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Old 16th September 2012, 12:48 PM   #64167  /  #1
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Mafia game balance is serious business: notes for new GMs, aspies, and robots

Alongside playing Mafia I've been thinking a bit about how to judge game balance. Part of the motivation comes from the fact that I'm quasi-aspie and enjoy working on these little problems as much as I enjoy watching a good movie. Or as much as I enjoy playing Mafia for that matter. Another part comes from having been unable to find detailed balancing rules that don't have a very arbitrary feel to them (e.g. some of the advice in Mafiascum's Comprehensive Modding Guide or point-based systems).

Below are some balance indicators that I found useful for getting a feel for balance, especially counter-intuitive effects. Maybe others will learn something from them too. They are all based on the assumption that players behave like fairly simple robots, so one still needs to take into account the most important differences between robots and actual players when designing games. For example, actual scum players may get tired faster than town players, so that games that last longer favor town more. How far to deviate from "robot balance" also depends on one's opinion about what consistitues baseline town and scum play. Does scum blend in perfectly or does the baseline include some scum manipulation of the lynch voting, special hunting, etc.? Does town baseline play include successful scum hunting, successful analysis of scum lynch-voting manipulation, etc.?
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Old 16th September 2012, 12:48 PM   #64168  /  #2
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All-vanilla games

In order to start simple, consider a pure vanilla game, where a completely random player is lynched each day and a random town player is killed each night. Call this the Vanilla-Random-Lynch (VRL) model and let

VRL(s,n) = "probability of a scum win starting from s scum players out of n players in total"

Clearly, VRL(0,n) = 0, VRL(1,2) = 2/3, and VRL(s,n) = 1 whenever 2s >= n (standard scum win condition). Other values ultimately derive from these via the relation

VRL(s,n) = s/n * VRL(s-1,n-2) + (1-s/n) * VRL(s,n-2)

Starting from the smallest values of s, n and working upwards it is easy to tabulate these probabilities.

VRL model 1 scum2 scum3 scum4 scum5 scum6 scum
3 players 0.667 1.000 1.000 - - -
4 players 0.750 1.000 1.000 1.000 - -
5 players 0.533 0.867 1.000 1.000 1.000 -
6 players 0.625 0.917 1.000 1.000 1.000 1.000
7 players 0.457 0.771 0.943 1.000 1.000 1.000
8 players 0.547 0.844 0.969 1.000 1.000 1.000
9 players 0.406 0.702 0.886 0.975 1.000 1.000
10 players 0.492 0.784 0.931 0.988 1.000 1.000
11 players 0.369 0.648 0.835 0.942 0.988 1.000
12 players 0.451 0.736 0.895 0.969 0.995 1.000
13 players 0.341 0.605 0.792 0.909 0.971 0.995
14 players 0.419 0.695 0.860 0.948 0.985 0.998
15 players 0.318 0.570 0.755 0.878 0.950 0.985
16 players 0.393 0.661 0.829 0.926 0.974 0.993
17 players 0.300 0.540 0.722 0.849 0.929 0.973
18 players 0.371 0.631 0.801 0.904 0.960 0.987
19 players 0.284 0.515 0.693 0.822 0.908 0.959
20 players 0.352 0.605 0.776 0.884 0.946 0.979

A fun pattern is that an odd number of players is always better for town than the nearby even numbers. In symbols, VRL(s,2k-1) <= VRL(s,2k) and VRL(s,2k+1) <= VRL(s,2k).

(Googling will turn up similar analyses of the VRL model, but the numbers may vary depending on the version of the scum win condition. E.g. some people don't take daybreak with 1 scum vs. 1 town to be an automatic scum win, but break the tie randomly.)


