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On December 03 2013 04:42 Alakaslam wrote:
This has my utmost thanks coming your way. When I finally earn the ability to host, this will be very valuable to me! I appreciate your work even not having used it yet! :D
Would this be able to account for nonstandard mechanics or is that like trying to determine the load characteristics of a one of a kind experimental aircraft?
Nice to hear  It's certainly meant for experimenting with different (somewhat) normal setups. So for example, if you had vague ideas or even concrete plans for different setups, you could use it as a guideline for what's relatively balanced and what's not. It's not exact science, but it should give a good general picture of balance.
Unfortunately, it's pretty hard (or impossible?) to use this kind of balancing tool for themed setups. As you can see, even the most basic roles require tons of evaluation and testing before being decently balanced. It'd be an unreliable shot in the dark to try automatically balancing setups without necessary basic information beforehand. Maybe some kind of a learning algorithm or a very complicated algorithm with all possible situations pre-programmed could do it, but that seems like pretty much a pipe dream 
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On December 03 2013 04:49 Mid or Feed wrote:
I highly doubt non-traditional mechanics can be balanced like this.
Hell, it's almost impossible to balance them by hand.
Yeah, pretty much
By the way, what do you think of the current balance values (in comparison to your poll results and otherwise)?
Can you elaborate on your opinion of the neutral roles? I agree that they're in the worst position of the balance tester, but it's pretty hard to balance them... So any help is good
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Cool.
I am more a flavah dude than a new roles dude but I can try and do both.
Mah flavah games will be usin' your tools
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I probably won't have time to detail my system more until this weekend.
As far as values go, right now they seem decent to me. If you can't decide if goon is 4 or 5, make it 4.5 - don't limit yourself to integers for no reason.
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On December 03 2013 20:33 iGrok wrote:
I probably won't have time to detail my system more until this weekend.
As far as values go, right now they seem decent to me. If you can't decide if goon is 4 or 5, make it 4.5 - don't limit yourself to integers for no reason.
Okay, I'll be busy until the weekend anyways
Actually, according to Foolishness, one Goon is worth approximately 4,25 VT's. I guess it might be better to start using decimals (or maybe just larger integers) to be slightly more accurate. The original idea was to have VT as the "base value" and derive everything else from that, but that isn't really necessary, in the end.
Yeah, I think it's overall better to just be more accurate with the balance values. It makes it harder to get to 0 ("perfect") balance, but if that "perfect" balance is not perfectly accurate, then it's more like an illusion of perfect balance
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kitaman27
United States9245 Posts
On December 03 2013 04:59 Xatalos wrote:Show nested quote +On December 03 2013 04:49 Mid or Feed wrote:
I highly doubt non-traditional mechanics can be balanced like this.
Hell, it's almost impossible to balance them by hand. Yeah, pretty much By the way, what do you think of the current balance values (in comparison to your poll results and otherwise)? Can you elaborate on your opinion of the neutral roles? I agree that they're in the worst position of the balance tester, but it's pretty hard to balance them... So any help is good
I wouldn't be too concerned about matching the poll results since I don't necessarily agree with them. A good basis would probably be commonly accepted mini-game setups like 2of4 or C9++, although even those have issues.
Here is my general thought process with balancing a serial killer. I'm sure I'm overlooking several factors and a lot of it is guesswork. It's tricky to define what a serial killer is, since it varies so often from game to game. Are they bulletproof or 1-shot bulletproof. Do they have 1 bullet or unlimited shots? Can a roleblocker block their kp? Are they compulsive? Is the setup open? How are win conditions handled at endgame? A serial killer's victory odds is probably going to be impacted more on these factors, rather than the setup itself, aside from the number of players.
Lets look at a possible C9++ setup. Suppose there are 13 players: 3 mafia, 9 town, 1 SK (Unlimited shot)
Serial Killer needs to reach night at 2v1 before they are lynched or mafia gains majority during the day.
Assuming there a no blue roles (a flawed assumption), the game is likely ending on night four. Even with blues, a n4 or d5 endgame is most likely.
d1: 13
n1: 12
d2: 10
n2: 9
d3: 7
n3: 6
d4: 4
n4: 3
Random lynching during these four cycles results in 1/13 + 1/10 + 1/7 + 1/4 = 57% odds of the serial killer surviving to n4.
