Tic-Tac-Toe Confusion - Seeing Wrong
Jan 15th, 2008 by Mike Bennett
Time for a quick hop skip and jump into cognitive science. Yep, I’ve already broken a New Year resolution by writing a longer post than I aimed for….though it is about some really interesting research that goes directly to the heart of User Designer: Are there benefits and dangers of changing artifacts and tools to cater for individual abilities and interests?

Many many years ago myself and friends went through a short phase of playing Tic-Tac-Toe (TTT), also called Noughts and Crosses. You win this simple two player game by forming a horizontal, vertical or diagonal straight line of three Xs or three Os. If both players play properly then neither player can win and the game finishes as a draw.
Early in the 90s Jiajie Zhang, as part of his PhD, did a number of experiments where he tested how well people could play TTT against a computer. What he wondered was whether different visual representations effected people’s ability to play the simple childhood game of TTT. Below are four (A to D) different graphical and conceptual layouts of TTT. If you play the (C) Shape version of TTT would you win more or less than if you play against the computer on the (D) Colour version of TTT?
Each of these graphical representations is called an isomorph of TTT. When you use these isomorphs to play TTT you are trying to solve the same problem as in TTT except the problem is presented differently, i.e. to win you still need to create a group of three items.

When playing (A) Line you colour three circles in a line to win, (B) Number you colour three circles so the numbers add to 15, (C) Shape you colour three circles so they share at least one shape in common and (D) Colour you colour three circles so they share at least one common colour.
What he found was that people’s ability to play TTT, this simple childhood game, was seriously effected by what isomorph version of TTT they played on! In one experiment he found that more than 50% of the players failed to get 10 draws in a row in the first 50 games when they played on the (B) Number version.
Depending on the computer’s opening moves (he did a number of experiments where he controlled what sequence of opening moves the computer could make) he showed that (A) Line was easier than (D) Colour, which was easier than (C) Shape which was around the same hardness as (B) Number.
Not only did the visual representation effect how well players did, but what options they had for their next move on the visual representation also effected their playing ability.
For the full paper with far more details about the experimental results you should download at least one of Zhang’s papers about the research The Interaction between Perceptual and Cognitive Processes in a Distributed Problem Solving Task.
A good starting point for learning more about this area is to read about representational determinism and distributed cognition. Mike Scaife’s and Yvonne Rogers paper External cognition: how do graphical representations work? is a good introduction.
Do you think people’s ability to play the isomorphic versions of TTT was affected by their familiarity with the graphical layouts? If a player was given enough practice would they play TTT as well no matter how the game looked? If they could practice would the speed at which they learn to play better be due to the visual representation? Why would one visual representation be easier to learn with than another?
The benefit of this research is it highlights an interesting danger of an individual centered user experience: People could end up shaping and creating tools that make it subtly hard to use the tools for thinking and problem solving. For example if you were an accountant or scientist looking at lots of numbers there is software that makes it easier to create visualisations of the numbers: How do you know that your visualisation isn’t playing with your mind by making it harder to think about the numbers?
Enjoyed this post? Then you might also like:
- Irish Human Computer Interaction Conference 2007
- Physiological Differences: Different Eyes, Different Tongues
- kameraflage: You See, It Sees - Different Sights
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