Vanilla games with cleared players

Some insight into the value of cleared players is obtained by introducing the Innocent Child role into the VRL model. Assume that all innocent children role claim immediately, and that scum nightkills them off first. Call this the Vanilla-Innocent child-Random-Lynch (VIRL) model and let

VIRL(s,i,n) = "probability of a scum win starting from s scum players and i innocent children out of a total of n players"

Clearly, this reduces to the VRL model when i = 0. In general, for i > 0, the probabilities can be tabulated using

VIRL(s,i,n) = s/(n-i) * VIRL(s-1,i-1,n-2) + (1 - s/(n-i)) * VIRL(s,i-1,n-2)

VIRL model 1 scum2 scum3 scum4 scum5 scum6 scum
8 players, 0 cleared0.547 0.844 0.969 1.000 1.000 1.000
----------- 1 cleared0.536 0.833 0.964 1.000 1.000 1.000
----------- 2 cleared0.500 0.800 0.950 1.000 1.000 1.000
----------- 3 cleared0.400 0.700 0.900 1.000 1.000 -
----------- 4 cleared0.250 0.500 0.750 1.000 - -
----------- 5 cleared0.000 0.000 0.000 - - -
9 players, 0 cleared0.406 0.702 0.886 0.975 1.000 1.000
----------- 1 cleared0.400 0.693 0.879 0.971 1.000 1.000
----------- 2 cleared0.381 0.667 0.857 0.962 1.000 1.000
----------- 3 cleared0.333 0.600 0.800 0.933 1.000 1.000
----------- 4 cleared0.200 0.400 0.600 0.800 1.000 -
----------- 5 cleared0.000 0.000 0.000 0.000 - -
10 players, 0 cleared0.492 0.784 0.931 0.988 1.000 1.000
----------- 1 cleared0.486 0.778 0.927 0.986 1.000 1.000
----------- 2 cleared0.469 0.759 0.915 0.982 1.000 1.000
----------- 3 cleared0.429 0.714 0.886 0.971 1.000 1.000
----------- 4 cleared0.333 0.600 0.800 0.933 1.000 1.000
----------- 5 cleared0.200 0.400 0.600 0.800 1.000 -
11 players, 0 cleared0.369 0.648 0.835 0.942 0.988 1.000
----------- 1 cleared0.366 0.643 0.830 0.939 0.987 1.000
----------- 2 cleared0.356 0.628 0.817 0.930 0.984 1.000
----------- 3 cleared0.333 0.595 0.786 0.910 0.976 1.000
----------- 4 cleared0.286 0.524 0.714 0.857 0.952 1.000
----------- 5 cleared0.167 0.333 0.500 0.667 0.833 1.000
12 players, 0 cleared0.451 0.736 0.895 0.969 0.995 1.000
----------- 1 cleared0.447 0.731 0.891 0.967 0.994 1.000
----------- 2 cleared0.438 0.719 0.882 0.963 0.993 1.000
----------- 3 cleared0.417 0.694 0.863 0.952 0.990 1.000
----------- 4 cleared0.375 0.643 0.821 0.929 0.982 1.000
----------- 5 cleared0.286 0.524 0.714 0.857 0.952 1.000
13 players, 0 cleared0.341 0.605 0.792 0.909 0.971 0.995
----------- 1 cleared0.339 0.601 0.789 0.907 0.969 0.994
----------- 2 cleared0.332 0.592 0.779 0.900 0.965 0.993