The lynches aren't going to be completely random due to mafia influence and the serial killer's ability to shoot threats at night. I'd think the survival percentage would be a bit less than random taking these two factors into account, but you could argue the other way. Either way, lets call this change in win percentage X.
There is a small possibility that the mafia team reaches day four at 3-0-1 or slightly higher possibility at 2-1-1. This is also going to decrease the survival percentage by a small amount. Lets call this Y.
We also have blues to consider. I'm not putting much thought into this part, but overall I'd think it's safe to conclude this would also decrease the serial killer's chances. Lets call this Z.
Assuming the serial killer is bulletproof, we have their win percentage as .57 - X - Y - Z
However, the c9++ serial killer is only 1-shot bulletproof.
If the mafia team shoots the serial killer on n1, n2, or n3 and is able to identify their target as the serial killer (not automatic, but likely), they will kill the serial killer on n4, before the SK is able to achieve victory.
I'm probably doing some fuzzy math, but shooting it random would be around 40%.
We would now be at .17 - X - Y - Z.
In theory, you want to create a setup where third party roles to have a chance of winning equal to the mafia or town factions. However, I'm not sure if this is ever very realistic. Obviously, .17 - X - Y - Z is going to be nowhere near the 33% we were hoping to achieve in the balancing stage, yet this is still considered one of the better setups, which shows how difficult balancing a setup really is.
Is it possible to apply a decent estimation to the value of X, Y, and Z that we can be confident about? Probably not.
Looking at Third Party win percentages at completed games might be your best bet, but the sample size is far too low and there are too many other external factors to consider.
As for a neutral survivor, looking at their odds of surviving the lynch and night shots at random is flawed because they can simply claim survivor at the beginning of the game. This won't always result in a victory, but it's tough to estimate a victory percentage, other than looking at completed games. Maybe I could take a look at the database of tl games to see how successful they have been in the past, since they are probably less reliant on setup.
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On December 04 2013 06:44 kitaman27 wrote:Show nested quote +On December 03 2013 04:59 Xatalos wrote:On December 03 2013 04:49 Mid or Feed wrote:
I highly doubt non-traditional mechanics can be balanced like this.
Hell, it's almost impossible to balance them by hand. Yeah, pretty much By the way, what do you think of the current balance values (in comparison to your poll results and otherwise)? Can you elaborate on your opinion of the neutral roles? I agree that they're in the worst position of the balance tester, but it's pretty hard to balance them... So any help is good I wouldn't be too concerned about matching the poll results since I don't necessarily agree with them. A good basis would probably be commonly accepted mini-game setups like 2of4 or C9++, although even those have issues. Here is my general thought process with balancing a serial killer. I'm sure I'm overlooking several factors and a lot of it is guesswork. It's tricky to define what a serial killer is, since it varies so often from game to game. Are they bulletproof or 1-shot bulletproof. Do they have 1 bullet or unlimited shots? Can a roleblocker block their kp? Are they compulsive? Is the setup open? How are win conditions handled at endgame? A serial killer's victory odds is probably going to be impacted more on these factors, rather than the setup itself, aside from the number of players. Lets look at a possible C9++ setup. Suppose there are 13 players: 3 mafia, 9 town, 1 SK (Unlimited shot) Serial Killer needs to reach night at 2v1 before they are lynched or mafia gains majority during the day. Assuming there a no blue roles (a flawed assumption), the game is likely ending on night four. Even with blues, a n4 or d5 endgame is most likely. d1: 13 n1: 12 d2: 10 n2: 9 d3: 7 n3: 6 d4: 4 n4: 3 Random lynching during these four cycles results in 