2u said:
Rule # 5h05: players should not attempt to use or manipulate the mod for any purpose.- LicketyQuickety
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LicketyQuickety Survivor
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mith Godfather
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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.- LicketyQuickety
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LicketyQuickety Survivor
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I understand everything up until this point.. No idea where 1/2 and 3/4 come in...
I was anything worse than you! Anything worse than you was I!
You was doided teh aposit_tisopa het dedoid saw em.- mith
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mith Godfather
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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.- LicketyQuickety
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LicketyQuickety Survivor
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Thanks for explaining that.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.I was anything worse than you! Anything worse than you was I!
You was doided teh aposit_tisopa het dedoid saw em.- shos
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shos Survivor
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Cool, never thought I'd get an answer eventually lol ^_^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.
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!In post 836, Lucky2u said:
Rule # 5h05: players should not attempt to use or manipulate the mod for any purpose. - shos
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