Friday, August 27, 2010

Ranked Preferences in Spades

(Those of you who don't know much about the spades card game won't get much out of this post, though a brief recap of the rules is here.)

In spades, you have to choose between two opposing goals--bagging or setting--and often have to switch strategies in the middle of the hand.

Your strategy can change dramatically if one team is close to the winning score, if one team has a high number of bags, or if a player has gone nill. For this example, assume that none of these factors is in play and that your team has bid 7 and your opponents have bid 3.

Your best outcome is taking 11 tricks, which makes your bid and sets your opponents, while taking the minimum amount of extra bags. Twelve or 13 tricks (nearly impossible in real life) are next best, as they also set your opponents but give you a few extra bags.

Next best is 7 tricks. You make your bid while taking no bags. Then you'd prefer 8, 9, or 10 tricks, which give you a few bags but don't set your opponents.

If you get fewer than 7 tricks, you don't make your bid. In this unfortunate scenario, you want to take as few tricks as possible, to maximize your opponents' bags. Zero is the best and 6 is the worst.

In sum, here are the number of tricks you could take, in order of your preference:

11, 12, 13, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6

What makes the game fun is that when you aim for 7 (the fourth best option), you risk ending up with 6 (the worst option). When you aim for 11 (the best), you risk ending up with 10 (the seventh best).

Of course, you must also play in sync with your partner, who may be trying to bag while you're trying to set (or vice versa). And you should be watching which cards have been played, which gives you information on which cards the other players are likely to be holding and thus your chances of reaching your goal. And you may need to take into consideration some of the other things that I've assumed away (if one team is close to the winning score, if one team has a lot of bags, etc.). It can get complicated.


kerpowski said...

Your expected value calculation in this particular situation is slightly off. The best way to think of this is to look at the total delta in score (your score delta minus the opponent's score delta) after the round is over, counting a sandbag as -9 points (+1 for the bag, -1/10th of the 100 penalty). Granted, this still doesn't take into account how close you are to the 500 point end-game criteria but it is far more accurate if the game were infinitely repeated or if it is early in the game.

The more accurate trick preferences for this bid, with the net score deltas are:

7 - +67
11 - +64
12 - +55
8 - +49
13 - +46
9 - +31
10 - +13
0 - -10
1 - -19
2 - -28
3 - -37
4 - -46
5 - -55
6 - -64

Greg Finley said...

I think -9 is an overly highly estimate of how bad bags are. They are only bad once you get 10. If the last digit of the number of bags you would get the rest of the game is uniformly distributed (probably not exactly right, but it's close enough), four extra bags only sets you back another hundred points 40% of the time. You seem to acknowledge this point somewhat, and we can both agree that spades is a very complex game! Thanks for reading.