1/13 + 1/10 + 1/7 + 1/4 = 57% odds of the serial killer surviving to n4. The lynches aren't going to be completely random due to mafia influence and the serial killer's ability to shoot threats at night. I'd think the survival percentage would be a bit less than random taking these two factors into account, but you could argue the other way. Either way, lets call this change in win percentage X. There is a small possibility that the mafia team reaches day four at 3-0-1 or slightly higher possibility at 2-1-1. This is also going to decrease the survival percentage by a small amount. Lets call this Y. We also have blues to consider. I'm not putting much thought into this part, but overall I'd think it's safe to conclude this would also decrease the serial killer's chances. Lets call this Z. Assuming the serial killer is bulletproof, we have their win percentage as .57 - X - Y - Z However, the c9++ serial killer is only 1-shot bulletproof. If the mafia team shoots the serial killer on n1, n2, or n3 and is able to identify their target as the serial killer (not automatic, but likely), they will kill the serial killer on n4, before the SK is able to achieve victory. I'm probably doing some fuzzy math, but shooting it random would be around 40%. We would now be at .17 - X - Y - Z. In theory, you want to create a setup where third party roles to have a chance of winning equal to the mafia or town factions. However, I'm not sure if this is ever very realistic. Obviously, .17 - X - Y - Z is going to be nowhere near the 33% we were hoping to achieve in the balancing stage, yet this is still considered one of the better setups, which shows how difficult balancing a setup really is. Is it possible to apply a decent estimation to the value of X, Y, and Z that we can be confident about? Probably not. Looking at Third Party win percentages at completed games might be your best bet, but the sample size is far too low and there are too many other external factors to consider. As for a neutral survivor, looking at their odds of surviving the lynch and night shots at random is flawed because they can simply claim survivor at the beginning of the game. This won't always result in a victory, but it's tough to estimate a victory percentage, other than looking at completed games. Maybe I could take a look at the database of tl games to see how successful they have been in the past, since they are probably less reliant on setup.
Well, that's some detailed analysis!
I think you'd have to assume that SK is probably not a likely NK target (pro-town etc.) which would lessen the chances of him being NK'd. Even if Mafia thought that someone was SK, it would probably not be wise to shoot him...
1) Enemy of my enemy is my friend - town is the worse enemy for Mafia than SK (at least for the early game)
2) There's a considerable chance that SK might be bulletproof (at least in common TL setups where he can choose check-immunity or NK-immunity) - making it more lucrative to get the SK lynched instead of NK'd
3) Even if he does get NK'd, he could be bulletproof
All in all, I think the threat of being NK'd is considerably lower for SK than for town (on average).
I took a look at your Mafia database and here's the win count per alignment (non-newbie games):
Mafia 108 (52%)
Third Party 19 (9%)
Town 79 (38%)
Doesn't seem exactly balanced :O
The very low chances of 3rd parties are probably also affected by the fact that not every game even has 3rd parties. Still, I think it's safe to say that if you're playing as a 3rd party, you're playing at a disadvantage (on average).
I'm quite surprised to see that Mafia dominates so hard, though. I wonder if the TL setups are generally Mafia-favored or if the players are generally better at playing Mafia than town. I guess it could be a combination of both.
In the end, I think predicting the victory odds for neutral roles is very hard - probably a rough estimate would be enough. I'm more focused on town vs Mafia at the moment.
If you had to give a rough estimate, what kind of a victory percentage would you give for each of the neutral roles?
Also, here's the math on how I currently calculate the neutral role victory odds (pretty flawed probably ). I guess you'd be interested to comment on that.