----------- 3 cleared0.320 0.573 0.760 0.885 0.957 0.990
----------- 4 cleared0.296 0.537 0.722 0.854 0.939 0.984
----------- 5 cleared0.250 0.464 0.643 0.786 0.893 0.964
14 players, 0 cleared0.419 0.695 0.860 0.948 0.985 0.998
----------- 1 cleared0.416 0.692 0.858 0.946 0.985 0.998
----------- 2 cleared0.410 0.684 0.851 0.942 0.983 0.997
----------- 3 cleared0.398 0.668 0.838 0.933 0.979 0.996
----------- 4 cleared0.375 0.639 0.812 0.917 0.971 0.994
----------- 5 cleared0.333 0.583 0.762 0.881 0.952 0.988
15 players, 0 cleared0.318 0.570 0.755 0.878 0.950 0.985
----------- 1 cleared0.317 0.567 0.752 0.876 0.949 0.984
----------- 2 cleared0.313 0.561 0.745 0.870 0.945 0.983
----------- 3 cleared0.305 0.549 0.732 0.859 0.938 0.979
----------- 4 cleared0.291 0.527 0.709 0.839 0.924 0.972
----------- 5 cleared0.267 0.489 0.667 0.802 0.897 0.957
16 players, 0 cleared0.393 0.661 0.829 0.926 0.974 0.993
----------- 1 cleared0.391 0.658 0.827 0.924 0.973 0.993
----------- 2 cleared0.387 0.653 0.822 0.921 0.971 0.992
----------- 3 cleared0.379 0.642 0.813 0.914 0.967 0.991
----------- 4 cleared0.365 0.623 0.795 0.902 0.960 0.988
----------- 5 cleared0.341 0.591 0.765 0.879 0.946 0.982
17 players, 0 cleared0.300 0.540 0.722 0.849 0.929 0.973
----------- 1 cleared0.298 0.538 0.720 0.847 0.928 0.972
----------- 2 cleared0.296 0.534 0.715 0.843 0.925 0.970
----------- 3 cleared0.290 0.526 0.706 0.835 0.918 0.967
----------- 4 cleared0.281 0.511 0.690 0.820 0.908 0.960
----------- 5 cleared0.267 0.488 0.664 0.796 0.889 0.948
18 players, 0 cleared0.371 0.631 0.801 0.904 0.960 0.987
----------- 1 cleared0.370 0.629 0.800 0.903 0.960 0.986
----------- 2 cleared0.367 0.625 0.796 0.900 0.958 0.985
----------- 3 cleared0.361 0.617 0.788 0.895 0.954 0.984
----------- 4 cleared0.352 0.604 0.776 0.885 0.948 0.981
----------- 5 cleared0.337 0.583 0.756 0.869 0.938 0.975
19 players, 0 cleared0.284 0.515 0.693 0.822 0.908 0.959
----------- 1 cleared0.283 0.514 0.692 0.821 0.907 0.958
----------- 2 cleared0.281 0.510 0.688 0.817 0.904 0.956
----------- 3 cleared0.277 0.504 0.681 0.811 0.899 0.953
----------- 4 cleared0.271 0.494 0.670 0.800 0.891 0.947
----------- 5 cleared0.261 0.478 0.652 0.783 0.877 0.938
20 players, 0 cleared0.352 0.605 0.776 0.884 0.946 0.979
----------- 1 cleared0.351 0.603 0.774 0.883 0.946 0.978
----------- 2 cleared0.349 0.600 0.771 0.880 0.944 0.977
----------- 3 cleared0.345 0.594 0.766 0.876 0.941 0.976
----------- 4 cleared0.338 0.585 0.756 0.868 0.936 0.973
----------- 5 cleared0.328 0.571 0.742 0.856 0.927 0.968

