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I recently played a couple of games (i.e. six rounds) of Saboteur with ten and then nine players. The miners found the gold every round, and it was only a close thing once.

The saboteurs win a bit more gold than the miners if they're successful, but I'd be surprised if this was enough to balance the game.

There's a similar question about ways to balance the win ratios, but I'm interested in whether the game as it stands has a balanced expected return for both sides.


Edited to add game information:

Rules

The rules for Saboteur are available from the ZMan games site.

Role Cards

The role deck contains 11 cards:

  • 7 gold miner cards (whose aim is to find the gold)
  • 4 saboteur cards (whose aim is to prevent the miners from finding the gold).

Gold distribution

The gold deck contains 28 cards in the following denominations:

  • 16 cards with 1 nugget
  • 8 cards with 2 nuggets
  • 4 cards with 3 nuggets

If the miners win a round in an n player game, then n randomly select gold cards are distributed amongst the miners (for a 10 player game only 9 cards are distributed). If the (1/2/3/4) saboteurs win a round then they are awarded (4/3/3/2) gold each (respectively).


Question clarification:

I am interested in the expected amount of gold for those playing as miners, and for those playing as saboteurs. This is almost certainly different for different numbers of players, but I am interested to know whether the expected winnings is anywhere near the same for both sides.

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The rules seem to indicate keep gold nugget cards between rounds. This will change the distribution of gold nuggets for rounds 2 and 3. Are you interested in just the R1 expected gold winnings, or are you interested in the possible differences round to round. Further, are you interested in the expected amount of gold if a miner should win, or the odds of winning. The latter would require a Monte Carlo simulation, or a large game database (cannot seem to find an online database at this time of Saboteur win rates) –  user1873 Mar 31 '12 at 12:19
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@user1873 For simplicity I'm interested in the first round. The other distributions will only be different if the gold cards remaining have been biased, which can only happen when the saboteurs win. I'm interested in the expected gold gained in a round, given that a player has drawn a miner card (/saboteur card). I.e. The expected gold gained by a winning miner, multiplied by the probability of winning as a miner (and the same for the saboteurs). What's more I'm really interested in a rough value for these expected values, and whether they are roughly equal or not. –  tttppp Apr 1 '12 at 9:03
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2 Answers

EndersGame has a post on BGG talking about a teams chances of winning a particular round. It doesn't take into account the fact that the game is played over multiple rounds for points, so you would have to take into account ACT points for each player when they win, and self sabaotague from teammates trying to get the most points by finding the gold.

There is at least one large game database of results you could consult to draw some conclusions. Board Game Arena has 1500+ online games recorded for Saboteur (bottom left of page). On the Saboteur page itself, you can review the results of previous games, and some interesting statistics about that particular game.

You would be interested in Number of gold nuggets earned by saboteurs/miners, but some of the other statistics might be useful. Unfortunately, you must either donate money to BGA to become a member, or get other players to join BGA through referrals to examine the statistics. It also appears to me while looking over a handful of 100 or so games, that few if any games are played with 9+ players. Most of the large games are 7 player. If you have too small of a sample size, you can't draw any accurate conclusions.

The interface for displaying the old game results isn't very well designed for gathering data across a large number of games. I haven't dug too deeply into the GET/POST messages that my browser sends to their server to see if it is possible to extract only the information that you are interested it, but I mention it here in case any other code monkey wants to dig into the problem themselves.

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I've updated the question with additional information. I was expecting to receive a rough answer based on experience of play, but I would be more than happy with an answer based on calculation instead! –  tttppp Mar 31 '12 at 7:53
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Saboteur 1 does seem to be biased towards the "good dwarves" if you don't play it in really cutthroat fashion. If the good dwarves just cooperate and go for the gold, they will win most of the time.

However, if the good dwarves break each OTHER in order to keep competitors from getting gold, it gives the Saboteurs a much better chance, obviously.

I think Saboteur was designed with an expectation that good dwarves would be more cutthroat and selfish than a lot of groups play them instinctually.

That said, I recommend you pick up Saboteur 2, which adds (and replaces) some cards and roles. It's much more well-balanced and more consistently fun.

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With the rule that Gold nugget distribution is handled counter-clockwise, wouldn't it make more sense to try to assist the next player in getting to the gold (in a 10P game you would get 2/3 g on avg as P2, and P1 would get 4/3 on avg, where miner 6/7 only gets 1? The game doesn't speak to seating order before each round, so if you redistribute players seating position randomly, it might balance it more. –  user1873 Mar 31 '12 at 12:29
    
Correction, the rules do mention the next starting player is the player to the left, indicating that seating order shouldn't change, but I wonder if rotating seating order and determining starting player in some random way would add more balance. –  user1873 Mar 31 '12 at 12:38
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