if (team == 2) { // 2 = Serial Killer
if (skRoles.size() == 0) {
return 0; // if there are no SK's = zero chance to win
}
if (mafiaRoles.size() >= townRoles.size() + skRoles.size()) {
return 0; // if there are more Mafia than town + SK's combined = automatic loss for SK
}
return (double) (skScore / skRoles.size()) / allScore;
// otherwise SK's victory odds are basically the balance value of a single SK divided by the balance value of all // town, Mafia and SK's combined
}
if (team == 3) {
if (survivorRoles.size() == 0) {
return 0;
}
if (!chosenRoles.contains(getSpecificRole(21))) {
return 0;
}
if (mafiaRoles.size() >= townRoles.size() + skRoles.size()) {
return 1;
}
return (double) (townScore + mafiaScore) / allScore / 4;
// Survivor's victory odds are generally the victory odds of (town + Mafia) / 4
}
if (team == 4) {
if (antitownSurvivorRoles.size() == 0) {
return 0;
}
if (mafiaRoles.size() == 0) {
return (double) mafiaScore / allScore;
}
if (!chosenRoles.contains(getSpecificRole(22))) {
return 0;
}
if (mafiaRoles.size() >= townRoles.size() + skRoles.size()) {
return 1;
}
if (mafiaRoles.size() + 1 >= townRoles.size() + skRoles.size() && dayStart == false) {
return 1;
}
return (double) (mafiaScore / 2) / allScore;
// for Anti-town Survivor it's the victory odds of Mafia / 2
}
if (team == 5) {
if (assassinRoles.size() == 0) {
return 0;
}
if (assassinRoles.size() == 1) {
return 1;
}
return 1 / (double) assassinRoles.size();
// for Assassin it's simply 1 / the amount of Assassins
}
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As a sidenote... There's been a typo and one of my games is under "Xalatos" (lol) in the game database...
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kitaman27
United States9245 Posts
On December 04 2013 07:39 Xatalos wrote:
Well, that's some detailed analysis!
I think you'd have to assume that SK is probably not a likely NK target (pro-town etc.) which would lessen the chances of him being NK'd. Even if Mafia thought that someone was SK, it would probably not be wise to shoot him...
1) Enemy of my enemy is my friend - town is the worse enemy for Mafia than SK (at least for the early game)
2) There's a considerable chance that SK might be bulletproof (at least in common TL setups where he can choose check-immunity or NK-immunity) - making it more lucrative to get the SK lynched instead of NK'd
3) Even if he does get NK'd, he could be bulletproof
All in all, I think the threat of being NK'd is considerably lower for SK than for town (on average).
Identifying the serial killer can be fairly difficult at times. If the mafia team does manage to develop correct suspicions that a player is the SK, the NK odds may go down, but then you have to account for the increased lynch odds since they would become the priority lynch target.
As mafia, I'd always consider the serial killer a greater threat than individual town members, even during the early game, though that's just my personal opinion.
On December 04 2013 07:39 Xatalos wrote:
I took a look at your Mafia database and here's the win count per alignment (non-newbie games):
Mafia 108 (52%)
Third Party 19 (9%)
Town 79 (38%)
Doesn't seem exactly balanced :O
The very low chances of 3rd parties are probably also affected by the fact that not every game even has 3rd parties. Still, I think it's safe to say that if you're playing as a 3rd party, you're playing at a disadvantage (on average).
I'm quite surprised to see that Mafia dominates so hard, though. I wonder if the TL setups are generally Mafia-favored or if the players are generally better at playing Mafia than town. I guess it could be a combination of both.
I think the Win Percentage By Alignment statistic would be a bit closer to what you are looking for:
Town 40.6%
Mafia 52.1%
Third Party 30.3%
I'm not sure how reliable it is however since I haven't had the chance to update the query or verify the results. Based on another set of polls, most people consider themselves better at mafia than town. I'm don't know how much setup plays a role in the gap.
On December 04 2013 07:39 Xatalos wrote:
If you had to give a rough estimate, what kind of a victory percentage would you give for each of the neutral roles?
I'm not really sure to be honest. Your assassin calculation makes sense. For survivor, I'd be pretty confident that I'd be able to pull it off with a simple d1 role claim like I mentioned, so maybe something like 75%? This might not apply to everyone though?
Serial killer is much tougher, so it really would be a random guess not taking setup into account. Maybe aim for around 20%?
On December 04 2013 08:55 Xatalos wrote:As a sidenote... There's been a typo and one of my games is under "Xalatos" (lol) in the game database...
You should be able to go in and fix it yourself, though it may be a while before it is reflected in the OP
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Kita, I think a better stat for T/M/3rd winrates would be to exclude themed games from the count. Just a thought.
Also, 15-20% sounds about right for 3rd parties, its what I aim for.
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United Kingdom36161 Posts
On December 05 2013 02:54 iGrok wrote:
Kita, I think a better stat for T/M/3rd winrates would be to exclude themed games from the count. Just a thought.
Also, 15-20% sounds about right for 3rd parties, its what I aim for.