That an odd number of players is better for town than an even number seems to hold also in the VIRL model.

In general, the value of cleared players is much smaller than I had expected.
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Old 16th September 2012, 12:49 PM   #64169  /  #3
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Vanilla + vig games

In a vanilla game, only 50% of the kills (i.e. lynch kills as opposed to nightkills) put scum at risk of being removed from the game. During the time a vig is in the game, this becomes 66% of the kills.

Consider a game with s scum, 1 vig, and n players in total. Assume random lynching and also that the vig kills a random player (excluding him-/herself, naturally). Furthermore, assume that the vig runs the same risk as anyone else of being lynched, and the same risk as any other townie of being nightkilled by scum.

Because of the many possibilities (lynch scum, lynch townie other than vig, lynch vig; vig kills scum, vig kills town; scum kills vig, scum kills other townie), it is harder to analyze this model. Splitting up the three types events gives

Lynch(s,n) = s/n Vig(s-1,n-1) + (1-(s+1)/n) Vig(s,n-1) + 1/n VRL(s,n-2)
Vig(s,n) = s/(n-1) ScumNK(s-1,n-1) + (1-s/(n-1)) ScumNK(s,n-1)
ScumNK(s,n) = (1-1/(n-s)) Lynch(s,n-1) + 1/(n-s) VRL(s,n-1)

The termination conditions depend on when win conditions are checked (daybreak and/or nightfall). Taking win conditions to be checked at daybreak only results in the following table of scum win probabilities.

VigVRL model 1 scum2 scum3 scum4 scum5 scum6 scum
3 players 0.333 1.000 - - - -
4 players 0.500 1.000 1.000 - - -
5 players 0.533 0.867 1.000 1.000 - -
6 players 0.347 0.639 1.000 1.000 1.000 -
7 players 0.398 0.724 0.925 1.000 1.000 1.000
8 players 0.411 0.698 0.875 1.000 1.000 1.000
9 players 0.313 0.566 0.790 0.942 1.000 1.000
10 players 0.339 0.611 0.805 0.924 1.000 1.000
11 players 0.348 0.609 0.789 0.911 0.978 1.000
12 players 0.284 0.512 0.702 0.847 0.941 1.000
13 players 0.301 0.545 0.730 0.858 0.941 0.986
14 players 0.308 0.546 0.721 0.845 0.928 0.974
15 players 0.261 0.474 0.649 0.787 0.886 0.952
16 players 0.273 0.497 0.672 0.802 0.892 0.951
17 players 0.279 0.500 0.670 0.796 0.885 0.943
18 players 0.242 0.443 0.607 0.739 0.839 0.912
19 players 0.252 0.462 0.629 0.758 0.852 0.917
20 players 0.256 0.464 0.628 0.753 0.845 0.910
21 players 0.227 0.417 0.575 0.703 0.803 0.878
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Old 16th September 2012, 12:49 PM   #64170  /  #4
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Agent-based simulation of complex games

It quickly gets unwieldy to derive exact equations for complex game designs and/or player behavior. Instead, I wrote a computer program to simulate games. I didn't spend a lot of time testing (and anyway don't have much independent data to test against) so I can't guarantee it's bug free, but the results look reasonable. The lynch model is more complicated than the above random lynch models and some special roles are incorporated:

* Public information is kept track of in the form of all special claims and the reported seer views. The public information also contains values measuring the "intersubjective scumminess" of each player. These values are simply randomized in the same way for scum and town. They are not intended to account for successful scum-hunting, but rather to account for coordinated voting and for voting based on scum tells recognized most of the player community.

* Town players also maintain private lists of "subjective scumminess" of each player, also randomized. They lynch-vote just once without checking the vote tally first. The lynch-vote is based on a weighted average of their "subjective" reads and the "objective" reads from the public info. Special claims result is substantially lowered "scumminess" values and outed seer views very strongly affect the values too. As it happens, the choice of weighting factor between "subjective" and "objective" scumminess does not appear to matter much.

* Seers, docs, vigs, and blockers all role claim if they are up for lynch. Their "scumminess" values then get substantially reduced and every player revotes. Lynching of specials is thus possible but improbable.

* Seers out when they have a useful scum view and when the number of useful town views is larger than about a fifth of the total number of living players. View targets are chosen randomly among living players not previously viewed. When lynch-voting, seers take into account their private (still not outed) views as well as any views from others seers in the public info.

* Docs protect a randomly chosen claimed special that was protected the previous night. If that is not applicable, they protect a randomly selected player that was not protected the previous night.

* Vigs target a random player among those neither have made role claims or those that are publically known to have been viewed as town. If no such target exist, they prioritize avoiding killing players with role claims over avoiding killing players viewed as town.

* Blockers target a random player among those who haven't made any role claims. In principle, when a blocker makes a role claim the list of block targets is informative. However, none of the players in the simulation attempts to make use of block info.

