Prisoner's Quadrangle

Prisoner’s Quadrangle

Overview:

The black cards represent cooperation, and the red cards represent competition. The team that cooperates the best will win the round. However, the spoils for winning are rewarded disproportionally – the more competitive member of each team will steal a bigger share of the loot!

Players: 4

Equipment: Two decks of cards

Pad or chips to keep score

Setup:

Remove all royalty (J-K) from each deck. Give each player all number cards from a red suit and a black suit from one of the decks. (In other words, one player could get 1-10 clubs and diamonds from deck A, one player 1-10 spades and hearts from deck A, one player 1-10 clubs and diamonds from deck B, and one player 1-10 spades and hearts from deck B).

How to play:

A complete game will consist of three rounds, which will constitute the three possible two-on-two matchups that are possible with four players. Designate a dealer at the start of a game. For the first round, the dealer’s partner will be the person sitting on the dealer’s left; for the second round, everyone’s partner will be sitting across from him or her, and for the third round, the dealer’s partner will be sitting to her right.

During each round, everyone secretly chooses two cards, a red card and a black card. These two cards must add up to exactly 11. Once everyone has chosen their cards, they reveal them simultaneously.

Scoring:

First, add up the total of the black cards from each team. The higher total is declared to be the winning team.

Within each team, the player with the higher red card is considered to be the Top Competitor, and the other player is the Underdog.

Award points as follows:

Underdog, losing team: 0 points

Top competitor, losing team: 1 point

Underdog, winning team: 1 point

Top competitor, winning team: 3 points

Ties:

Whenever there is a tie, treat it as if both sides have lost. So if both teams have the same total of black cards, both sides score as losers, and if two members of the same team have the same combination of cards, they both score as underdogs.

Players may use the same combination of cards in multiple rounds.

Theme:

The first theme that occurred to me is basketball. The team that cooperates better is more likely to win games, but on the winning team, the flashy ball-hog is the one likely to get the big Nike contracts. Which is better, to be the star of a losing team or a supporting member of a winning one? In this game, they’re about the same.

As I thought about it more, it occurred to me that there are a lot of business parallels as well. The companies that cooperate better are likely to do better than their competition and win big contracts. But within such a company, if you focus too much on cooperation and allow other people to steal credit for your work, you will never receive raises and promotions.

Now that I think about it, this version seems like it may have more real-world applications than the original Prisoner’s Dilemma.

Notes:

Obviously the trickiest thing about the design is how to assign the points for the relative positions. It seemed to me that if the top spot only got two points, there might be too much temptation to just play black tens all the time, hoping to get the steady one points that come from being the underdog on the winning team (not guaranteed, but likely). With three points for the top spot, it seems as if you would not be able to afford taking yourself out of the running for it.

Strategy:

Most of the play seems as if it would take place in the black 5-8 range. You wouldn’t want to play a black 10 very often, since it would guarantee that you couldn’t score higher than one point that round. So a little bit of competition is always a good thing. And occasionally you might want to play a red 10, since that would almost guarantee you a point as well, unless your partner also played a red 10. Playing red 7-9 would seem to be a losing proposition, though, since they would increase your chances of getting in the dreaded zero point spot if your partner plays a red 10. Perhaps if the entire table was shifting in the red direction it might make a viable strategy.

The metagame strategy would start to kick in after the first round, when you start having clear winners. If you’re paired up with the leader, perhaps it’s a good idea to take a red 10, and thus make sure your partner will be likely to not score anything this round. But what if he anticipates that you’re going to do this, and also takes a red 10 so you’re both screwed? And why should you take yourself out of the running for the top prize just to nail the leader, anyway?