Mafia is a social game created by Dmitry Davidoff played a generally a 10+ audience. The game consists of a group of people who receive random positions to either be the Mafia and kill off a townsmen each round or be in the townsmen and kill off the Mafia first. Many spice up the game or balance it through roles such as nurse who can save a person each round or detective who can guess who the Mafia is. The winning conditions include the Mafia killing everyone but one person or the town voting-off the Mafia before that happens.
In Mafia, balance between the townsmen and the mafia is a huge factor in making sure people have a fair chance of winning. However, with varying group sizes, creating these dynamics are difficult and drive the game towards opposite directions.
In the game intransitive balance is presented by increasing the value of members in the townsmen to nurse and detective. These roles help optimize the town for winning given that the people themselves are objects in the game. Transitive balance can be seen the count of mafia to townsmen ratio. Since certain people “cost” less than others, to make it fair there are less of the mafias who are more powerful. Fruity balance is not in the game since all the elements can be compared to one another.
With regards to balance with single player, since it is a group game, it is not applicable. Balance with asymmetry is a huge problem in Mafia though and it is offset by having different ratios of mafias to people and by having different roles or powers on the towns side. This helps with creating more balance in strategies for the game because it allows people to capitalize on powers and skills and win through deception as roles become more complicated. Lastly, given that the “objects” in Mafia are the people, the balance in objects comes down the ratio and the number of each type of player that is allowed. It can also be balance with conditions on roles such as the nurse only being able to save themselves once during the game. The randomization helps create a more balanced game overall.