* Scum perform perfect simulation of vanilla town voting behavior. They never coordinate votes, even when town is in a must-lynch situation. Scum also never make fake role claims. Scum prioritize nightkilling outed specials if there are any, then players publically known to view as town, then randomly selected town players.

The fraction of scum wins seen in simulations (10,000 repetitions) is shown below for some 3-scum and 4-scum designs. The column-heading "s" means that town has a seer, "v" that town has a vig, "sd" that town has a seer + doc, "sdv" that town has seer + doc + vig, and "sdvb" that town has seer + doc + vig + blocker.

simulation all-vanilla s v sd sdv sdvb
12 players, 3 scum 0.90 0.80 0.62 0.54 0.30 0.21
13 players, 3 scum 0.79 0.68 0.62 0.52 0.30 0.21
14 players, 3 scum 0.86 0.77 0.57 0.52 0.28 0.20
15 players, 3 scum 0.75 0.63 0.58 0.51 0.29 0.21
16 players, 3 scum 0.83 0.73 0.57 0.50 0.29 0.22
17 players, 3 scum 0.73 0.60 0.54 0.49 0.29 0.22

simulation all-vanilla s v sd sdv sdvb
15 players, 4 scum 0.88 0.80 0.72 0.68 0.40 0.30
16 players, 4 scum 0.92 0.87 0.70 0.67 0.39 0.30
17 players, 4 scum 0.85 0.76 0.68 0.66 0.38 0.31
18 players, 4 scum 0.91 0.84 0.67 0.65 0.40 0.31
19 players, 4 scum 0.82 0.75 0.67 0.66 0.39 0.32
20 players, 4 scum 0.88 0.82 0.65 0.64 0.39 0.32
21 players, 4 scum 0.80 0.72 0.64 0.65 0.38 0.33

The all-vanilla column agrees very well with the VRL model above---an indication that the more complex lynch model made no difference. The "v" column agrees fairly well with the VigVRL model above, but the fraction of scum wins is somewhat lower. This is the effect of the vig being able to avoid many lynches by role claiming. Insofar as the simulation model succeeds in modeling the baseline play that defines balance, 3 scum vs. seer + doc + 7-12 vanilla seems like a magic recipe for a small balanced game.

I would expect game duration to also be a factor in actual games, as town and scum may become tired at different rates. Below are the average length in game days of the games won by scum (red) and town (blue), respectively.

simulation all-vanilla s v sd sdv sdvb
12 players, 3 scum 3.88 4.19 3.42 4.99 3.67 3.73
4.67 4.53 3.72 5.13 3.73 3.84
13 players, 3 scum 5.06 5.35 3.88 5.64 4.19 4.28
5.50 5.38 3.98 5.53 4.01 4.14
14 players, 3 scum 4.99 5.28 4.40 6.13 4.71 4.76
5.49 5.30 4.34 5.94 4.28 4.42
15 players, 3 scum 6.15 6.41 4.74 6.73 5.12 5.29
6.38 6.13 4.58 6.27 4.55 4.72
16 players, 3 scum 6.09 6.37 5.25 7.21 5.57 5.73
6.32 6.05 4.91 6.72 4.86 4.99
17 players, 3 scum 7.23 7.47 5.67 7.81 6.06 6.19
7.25 6.92 5.25 7.09 5.16 5.30


simulation all-vanilla s v sd sdv sdvb
15 players, 4 scum 5.47 5.90 4.27 6.33 4.78 4.85
6.65 6.52 4.83 6.80 4.87 5.06
16 players, 4 scum 5.39 5.78 4.81 6.82 5.23 5.36
6.62 6.47 5.21 7.27 5.22 5.35
17 players, 4 scum 6.63 7.00 5.17 7.43 5.70 5.86
7.53 7.40 5.46 7.62 5.48 5.67
18 players, 4 scum 6.53 6.91 5.68 7.93 6.16 6.36
7.50 7.27 5.83 8.10 5.82 5.99
19 players, 4 scum 7.75 8.07 6.11 8.49 6.66 6.82
8.46 8.21 6.17 8.53 6.08 6.33
20 players, 4 scum 7.65 7.98 6.61 9.03 7.10 7.27
8.38 8.16 6.48 8.94 6.41 6.62
21 players, 4 scum 8.82 9.11 6.96 9.57 7.56 7.74
9.31 9.16 6.77 9.39 6.71 6.94

