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'''Vanilla Mafia''' (also referred to as Mountainous) is the most basic setup for a Mafia game, with only [[Goon|Mafia Goons]] and [[Townie|Vanilla Town]], along with standard rules (alternating between [[Day]] lynches by the Town and [[Night]] kills by the Mafia.
 
Vanilla setups have been run with different player counts, with each count having a different [[Game Balance|Balance]].
 
===EV Calculations===
The [[EV]] of a [[Day Start]] setup with M Goons and T Townies (with total number of players M+T odd) can be calculated as follows:
 
*During Day, there are M+T total players. The probability of lynching Mafia is therefore M/(M+T), while the probability of lynching Town is T/(M+T).
*If Mafia is lynched, then after the Mafia kill a Townie at Night, there will be M-1 Mafia and T-1 Townies remaining for the next day.
*If Town is lynched, then after the Mafia kill another Townie at Night, there will be M Mafia and T-2 Townies remaining for the next day.
 
Putting this all together gives the following recursive formula:
 
EV[M,T] = M/(M+T) * EV[M-1,T-1] + T/(M+T) * EV[M,T-2]
 
This formula, combined with the fact that EV[0,T] = 1 (Town wins if there are no Mafia left) and EV[M,X] = 0 if M >= X (Mafia wins if they make up half the town), can be used to calculate any specific size and composition of game.
 
If the total number of players is even, Town should [[No Lynch]] - this is because the number of [[Mislynch|mislynches]] is unchanged, while the probability of lynching Mafia is increased with one fewer Townie.
 
===EV for Select Setups===
 
The EV calculated in this table is the expected win percentage for Town. To calculate for Mafia, subtract each from 100%.
 
EV has been calculated up to M {{=}} 1000 (and T > 4000000); a table of values up to 99 Players and up to 10 Mafia can be found [https://forum.mafiascum.net/viewtopic.php?p=8088743#p8088743 here].
 
