[SETUP] The Colosseum

This forum is for discussion of individual Open Setups, including theoretical balance.
User avatar
BlackVoid
BlackVoid
Mafia Scum
User avatar
User avatar
BlackVoid
Mafia Scum
Mafia Scum
Posts: 2725
Joined: September 15, 2016

[SETUP] The Colosseum

Post Post #0 (ISO) » Thu Sep 29, 2016 4:43 pm

Post by BlackVoid »

It'll probably be a long time before I can mod on this site but there was a mafia setup I've been playing around with that I'd love to hear feedback on to see if it's viable to run.

Size: 14 players (5 mafia goons, 9 vanilla townies).
Mafia can converse in private at all times.

D1 lynch works normally. With 14 players, it's 8 to lynch. But this is a crucial lynch as the outcome determines what happens next. If there is a no lynch, mafia choose someone to nightkill N1. Otherwise, it's nightless.

Starting from D2, each day mafia set up a duel between one of their members and a town player. The same player on either side cannot be chosen twice. During each duel, the only players that can be voted for are the two duelers. The duelers can't vote. The duels are always between one town player and one scum player.

Anytime a scum player is lynched, the townie who won the duel is confirmed town by the mod and made into a tree stump who can offer opinions but not vote. When a town is lynched, the winning scum is confirmed scum and can continue posting in the mafia private thread but is not allowed to post in the main thread (to prevent trolling spam). The losing players are dead and can't post in any capacity in the game. No lynch at any point counts as a scum win of that duel.



Here are the two gamestates that the game can possibly go into:

Gamestate #1: Mafia is lynched D1


This leaves 4 mafia, 9 town - total 13. All four mafia each need to duel a town player. Town need to lynch 2/4 right to win. Mafia need 3/4 mislynches to win.

Spoiler: Test cases
Test scenario:

D2: With 11 voters, 6 to lynch. 3 are scum, 8 are town. Town is lynched.
D3: With 9 voters, 5 to lynch. 2 are scum, 7 are town. Town is lynched.
D4: With 7 voters, 4 to lynch, 1 is scum, 6 are town. Lynch or lose (lylo). Scum is lynched.
D5: With 5 voters, 3 to lynch, all 5 are town and thus confirmed. Lynch or lose (lylo). If scum is lynched, town win, if town is lynched, scum win.

Worst case town win scenario:

D2: With 11 voters, 6 to lynch. 3 are scum, 8 are town. Scum is lynched.
D3: With 9 voters, 5 to lynch. 2 are scum, 7 are town. Scum is lynched, town win.

Worst case scum win scenario:

D2: With 11 voters, 6 to lynch. 3 are scum, 8 are town. Town is lynched.
D3: With 9 voters, 5 to lynch. 2 are scum, 7 are town. Town is lynched.
D4: With 7 voters, 4 to lynch, 1 is scum, 6 are town. If town is lynched, scum win.


Gamestate #2: Town is lynched D1
(or there is a no lynch and a nightkill)

This leaves 5 mafia, 8 town - total 13. The mafia can choose which four of their members are going to duel. Town need to lynch 3/4 right to win. Mafia only need 2/4 mislynches to win.

Spoiler: Test cases
Test scenario:

D2: With 11 voters, 6 to lynch. 4 are scum, 7 are town. Town is lynched.
D3: With 9 voters, 5 to lynch. 3 are scum, 6 are town. Lynch or lose (lylo). Scum is lynched.
D4: With 7 voters, 4 to lynch, 2 are scum, 5 are town. Lynch or lose (lylo). Scum is lynched.
D5: With 5 voters, 3 to lynch, 1 is scum, 4 are town. Lynch or lose (lylo). If scum is lynched, town win, if town is lynched, scum win.

Worst case town win scenario:

D2: With 11 voters, 6 to lynch. 4 are scum, 7 are town. Scum is lynched.
D3: With 9 voters, 5 to lynch. 3 are scum, 6 are town. Scum is lynched.
D4: With 7 voters, 4 to lynch, 2 are scum, 5 are town. If scum is lynched, town win.

Worst case scum win scenario:

D2: With 11 voters, 6 to lynch. 4 are scum, 7 are town. Town is lynched.
D3: With 9 voters, 5 to lynch. 3 are scum, 6 are town. Lynch or lose (lylo). If town is lynched, scum win.




On the whole including the D1 lynch, it looks like town need to lynch 3 scum to win, scum need to mislynch 3 town to win. But a D1 scumlynch heavily advantages the town and a D1 mislynch heavily advantages the mafia. Based on that, there can be a lot of scumhunting going on given the mafia have a ton of motivation to push a mislynch.

The outcome pretty much comes down to who can win these 1v1s. I think having a 50% chance of lynching scum in each duel compensates town for having fewer mislynches in hand than normal - typically I've seen it as one more mislynch than the number of scum. There's also the fact that regardless of whether the town mislynches or lynches scum, they have confirmed scum after every duel to look for interactive tells although lack of wagons might hamper that a bit.

One concern I have is that it's rather unlikely to lynch scum D1 unless they bus. Getting 8/9 town players to agree on a lynch would be quite difficult so in most cases, you are looking at gamestate #2 which could lead to a pretty quick town loss. But the large number of scum players mean a lot of associative-tell hunting. The second concern is in the test scenario of gamestate #1. When the last scum duels, everybody but the duelers is confirmed town. That would lead to an interesting interaction.