Converting one vanilla scum to a scum don seems to have a rather modest effect. In most cases, the probability of a scum win is increased by about 0.05. This value might drop slightly under another voting model, since the voting model used makes lynching of players viewed as town quite rare. However, the low value is mostly due to the fact that the don only gets viewed in a small fraction of the games.

simulation all-vanilla s s+don sd sd+don sdv sdv+don sdvb sdvb+don
12 players, 3 scum 0.90 0.80 0.83 0.54 0.62 0.30 0.36 0.21 0.26
13 players, 3 scum 0.79 0.68 0.72 0.52 0.61 0.30 0.35 0.21 0.26
14 players, 3 scum 0.86 0.77 0.81 0.52 0.60 0.28 0.34 0.20 0.26
15 players, 3 scum 0.75 0.63 0.68 0.51 0.60 0.29 0.35 0.21 0.26
16 players, 3 scum 0.83 0.73 0.77 0.50 0.58 0.29 0.34 0.22 0.27
17 players, 3 scum 0.73 0.60 0.66 0.49 0.58 0.29 0.35 0.22 0.27

simulation all-vanilla s s+don sd sd+don sdv sdv+don sdvb sdvb+don
15 players, 4 scum 0.88 0.80 0.82 0.68 0.73 0.40 0.45 0.30 0.35
16 players, 4 scum 0.92 0.87 0.89 0.67 0.71 0.39 0.44 0.30 0.36
17 players, 4 scum 0.85 0.76 0.79 0.66 0.71 0.38 0.45 0.31 0.36
18 players, 4 scum 0.91 0.84 0.86 0.65 0.70 0.40 0.45 0.31 0.36
19 players, 4 scum 0.82 0.75 0.76 0.66 0.70 0.39 0.43 0.32 0.36
20 players, 4 scum 0.88 0.82 0.84 0.64 0.70 0.39 0.44 0.32 0.37
21 players, 4 scum 0.80 0.72 0.75 0.65 0.70 0.38 0.44 0.33 0.37

Taking the model at face value, 3 scum + 1 scum don vs. seer + doc + vig + 7-14 vanilla seems like another magic recipe.
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Old 16th September 2012, 12:50 PM   #64171  /  #5
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Simulation of games with a survivor SK

I also tried to get some idea of balance issues with the SK role, specifically SK's with survivor win condition (as opposed to last man standing win condition). Coming up with a good simple robotic behavior that has about the same effect as an SK role in an actual game seems like a challenge. Intuitively, a survivor-SK should make the game more unstable. That is, once either town or scum gains an advantage, a survivor-SK will try to reinforce that advantage. I'm not sure how to best model this effect.

The survivor-SKs in the simulation behave in the following way:

* They view as town to a seer.
* Their nightkills are processed before vig kills and scum kills.
* During the game day, they perfectly simulate vanilla town voting behavior.
* If they are up for lynch, they role-claim town vig. This makes their lynch unlikely, but is nonetheless almost a death sentence since they now become prioritized scum NK targets.
* They allow 1 outed town special to live and 1 player who is publically known to view as town. If there are 2 or more outed town specials, they target one of them randomly. If there are 2 or more players the seer has said views as town, they target one of them randomly. If none of the previous considerations apply, they just pick a completely random night-kill target. (The rationale for this is: (a) If they have to role claim or become seer-cleared, it's good to not be the only prioritized scum-NK target. OTOH, too many cleared players increases the risk of them coming up for lynch. (b) They don't want to waste their NK on somebody scum will kill anyway.)

