Posted by Ezra Resnick in Game theory, Reason.

I often play online Spades. Spades is a trick-taking card game for four players (like Bridge, Whist, Hearts, etc.), meaning that every round is composed of thirteen tricks in which each player lays one card. The winner of each trick (determined by simple rules) begins the next trick. The first cool thing about Spades is that it’s a partnership game: players seated opposite each other are on the same team. The objective of the game is to be the first team to reach a predetermined score (e.g., 500 points). Points are given at the end of each round based on the number of tricks won by each team relative to their bid – the number of tricks they declared they would take at the start of the round. The scoring rules are what actually determine the character of the game, and the scoring rules for Spades are pretty simple:

• A team which won at least the number of tricks they bid receives 10 points for each trick they bid, plus 1 point for each additional trick they won (on top of their bid). However, they are also given 1 penalty point (a bag) for each of the additional tricks. For example, if a team bid 3 but won 5 tricks they receive 32 points plus 2 bags. If a team accumulates 10 bags they are penalized 100 points.
• A team which won less tricks than they bid is said to be set, and they lose 10 points for each trick they bid. For example, if a team bid 3 but won 2 tricks (or 1, or none), they lose 30 points.

From these rules we can extrapolate some basic strategy. Taking even one trick less than you bid is usually much worse than taking a few extra, so you should only bid an amount you are reasonably sure you can get (when in doubt, underbid). Consequently, the sum of a round’s bids is almost always less than 13 – usually between 10 and 12 (and an occasional sum of 8 or 9 is not unheard of). The asymmetry between overshooting and undershooting also means that it’s often worth taking more tricks than you bid in order to set the other team. This is where things get tricky: the question you are always asking yourself in Spades is, “set or bag?” If you think you have a chance of setting the other team, you may try to take as many tricks as you can, but if you think a set is unlikely then it’s probably better not to take any extra tricks and get your opponents to take all the bags. This razor’s edge is where skill comes into play: you may start a round trying to set your opponents, then switch to bagging them once you realize a set is improbable, or vice versa.

Another thing that makes Spades interesting is the partnership aspect. Your optimal play is obviously dependent on your partner’s cards, and it’s essential that the two of you cooperate on the same plan (e.g., set or bag) – but you don’t know what’s in your partner’s hand (and any discussion of your cards or your preferred strategy is forbidden). Therefore, you must try to infer what your partner has and what strategy he is favoring based on his play, and likewise, you must try to signal your intentions to your partner via your actions within the game. Of course, any such signals can be seen by the opponents as well…

Playing online, you will inevitably encounter some annoying players. Some people can’t resist the urge to berate their partner over an unsuccessful round, even when bad luck is actually to blame. A more interesting example of irrationality, however, is opponents who get upset when they feel you are using a strategy that makes the game “not fun.” David Sirlin, in his “Playing to Win” manifesto, calls such players scrubs. In Spades, scrubs are typically revealed when the sum of bids was low (10 or under), and you have skillfully maneuvered your opponents into taking all the bags. They will then accuse you of being “a bagger” or of playing a “bag game,” i.e., purposely underbidding in order to give the other team more bags. Now, I happen to prefer it when the sum of bids is high, and I usually bid aggressively, but even if I were playing a “bag game” on purpose, this complaint would make no sense. We are all presumably trying to win, so we ought to use whatever strategy works best. If being a “bagger” is a winning strategy (which I don’t think it is), wouldn’t I be a fool not to use it? The thing is, some people only know one strategy, and they get annoyed if their opponent somehow causes it to backfire. But that is the whole point of the game. If the strategy you have chosen is not working well against your opponent’s play, you need to come up with a different strategy. Scrubs will claim that always “playing to win” makes the game less fun, but for me, the fun is in trying to anticipate what the other players will do and figure out how to maximize my chances of success in any given situation. If playing the winning strategy really makes the game no fun for you, find a different game. But don’t be a scrub.