Potential changes I'm looking at is possibly including an Innocent Child to increase the chances of a scum lynch D1. At a minimum, there'll be four townies that'll never be in a duel. Potentially, the strongest, most obv-town players. Using an IC would require the scum to duel a stronger player. Alternatively, I could change the D1 mechanics so if town is lynched, they don't die but instead become an IC and town gets another shot for their D1 lynch. This way the IC is the scummiest townie as opposed to randomly chosen by the mod which should reduce swing.

Something I've seen with other setups and on the wiki is this concept called EV which I don't fully understand and presumably is a tool to balance games. Perhaps someone in the know can educate me on how it works and how I can apply it here. Also, general comments and feedback are very welcome.
User avatar
callforjudgement
callforjudgement
Microprocessor
User avatar
User avatar
callforjudgement
Microprocessor
Microprocessor
Posts: 3972
Joined: September 1, 2011

Post Post #1 (ISO) » Mon Oct 03, 2016 2:49 pm

Post by callforjudgement »

OK, so an EV calculation works like this: you assume that players are all equally bad/good at dayplay, and in particular there's no way to determine who's scum via looking at posts in the thread, only via night actions. Then you work out the best possible strategy for scum and town (which in most symmetrical setups like this one is acting randomly because there's no way to distinguish one player from another). Finally, you work out the probability that town will win. A good EV depends on how much control scum have over who dies, and tends to range from about 30% for Nightless setups (in which scum can only eliminate players via lynching), up to 50% or even slightly higher for setups where scum have an unrestricted choice of nightkill every night. (EV isn't the only requirement in balancing setups – you can easily create terrible setups that are just fine EV-wise – but it's a useful sanity check.)

For this setup, the "EV strategy" is fairly obvious: random lynch day 1 (everyone is identical), then lynch a random dueler until the game ends (because there's no way to tell the two duellers apart under EV assumptions). I'll do the maths here and set out all the steps so that you can see how it works (normally I'd combine some steps to save space); luckily the EV strategy is simple enough that the analysis isn't too long.

Probability of a D1 lynch on town is 9/14, on scum is 5/14.
Probability distribution of the number of townies who die D2-5: 0: 1/16; 1: 4/16; 2: 6/16; 3: 4/16; 4: 1/16 (assume that the game keeps on going even after the result becomes inevitable, it makes the maths easier and doesn't affect the result as the "extra" lynches will just waste time without changing the result)

Chance of town lynching town D1 and going on to win: 9/14 × (1/16 + 4/16) = 45/224
Chance of town lynching scum D1 and going on to win: 5/14 × (1/16 + 4/16 + 6/16) = 55/224

Total EV (chance of town winning via any method) = 45/224 + 55/224 = 100/224 = 25/56 = about 44.6%. I wouldn't call this unplayably low, although it's slightly lower than I'd like for a setup where scum have almost total control over who gets put up for lynch. So your instincts of making it slightly more townsided by restricting the early nightkills and/or increasing the chance of a D1 scumlynch were pretty good ones, I think.

As for the idea behind the setup, it follows fairly sound setup design principles (have a day that's free-for-all before breaking the town into chunks, keep swing within reasonable bounds). The only suggestion I'd make would be to make it a little clearer how the win conditions work (the voting is nontraditional so you can't figure it out from the voting rules). I wouldn't be too worried about scum refusing to bus D1 as it's normally something that becomes visible in retrospect.

Finally, I'm impressed by how much thought you've put into this. When most players submit their first Open setups, they have obvious issues, but this one looks pretty solid and it's clear that you've thought about how it works.
scum
· scam · seam · team · term · tern · torn ·
town
User avatar
BlackVoid
BlackVoid
Mafia Scum
User avatar
User avatar
BlackVoid
Mafia Scum
Mafia Scum
Posts: 2725
Joined: September 15, 2016

Post Post #2 (ISO) » Thu Oct 06, 2016 4:49 pm

Post by BlackVoid »

That was super helpful, thanks.

Just to clarify, in your EV calculation, the odds of a scum lynch increase with larger proportion of scum. But that doesn't seem to account for how hard it is to lynch scum when there are more of them. For example, I'd say it's easier to lynch scum D1 in a 13 player game than in 7 player lylo. Is there a way to adjust for that?

Regarding the scumsidedness, I agree. I think something like "if town lynches scum D1 on their first try, a town player is randomly chosen to be an IC and the game continues onto D2. If a town is lynched, they don't get lynched instead automatically becoming the IC and town gets a second shot at a D1 lynch" would be a nice addition.

As for wincons, I'm going to try and put it in point form. A mafia lynch gives town one point. A town lynch or a no lynch gives mafia one point. Whoever gets to three points first wins.
User avatar
callforjudgement
callforjudgement
Microprocessor
User avatar
User avatar
callforjudgement
Microprocessor
Microprocessor
Posts: 3972
Joined: September 1, 2011

Post Post #3 (ISO) » Fri Oct 07, 2016 6:14 am

Post by callforjudgement »

EV doesn't account for how difficult it is to lynch scum. (In practice, it tends not to get much harder when there are a lot of scum because scum typically need to bus to some extent to avoid the entire team being caught.)
scum
· scam · seam · team · term · tern · torn ·
town
Post Reply

Return to “Open Setup Discussion”