Fraction of scum (red), town (blue), and SK (black) wins below:

simulation all-vanilla s+don v sd+don sdv+don sdvb+don
12 players, sk, 3 scum 0.62 0.51 0.49 0.38 0.28 0.21
0.38 0.49 0.51 0.62 0.72 0.79
0.44 0.50 0.42 0.58 0.53 0.56
13 players, sk, 3 scum 0.62 0.55 0.46 0.38 0.27 0.21
0.38 0.45 0.54 0.62 0.73 0.79
0.40 0.46 0.41 0.56 0.52 0.54
14 players, sk, 3 scum 0.57 0.48 0.46 0.37 0.27 0.22
0.43 0.52 0.54 0.63 0.73 0.78
0.39 0.46 0.40 0.55 0.50 0.53
15 players, sk, 3 scum 0.58 0.50 0.45 0.38 0.27 0.22
0.42 0.50 0.55 0.62 0.73 0.78
0.40 0.45 0.39 0.52 0.49 0.51
16 players, sk, 3 scum 0.57 0.51 0.43 0.38 0.28 0.22
0.43 0.49 0.57 0.62 0.72 0.78
0.37 0.42 0.38 0.52 0.48 0.50
17 players, sk, 3 scum 0.55 0.47 0.42 0.38 0.26 0.21
0.45 0.53 0.58 0.62 0.74 0.79
0.37 0.42 0.37 0.50 0.47 0.49

simulation all-vanilla s+don v sd+don sdv+don sdvb+don
15 players, sk, 4 scum 0.72 0.63 0.58 0.49 0.35 0.29
0.28 0.37 0.42 0.51 0.65 0.71
0.38 0.44 0.36 0.51 0.47 0.50
16 players, sk, 4 scum 0.70 0.63 0.56 0.48 0.36 0.29
0.30 0.37 0.44 0.52 0.64 0.71
0.34 0.40 0.35 0.48 0.45 0.47
17 players, sk, 4 scum 0.68 0.61 0.55 0.48 0.35 0.29
0.32 0.39 0.45 0.52 0.65 0.71
0.34 0.39 0.34 0.47 0.44 0.46
18 players, sk, 4 scum 0.67 0.60 0.54 0.48 0.35 0.31
0.33 0.40 0.46 0.52 0.65 0.69
0.33 0.38 0.33 0.44 0.43 0.44
19 players, sk, 4 scum 0.67 0.60 0.52 0.48 0.35 0.30
0.33 0.40 0.48 0.52 0.65 0.70
0.32 0.36 0.32 0.43 0.42 0.43
20 players, sk, 4 scum 0.63 0.58 0.52 0.48 0.35 0.30
0.37 0.42 0.48 0.52 0.65 0.70
0.33 0.36 0.32 0.42 0.41 0.42
21 players, sk, 4 scum 0.65 0.59 0.51 0.48 0.34 0.30
0.35 0.41 0.49 0.52 0.66 0.70
0.31 0.34 0.30 0.40 0.40 0.41

In the simulation model, a survivor-SK has a substantial balancing effect, which is not in line with my expectation that they'll make the game more unstable. So perhaps this was not such a good SK model.

Last edited by Linus; 16th September 2012 at 12:56 PM.
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Old 16th September 2012, 01:14 PM   #64173  /  #6
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Old 16th September 2012, 01:51 PM   #64177  /  #7
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Read my posts with the following stupid accent: the thin one out of Laurel & Hardy
"quasi"
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Old 16th September 2012, 01:59 PM   #64179  /  #8
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Read my posts with the following stupid accent: Australia
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"quasi"
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Old 16th September 2012, 02:06 PM   #64180  /  #9
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Read my posts with the following stupid accent: Australia
I don't understand the scum/town/SK table. They add up to more than 1.000.

