Down the Intransitive Rabbit Hole

Citadels Theif Card

I found it somewhat easy to learn the basics of the card game Citadels. After a while I learned there are strategies within strategies, and these strategies are formed around counteracting other people’s strategies… What?

Yea, I found myself and the people who I have introduced it to getting higher and higher level in strategy with every game we played. This review explains the game pretty well (but you don’t need to read it to understand what I’m talking about).

  • The first time playing the game: learning the basic rules of the game.
  • The second time playing:  planning in order to accelerate one’s own success.
  • The third: playing assumptions of opponent strategies against them more than 2 turns ahead, ultimately improving the chances of one’s own success.

The simple game becomes very complicated very quickly, with near limitless possibilities and strategies for success. It reaches an apex of over-planning when playing opponents who are playing on a simpler level and can ultimately lead to “overthinking” and “beginners luck” which can always level a playing field.

Buy why? How does it work this well? How is this game so balanced? How is it so simple yet so complicated?

Intransitive Game Mechanics

Scary sounding, but a simple concept. It basically comes down to Rock, Paper, Scissors. The relationship of two of the options does not imply the relationship of the third. If it were transitive the rules would go as such:

if Scissors beats Paper => and Paper beats Rock => Scissors therefore beats Rock

You would imply that scissors also beats rock as it would be the lowest in the hierarchy. However, this is not the case since we all know that rock beats scissors. There is no true hierarchy and each choice has a weakness. Thus, the mechanic is intransitive. The Wikipedia entry is quite good at explaining this further

What makes this game interesting (up to a point)? The basic game is just pure chance and playing with the rules to try to win. However, there is actually some strategy to the game. Players can get play hands in order to influence their opponent’s assumptions about player’s next hands. Players can also try to guess what their opponents are about to play based on behavior observation and inference on future behavior. (,-Paper,-Scissors)

Now take this very basic mechanic and put it inside a larger version of this mechanic which itself is inside a larger version of the same mechanic. Think russian dolls of Rock, Paper, Scissors.

What does this mean for the game play? Bluff strategies start to come out more often as they do in Rock, Paper, Scissors. It allows for changing strategy mid stream as a reaction to an opponent decision. It also allows for playing a variety of strategies at different levels, e.g. playing defensively in micro turn-based moves, while playing aggressively with larger meta moves that may cost time or resources (saving up).

As soon as I realized that this is what was going on with Citadels, I felt like suddenly saw the Matrix code. There is no unseeing it now. This mechanic can be found all sorts of games. Chess, Poker, Street Fighter, etc.

Enjoy the rabbit hole.

Further reading on this mechanic: Game Balance Concepts Blog: Intransitive Mechanics

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One Comment

  1. Mike Altman (@mikealt)
    February 20, 2013

    New post: Down the Intransitive Rabbit Hole – How this #gamemechanic made me see the Matrix code

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