{| class="wikitable"
|-
! T \ M
! 0
! 1
! 2
! 3
! 4
! 5
|-
! 0
| N/A
| 0.00%
| 0.00%
| 0.00%
| 0.00%
| 0.00%
|-
! 1
| 100.00%
| 0.00%
| 0.00%
| 0.00%
| 0.00%
| 0.00%
|-
! 2
| 100.00%
| {{Hover|EV[1,2] {{=}} (1/3) * EV[0,1] + (2/3) * EV[1,0] {{=}} 33.33%|33.33%}}
| 0.00%
| 0.00%
| 0.00%
| 0.00%
|-
! 3
| 100.00%
| {{Hover|EV[1,3] {{=}} EV[1,2] (after no lynch)|33.33%}}
| {{Hover|EV[2,3] {{=}} (2/5) * EV[1,2] + (3/5) * EV[2,1] {{=}} 13.33%|13.33%}}
| 0.00%
| 0.00%
| 0.00%
|-
! 4
| 100.00%
| {{Hover|EV[1,4] {{=}} (1/5) * EV[0,3] + (4/5) * EV[1,2] {{=}} 46.67%|46.67%}}
| {{Hover|EV[2,4] {{=}} EV[2,3] (after no lynch)|13.33%}}
| {{Hover|EV[3,4] {{=}} (3/7) * EV[2,3] + (4/7) * EV[3,2] {{=}} 5.71%|5.71%}}
| 0.00%
| 0.00%
|-
! 5
| 100.00%
| {{Hover|EV[1,5] {{=}} EV[1,4] (after no lynch)|46.67%}}
| {{Hover|EV[2,5] {{=}} (2/7) * EV[1,4] + (5/7) * EV[2,3] {{=}} 22.86%|22.86%}}
| {{Hover|EV[3,5] {{=}} EV[3,4] (after no lynch)|5.71%}}
| {{Hover|EV[4,5] {{=}} (4/9) * EV[3,4] + (5/9) * EV[4,3] {{=}} 2.54%|2.54%}}
| 0.00%
|-
! 6
| 100.00%
| {{Hover|EV[1,6] {{=}} (1/7) * EV[0,5] + (6/7) * EV[1,4] {{=}} 54.29%|54.29%}}
| {{Hover|EV[2,6] {{=}} EV[2,5] (after no lynch)|22.86%}}
| {{Hover|EV[3,6] {{=}} (3/9) * EV[2,5] + (6/9) * EV[3,4] {{=}} 11.43%|11.43%}}
| {{Hover|EV[4,6] {{=}} EV[4,5] (after no lynch)|2.54%}}
| {{Hover|EV[5,6] {{=}} (5/11) * EV[4,5] + (6/11) * EV[5,4] {{=}} 1.15%|1.15%}}
|-
! 7
| 100.00%
| {{Hover|EV[1,7] {{=}} EV[1,6] (after no lynch)|54.29%}}
| {{Hover|EV[2,7] {{=}} (2/9) * EV[1,6] + (7/9) * EV[2,5] {{=}} 29.84%|29.84%}}
| {{Hover|EV[3,7] {{=}} EV[3,6] (after no lynch)|11.43%}}
| {{Hover|EV[4,7] {{=}} (4/11) * EV[3,6] + (7/11) * EV[4,5] {{=}} 5.77%|5.77%}}
| {{Hover|EV[5,7] {{=}} EV[5,6] (after no lynch)|1.15%}}
|-
! 8
| 100.00%
| {{Hover|EV[1,8] {{=}} (1/9) * EV[0,7] + (8/9) * EV[1,6] {{=}} 59.37%|59.37%}}
| {{Hover|EV[2,8] {{=}} EV[2,7] (after no lynch)|29.84%}}
| {{Hover|EV[3,8] {{=}} (3/11) * EV[2,7] + (8/11) * EV[3,6] {{=}} 16.45%|16.45%}}
| {{Hover|EV[4,8] {{=}} EV[4,7] (after no lynch)|5.77%}}
| {{Hover|EV[5,8] {{=}} (5/13) * EV[4,7] + (8/13) * EV[5,6] {{=}} 2.93%|2.93%}}
|-
! 9
| 100.00%
| {{Hover|EV[1,9] {{=}} EV[1,8] (after no lynch)|59.37%}}
| {{Hover|EV[2,9] {{=}} (2/11) * EV[1,8] + (9/11) * EV[2,7] {{=}} 35.21%|35.21%}}
| {{Hover|EV[3,9] {{=}} EV[3,8] (after no lynch)|16.45%}}
| {{Hover|EV[4,9] {{=}} (4/13) * EV[3,8] + (9/13) * EV[4,7] {{=}} 9.06%|9.06%}}
| {{Hover|EV[5,9] {{=}} EV[5,8] (after no lynch)|2.93%}}
|-
! 10
| 100.00%
| {{Hover|EV[1,10] {{=}} (1/11) * EV[0,9] + (10/11) * EV[1,8] {{=}} 63.06%|63.06%}}
| {{Hover|EV[2,10] {{=}} EV[2,9] (after no lynch)|35.21%}}
| {{Hover|EV[3,10] {{=}} (3/13) * EV[2,9] + (10/13) * EV[3,8] {{=}} 20.78%|20.78%}}
| {{Hover|EV[4,10] {{=}} EV[4,9] (after no lynch)|9.06%}}
| {{Hover|EV[5,10] {{=}} (5/15) * EV[4,9] + (10/15) * EV[5,8] {{=}} 4.97%|4.97%}}
|-
! 11
| 100.00%
| {{Hover|EV[1,11] {{=}} EV[1,10] (after no lynch)|63.06%}}
| {{Hover|EV[2,11] {{=}} (2/13) * EV[1,10] + (11/13) * EV[2,9] {{=}} 39.49%|39.49%}}
| {{Hover|EV[3,11] {{=}} EV[3,10] (after no lynch)|20.78%}}
| {{Hover|EV[4,11] {{=}} (4/15) * EV[3,10] + (11/15) * EV[4,9] {{=}} 12.18%|12.18%}}
| {{Hover|EV[5,11] {{=}} EV[5,10] (after no lynch)|4.97%}}
|-
! 12
| 100.00%
| {{Hover|EV[1,12] {{=}} (1/13) * EV[0,11] + (12/13) * EV[1,10] {{=}} 65.90%|65.90%}}
| {{Hover|EV[2,12] {{=}} EV[2,11] (after no lynch)|39.49%}}
| {{Hover|EV[3,12] {{=}} (3/15) * EV[2,11] + (12/15) * EV[3,10] {{=}} 24.52%|24.52%}}
| {{Hover|EV[4,12] {{=}} EV[4,11] (after no lynch)|12.18%}}
| {{Hover|EV[5,12] {{=}} (5/17) * EV[4,11] + (12/17) * EV[5,10] {{=}} 7.09%|7.09%}}
|-
! 13
| 100.00%
| {{Hover|EV[1,13] {{=}} EV[1,12] (after no lynch)|65.90%}}
