# JAIST Research: Game Refinement Theory

Game Information Dynamics [1] was developed by Prof. Hiroyuki Iida and Prof. Takeo Nakagawa from JAIST. It talks about the measurement of gameplay progression of a game in the form of flowing fluids. The measurement is derived from the number of information the players received during the gameplay. What information? The information in game can be in the form of many things, such as:

• number of possible moves,
• one’s remaining health,
• number of enemies,
• scores.
• time limit/remaining time,
• etc.

However, that information is eventually leads to the game conclusion: whether Win, Lose, or Draw. Assume the information of currently played game as matters/particles. Those particles are moving, flowing, from the game, to the players’ mind. Players’ accumulate that kind of information of the current game. Since that information is flowing like a fluid, the relatively close approach the newtonian physics. To generate a reasonable curve which match several games, this equation is used:

$\xi = \eta^m$

## Game Refinement Theory

Game Information Dynamics is a close relative of Game Refinement Theory [2], which states how to measure the sophistication of game from its predecessor model. Game Refinenment Theory talks only about the outcome of the game, not the whole process. On the other hand, Game Information Dynamics talks the whole gameplay progression, from the beginning until the end. That’s why Game Information Dynamics was modeled in fluid mechanics. But, for now, let’s talk abaout the Game Refinement Theory.

Game Refinement Theory talks about Force in Mind (wait, what!?). Why must we consider this model? Well, we are simply trying to build our foundation of how to measure and quantify everything related to game. The reasonable approach to quantify it was the newtonian physics model, with several adjustments.

1. Newtonian Physics is applied to physical objects, where their mechanical interactions are observable by human.
2. Game Information Dynamics is applied to players’ mind, or we can say: players’ state of mind. