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Subject: Game balance: odds in favour of Saboteurs based on player no rss

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Ender Wiggins
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How balanced is Saboteur, in terms of whether or not it favours Saboteurs or Gold-Diggers? As others have pointed out, it can depend on whether you play more as a team game or as an individual point game. But it seems to me that the odds in favour of the Saboteurs also depends significantly on the number of players. Why? Because the percentage of Saboteurs in the game varies according the player number.

Since one player card is removed randomly, I have calculated all the statistical percentages for the amount of players that will be Saboteurs in any given game:

3 players: 1 Saboteur and 3 Gold-Diggers
75% of games (3/4): Saboteur power 1/3 = 33%
25% of games (1/4): Saboteur power 0/3 = 0%

4 players: 1 Saboteurs and 4 Gold-Diggers
80% of games (4/5): Saboteur power 1/4 = 25%
20% of games (1/5): Saboteur power 0/4 = 0%

5 players: 2 Saboteurs and 4 Gold-Diggers
67% of games (4/6): Saboteur power 2/5 = 40%
33% of games (2/6): Saboteur power 1/5 = 20%

6 players: 2 Saboteurs and 5 Gold-Diggers
71% of games (5/7): Saboteur power 2/6 = 33%
29% of games (2/7): Saboteur power 1/6 = 17%

7 players: 3 Saboteurs and 5 Gold-Diggers
62% of games (5/8): Saboteur power 3/7 = 43%
38% of games (3/8): Saboteur power 2/7 = 17%

8 players: 3 Saboteurs and 6 Gold-Diggers
67% of games (6/9): Saboteur power 3/8 = 38%
33% of games (3/9): Saboteur power 2/8 = 25%

9 players: 3 Saboteurs and 7 Gold-Diggers
70% of games (7/10): Saboteur power 3/9 = 33%
30% of games (3/10): Saboteur power 2/9 = 22%

10 players: 4 Saboteurs and 7 Gold-Diggers
64% of games (7/11): Saboteur power 4/10 = 40%
36% of games (4/11): Saboteur power 3/10 = 30%

It seems evident from the percentages that the Saboteurs have the least chance of succeeding in 3, 4, 6, and 9 player games. For the most part, this is corroborated by the results in this thread:
Post your results: Win record of Gold-Diggers vs Saboteurs
http://www.boardgamegeek.com/thread/164370

Especially in games with this number of players, perhaps the Saboteurs could use a slight edge to improve their chances. If you're finding that the Saboteurs don't have much hope of winning in 6, 9 and maybe even 8 player games, you should consider the Werewolf Variant suggested by Aaron Kurtz, where the Saboteurs secretly reveal themselves to each other at the start of the game. Details here:
Saboteurs know each other variant
http://www.boardgamegeek.com/thread/141246
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Kelly Bass
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Re: Game balance: odds in favour of Saboteurs based on playe
Yes, I've noticed certain player numbers that make it seem unbalanced, so those stats don't surprise me.

I think to really balance the game, however, some math/stats/combinatorics whiz could come up with the average number of gold won by the good dwarves for each number of players based on number of gold cards taken and passed around among the good dwarves. Then compare that to the number of gold won by the saboteurs with the same number of players.

Then we could see just how imbalanced each number of players is for the saboteurs.
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Yo ghurt
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EndersGame wrote:
7 players: 3 Saboteurs and 5 Gold-Diggers
62% of games (5/8): Saboteur power 3/7 = 43%
38% of games (3/8): Saboteur power 2/7 = 17%

2/7 is about 29%, not 17%. However, thanks for the statistics.

chockle wrote:
I think to really balance the game, however, some math/stats/combinatorics whiz could come up with the average number of gold won by the good dwarves for each number of players based on number of gold cards taken and passed around among the good dwarves. Then compare that to the number of gold won by the saboteurs with the same number of players.

Then we could see just how imbalanced each number of players is for the saboteurs.

That's roughly what I intend to do:

Calculate the average amount of gold per miner/saboteur for each #players and calculate the optimal win/lose ratio between miners and saboteurs, so everyone gains the same average amount of gold. Then compare this optimal win/lose ratio with the average miner/saboteur ratio per #players, and then estimate if the game might be unbalanced for certain #players.

...of course this would be nothing more than an estimation, leaving many factors unconsidered.
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