| {{Hover|EV[2,13] {{=}} (2/15) * EV[1,12] + (13/15) * EV[2,11] {{=}} 43.01%|43.01%}}
| {{Hover|EV[3,13] {{=}} EV[3,12] (after no lynch)|24.52%}}
| {{Hover|EV[4,13] {{=}} (4/17) * EV[3,12] + (13/17) * EV[4,11] {{=}} 15.09%|15.09%}}
| {{Hover|EV[5,13] {{=}} EV[5,12] (after no lynch)|7.09%}}
|-
! 14
| 100.00%
| {{Hover|EV[1,14] {{=}} (1/15) * EV[0,13] + (14/15) * EV[1,12] {{=}} 68.17%|68.17%}}
| {{Hover|EV[2,14] {{=}} EV[2,13] (after no lynch)|43.01%}}
| {{Hover|EV[3,14] {{=}} (3/17) * EV[2,13] + (14/17) * EV[3,12] {{=}} 27.79%|27.79%}}
| {{Hover|EV[4,14] {{=}} EV[4,13] (after no lynch)|15.09%}}
| {{Hover|EV[5,14] {{=}} (5/19) * EV[4,13] + (14/19) * EV[5,12] {{=}} 9.20%|9.20%}}
|-
! 15
| 100.00%
| {{Hover|EV[1,15] {{=}} EV[1,14] (after no lynch)|68.17%}}
| {{Hover|EV[2,15] {{=}} (2/17) * EV[1,14] + (15/17) * EV[2,13] {{=}} 45.97%|45.97%}}
| {{Hover|EV[3,15] {{=}} EV[3,14] (after no lynch)|27.79%}}
| {{Hover|EV[4,15] {{=}} (4/19) * EV[3,14] + (15/19) * EV[4,13] {{=}} 17.76%|17.76%}}
| {{Hover|EV[5,15] {{=}} EV[5,14] (after no lynch)|9.20%}}
|-
! 16
| 100.00%
| {{Hover|EV[1,16] {{=}} (1/17) * EV[0,15] + (16/17) * EV[1,14] {{=}} 70.05%|70.05%}}
| {{Hover|EV[2,16] {{=}} EV[2,15] (after no lynch)|45.97%}}
| {{Hover|EV[3,16] {{=}} (3/19) * EV[2,15] + (16/19) * EV[3,14] {{=}} 30.66%|30.66%}}
| {{Hover|EV[4,16] {{=}} EV[4,15] (after no lynch)|17.76%}}
| {{Hover|EV[5,16] {{=}} (5/21) * EV[4,15] + (16/21) * EV[5,14] {{=}} 11.24%|11.24%}}
|-
! 17
| 100.00%
| {{Hover|EV[1,17] {{=}} EV[1,16] (after no lynch)|70.05%}}
| {{Hover|EV[2,17] {{=}} (2/19) * EV[1,16] + (17/19) * EV[2,15] {{=}} 48.51%|48.51%}}
| {{Hover|EV[3,17] {{=}} EV[3,16] (after no lynch)|30.66%}}
| {{Hover|EV[4,17] {{=}} (4/21) * EV[3,16] + (17/21) * EV[4,15] {{=}} 20.22%|20.22%}}
| {{Hover|EV[5,17] {{=}} EV[5,16] (after no lynch)|11.24%}}
|-
! 18
| 100.00%
| {{Hover|EV[1,18] {{=}} (1/19) * EV[0,17] + (18/19) * EV[1,16] {{=}} 71.62%|71.62%}}
| {{Hover|EV[2,18] {{=}} EV[2,17] (after no lynch)|48.51%}}
| {{Hover|EV[3,18] {{=}} (3/21) * EV[2,17] + (18/21) * EV[3,16] {{=}} 33.21%|33.21%}}
| {{Hover|EV[4,18] {{=}} EV[4,17] (after no lynch)|20.22%}}
| {{Hover|EV[5,18] {{=}} (5/23) * EV[4,17] + (18/23) * EV[5,16] {{=}} 13.19%|13.19%}}
|-
! 19
| 100.00%
| {{Hover|EV[1,19] {{=}} EV[1,18] (after no lynch)|71.62%}}
| {{Hover|EV[2,19] {{=}} (2/21) * EV[1,18] + (19/21) * EV[2,17] {{=}} 50.71%|50.71%}}
| {{Hover|EV[3,19] {{=}} EV[3,18] (after no lynch)|33.21%}}
| {{Hover|EV[4,19] {{=}} (4/23) * EV[3,18] + (19/23) * EV[4,17] {{=}} 22.48%|22.48%}}
| {{Hover|EV[5,19] {{=}} EV[5,18] (after no lynch)|13.19%}}
|-
! 20
| 100.00%
| {{Hover|EV[1,20] {{=}} (1/21) * EV[0,19] + (20/21) * EV[1,18] {{=}} 72.97%|72.97%}}
| {{Hover|EV[2,20] {{=}} EV[2,19] (after no lynch)|50.71%}}
| {{Hover|EV[3,20] {{=}} (3/23) * EV[2,19] + (20/23) * EV[3,18] {{=}} 35.49%|35.49%}}
| {{Hover|EV[4,20] {{=}} EV[4,19] (after no lynch)|22.48%}}
| {{Hover|EV[5,20] {{=}} (5/25) * EV[4,19] + (20/25) * EV[5,18] {{=}} 15.05%|15.05%}}
|}
 
===Balancing Vanilla Mafia===
The number of Townies needed to balance a given number of Mafia, M, grows quadratically with M (specifically, to balance a setup with M Mafia, about [https://forum.mafiascum.net/viewtopic.php?p=10027427#p10027427 4.1M<sup>2</sup> + 2.3M Townies are needed]). This means that, from a purely EV standpoint, it is impractical to have any Vanilla setup with more than 3 Mafia.
 
The counts closest to a 50% EV balance are:
 
1:4 (46.67%), 2:19 (50.71%), 3:40 (49.97%)
 
Note that, while in most cases it is expected that Town will outperform their EV for a given setup, for Vanilla Mafia the Town has typically underperformed.
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[[Category:Open Setups]]

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