As for the rest you want 0.500 when you make the game right? So theoretically both sides have a chance of winning?
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Old 16th September 2012, 02:16 PM   #64182  /  #10
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"quasi"
You're fooling no one---you've both lost sleep and neglected irl social interactions because of a textbased internet game. We're all brothers and sisters.
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Old 16th September 2012, 02:30 PM   #64183  /  #11
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I don't understand the scum/town/SK table. They add up to more than 1.000.
That's because SK win (survivor SK, not last man standing SK) is compatible with both town and scum win. The town and scum win fractions add up to 1.
Quote:
As for the rest you want 0.500 when you make the game right? So theoretically both sides have a chance of winning?
The models are not perfect and games don't have to perfectly balanced to be playable. But personally I would aim for approximately 0.5 if possible, perhaps slightly more based on the intuition that the net effect of unmodelled behavior favors town.
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Old 16th September 2012, 02:31 PM   #64184  /  #12
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gib I think linus is trying to tell us something
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Old 16th September 2012, 02:38 PM   #64185  /  #13
Adenosine
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Read my posts with the following stupid accent: Australia
Quote:
Originally Posted by Linus View Post
Quote:
Originally Posted by Adenosine View Post
I don't understand the scum/town/SK table. They add up to more than 1.000.
That's because SK win (survivor SK, not last man standing SK) is compatible with both town and scum win. The town and scum win fractions add up to 1.
Quote:
As for the rest you want 0.500 when you make the game right? So theoretically both sides have a chance of winning?
The models are not perfect and games don't have to perfectly balanced to be playable. But personally I would aim for approximately 0.5 if possible, perhaps slightly more based on the intuition that the net effect of unmodelled behavior favors town.
Of course. Cool. I get it.
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Old 16th September 2012, 04:00 PM   #64188  /  #14
gib
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Read my posts with the following stupid accent: the thin one out of Laurel & Hardy
diva i think aden might have been recruited
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Old 16th September 2012, 04:42 PM   #64189  /  #15
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Read my posts with the following stupid accent: Canada
Quote:
Originally Posted by Linus View Post
Quote:
Originally Posted by divagreen View Post
Quote:
Originally Posted by gib View Post
"quasi"
You're fooling no one---you've both lost sleep and neglected irl social interactions because of a textbased internet game. We're all brothers and sisters.
He's right.
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Old 16th September 2012, 06:09 PM   #64190  /  #16
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gib I think linus is trying to tell us something
A cry for help?
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Old 16th September 2012, 07:09 PM   #64191  /  #17
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gib I think linus is trying to tell us something
A cry for help?
I'm saying welcome to the quasi-aspie club, brothers and sisters.
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Old 16th September 2012, 08:05 PM   #64192  /  #18
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(((linus)))
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Old 16th September 2012, 08:08 PM   #64193  /  #19
gib
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Read my posts with the following stupid accent: the thin one out of Laurel & Hardy
first table row 8 - a single scum in a 10 player game has a 49.2% chance of winning?
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Old 16th September 2012, 09:25 PM   #64198  /  #20
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diva
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Old 16th September 2012, 09:29 PM   #64200  /  #21
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Quote:
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first table row 8 - a single scum in a 10 player game has a 49.2% chance of winning?
Yep, D1 the probability of mislynch is 9/10, D2 it's 7/8, D3 it's 5/6, D4 it's 3/4. Together it's 49.2%.
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Old 16th September 2012, 09:39 PM   #64202  /  #22
Adenosine
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Read my posts with the following stupid accent: Australia
Safety in numbers.
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Old 16th September 2012, 10:21 PM   #64204  /  #23
gib
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Read my posts with the following stupid accent: the thin one out of Laurel & Hardy
how does it work for vanilla model + 1 town blocker, ignoring ability to safeclaim

ie what is effect of 1 blocker on a say a 4 scum in 16 players game
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Old 16th September 2012, 10:46 PM   #64207  /  #24
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Linus :notworthy:
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Old 17th September 2012, 04:19 AM   #64219  /  #25
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It all sailed past the wicket keeper here

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