Tbh town probably does best in themed games...
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On December 05 2013 02:13 kitaman27 wrote:Show nested quote +On December 04 2013 07:39 Xatalos wrote:
Well, that's some detailed analysis!
I think you'd have to assume that SK is probably not a likely NK target (pro-town etc.) which would lessen the chances of him being NK'd. Even if Mafia thought that someone was SK, it would probably not be wise to shoot him...
1) Enemy of my enemy is my friend - town is the worse enemy for Mafia than SK (at least for the early game)
2) There's a considerable chance that SK might be bulletproof (at least in common TL setups where he can choose check-immunity or NK-immunity) - making it more lucrative to get the SK lynched instead of NK'd
3) Even if he does get NK'd, he could be bulletproof
All in all, I think the threat of being NK'd is considerably lower for SK than for town (on average). Identifying the serial killer can be fairly difficult at times. If the mafia team does manage to develop correct suspicions that a player is the SK, the NK odds may go down, but then you have to account for the increased lynch odds since they would become the priority lynch target. As mafia, I'd always consider the serial killer a greater threat than individual town members, even during the early game, though that's just my personal opinion. Show nested quote +On December 04 2013 07:39 Xatalos wrote:
I took a look at your Mafia database and here's the win count per alignment (non-newbie games):
Mafia 108 (52%)
Third Party 19 (9%)
Town 79 (38%)
Doesn't seem exactly balanced :O
The very low chances of 3rd parties are probably also affected by the fact that not every game even has 3rd parties. Still, I think it's safe to say that if you're playing as a 3rd party, you're playing at a disadvantage (on average).
I'm quite surprised to see that Mafia dominates so hard, though. I wonder if the TL setups are generally Mafia-favored or if the players are generally better at playing Mafia than town. I guess it could be a combination of both. I think the Win Percentage By Alignment statistic would be a bit closer to what you are looking for: Town 40.6% Mafia 52.1% Third Party 30.3% I'm not sure how reliable it is however since I haven't had the chance to update the query or verify the results. Based on another set of polls, most people consider themselves better at mafia than town. I'm don't know how much setup plays a role in the gap. Show nested quote +On December 04 2013 07:39 Xatalos wrote:
If you had to give a rough estimate, what kind of a victory percentage would you give for each of the neutral roles? I'm not really sure to be honest. Your assassin calculation makes sense. For survivor, I'd be pretty confident that I'd be able to pull it off with a simple d1 role claim like I mentioned, so maybe something like 75%? This might not apply to everyone though? Serial killer is much tougher, so it really would be a random guess not taking setup into account. Maybe aim for around 20%? Show nested quote +On December 04 2013 08:55 Xatalos wrote:As a sidenote... There's been a typo and one of my games is under "Xalatos" (lol) in the game database... You should be able to go in and fix it yourself, though it may be a while before it is reflected in the OP
Hmm. Not sure what's it about. My name was correct in the web interface, but misplaced in the actual thread...
![[image loading]](http://i.imgur.com/bYpmcgA.png)
In any case, that's pretty off-topic
Well, I guess that indeed SK is a bigger threat than an individual townie (at least a vanilla townie). Mostly I meant that a SK would be unlikely to be NK'd during the early nights (N1-N2 at least). Which in turn would improve SK's victory odds at least a bit.
On the other hand, a SK would probably be more likely lynched than the average townie. So maybe it just evens out.
Yeah, that's a more accurate statistic than the one I found. I think 30% is surprisingly high for neutral roles. Probably Survivors have the highest odds which makes all neutral roles look better as a group.
Or actually an Assassin always wins, so if there are 2 Assassins, a 50% victory chance is pretty good
Actually Foolishness gave me the 25% victory odds for Survivor and I think it's probably closer to the truth than 75%? But I really have no idea about that one. Maybe something closer to 30-40%.
SK is currently somewhere around 15% in general. I agree that it should probably be a bit higher.
I'll remember these comments for the next patch.
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Phew... I'm currently thinking of ways to implement iGrok's balancing method. It's definitely harder / more complicated than this +/- method. But we'll see how it works out.
