Tuesday, June 08, 2004
Median Poker: Mad Social Science you can try at home!
I occassionally play poker with a group of political scientists (and long suffering significant others). We try to keep things interesting by inventing politically-inspired games (e.g., French Election). My contribution is Median Poker (inspired by the "median", a less well-known but politically significant alternative to the mean).
The median is the middle element of a set. In median poker, the winning hand is not the highest, or the lowest hand, but the middle hand of those remaining when the hand is called. Let's do an example:
Five players deal a hand of five card draw, median poker style. Their hands (neglecting suits) are:
1) Q Q Q 5 4
2) 2 2 J 10 3
3) A J 9 7 6
4) K 9 8 4 2
5) J 10 8 7 5
If everyone stays in, the winning hand is 3, which ranks in the middle of the five according to the standard ranking of poker hands.
But suppose the players aren't total dummies. Player 1 realizes three queens is a very high hand for five-card draw, and folds. So does player 5, who figures there can't be many hands worse than his. There are three hands remaining, and the winner is player 3, again.
Ah! says the attentive reader, what if there are an even number left? Suppose player 1 drops, but player five stays in. Now the median is not clearly defined. Conventionally, the median would be calculated as the mean of the two central hands (in this case, 3 and 4), so perhaps 3 and 4 should split the pot. But there is no need to stand on convention (this is mad social science, after all!). Instead, I recommend that with an even number of hands, the higher of the two middle hands should win (in this case, player 3).
I've played this game a few times, and have some observations:
1. Beliefs about other players hands and strategies often play an important role in poker. Median poker takes this to another level: in addition to other considerations, each player tries to figure out where other players think the median will be (Ace high? A low pair? etc). This quickly becomes a game of "what do I think they think I think" .... ad infinitum. For this reason, after a shaky start, a group of players may settle into a consistent set of beliefs after several rounds, but different groups may vary in where the median is. (There are limits, of course; three of a kind will never be a good median poker hand. And there may be optimal strategies to play against a group that has settled on an unlikely median).
2. Wild cards probably are a bad idea for median poker.
3. Median poker is most fun with at least five players
4. The "higher central hand wins in even games" rule may help beliefs gel about what the best hand is, and in any event avoids a lot of boring pot-splitting.
5. You probably shouldn't try this game unless your players are willing to be patient as everyone learns the ropes.
6. Ace high tends to be a very good median poker hand in five card draw. (Not surprising, since Ace high is the median five-card hand dealt without drawing more cards.)
So go ahead! Experiment on your friends! If anyone out there tries this game, I'd be happy to hear your experiences.
The median is the middle element of a set. In median poker, the winning hand is not the highest, or the lowest hand, but the middle hand of those remaining when the hand is called. Let's do an example:
Five players deal a hand of five card draw, median poker style. Their hands (neglecting suits) are:
1) Q Q Q 5 4
2) 2 2 J 10 3
3) A J 9 7 6
4) K 9 8 4 2
5) J 10 8 7 5
If everyone stays in, the winning hand is 3, which ranks in the middle of the five according to the standard ranking of poker hands.
But suppose the players aren't total dummies. Player 1 realizes three queens is a very high hand for five-card draw, and folds. So does player 5, who figures there can't be many hands worse than his. There are three hands remaining, and the winner is player 3, again.
Ah! says the attentive reader, what if there are an even number left? Suppose player 1 drops, but player five stays in. Now the median is not clearly defined. Conventionally, the median would be calculated as the mean of the two central hands (in this case, 3 and 4), so perhaps 3 and 4 should split the pot. But there is no need to stand on convention (this is mad social science, after all!). Instead, I recommend that with an even number of hands, the higher of the two middle hands should win (in this case, player 3).
I've played this game a few times, and have some observations:
1. Beliefs about other players hands and strategies often play an important role in poker. Median poker takes this to another level: in addition to other considerations, each player tries to figure out where other players think the median will be (Ace high? A low pair? etc). This quickly becomes a game of "what do I think they think I think" .... ad infinitum. For this reason, after a shaky start, a group of players may settle into a consistent set of beliefs after several rounds, but different groups may vary in where the median is. (There are limits, of course; three of a kind will never be a good median poker hand. And there may be optimal strategies to play against a group that has settled on an unlikely median).
2. Wild cards probably are a bad idea for median poker.
3. Median poker is most fun with at least five players
4. The "higher central hand wins in even games" rule may help beliefs gel about what the best hand is, and in any event avoids a lot of boring pot-splitting.
5. You probably shouldn't try this game unless your players are willing to be patient as everyone learns the ropes.
6. Ace high tends to be a very good median poker hand in five card draw. (Not surprising, since Ace high is the median five-card hand dealt without drawing more cards.)
So go ahead! Experiment on your friends! If anyone out there tries this game, I'd be happy to hear your experiences.