It's possibly wasted time to tune the current system so I'll see how iGrok's system works next, I guess. Another very possible change is to make the roles show as "X x Rolename" instead of "Rolename Rolename Rolename (x X)" which would seem a bit cleaner. Otherwise the user interface is starting to feel pretty completed (for now).
Although I have an exam week & I start playing in Titanic Mafia soon so I probably won't have a ton of time to use.
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On December 04 2013 07:39 Xatalos wrote:
Mafia 108 (52%)
Third Party 19 (9%)
Town 79 (38%)
Doesn't seem exactly balanced :O
The very low chances of 3rd parties are probably also affected by the fact that not every game even has 3rd parties. Still, I think it's safe to say that if you're playing as a 3rd party, you're playing at a disadvantage (on average).
Hmmm.
Apart from some problems (I am assuming they are there)
A really important question is to ask what balanced is.
Scum winning 50% and town winning 50% seems to be an accepted desirable outcome.
I am not sure that a team with one person in it having an even (33%) chance of winning to a team which most people play on and considering that there are lots of people that never get a chance to to be the solo win team, that Sk probably ought be hard to win with.
You might argue the same about scum as that teams smaller, the ratio is different.
even at 9% scum win more often that their size.
but whats the metric
and what are your goals in balancing game and why
edit: nvm read the thread properly now.
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After some theoretical experimentation, it seems like the method iGrok suggested earlier isn't that well suited for automated balancing.
I'll be at least fine-tuning the balance tester (victory odds, user interface etc.) in the somewhat near future. Additional suggestions are very welcome, though! It's easier to implement changes in a single update rather than one at a time...
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Nice!
Now that the tool is here, it'd would indeed be nice for more analysis to be made on what actually makes a "balanced" game. That's the most important part. With the ease of tweeking this tool, it will certainly make that task easier!
Although, the +X -X things do seem a little too arbitrary, even if they are made with "common sense". Dunno you can actually state with precision that town or scum will win Y% of the time, just by adding +3 or -2 to the setup in an arbitrary way.
If you add probabilities of winning, you need to model those win conditions, and the conditions in which they can happen (what actions town/scum can make, etc), and maybe do some statistical work.
...someone volunteer?
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On December 11 2013 08:26 gonzaw wrote:
Nice!
Now that the tool is here, it'd would indeed be nice for more analysis to be made on what actually makes a "balanced" game. That's the most important part. With the ease of tweeking this tool, it will certainly make that task easier!
Although, the +X -X things do seem a little too arbitrary, even if they are made with "common sense". Dunno you can actually state with precision that town or scum will win Y% of the time, just by adding +3 or -2 to the setup in an arbitrary way.
If you add probabilities of winning, you need to model those win conditions, and the conditions in which they can happen (what actions town/scum can make, etc), and maybe do some statistical work.
...someone volunteer?
That sounds like a hell of a lot of coding specific role interactions. Having seen how poorly game theory that was not built with computer scripting in mind works when you attempt to script it (MODO), I pass.
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Coding can come naturally if you have a theoretical model of it. If you set the foundation, i.e, formally specify roles, win conditions, chance to win games, etc, then coding that is just translating that to a specific language and technology, which is much easier than doing that from the start.
The problem is that someone has to volunteer to do that!
Kind of a big problem if you ask me....but if you don't then these kind of algorithms and theories seem kind of arbitrary to me. E.g, you could use this tool for a very complex setup, and it says town/scum win 50% of the time each, yet when you put it in practice you see scum win 80% of the time. What guarantee is there in the "Mafia Game Balance" theory?
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Heh, I originally had something like that in mind (calculating a lot of different scenarios - kind of like a chess AI). But that's a lot of work. Then I found the +/- system with Google. I think it would be possible to do a system like that for a very small/basic setup (with like 1/2 days) but it gets exponentially harder with size/length of the game......
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The only thing I'd like to see is an accounting for inactivity mod-kills. I guess you can work around it if you just remove a certain number of townies from the game beforehand, but it would be nice if there is some kind of framework for working an a modkill rate.
Good to know that the upcoming game I am hosting should be pretty balanced, assuming 4 people get modkilled (randomly picked a number)
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EPT
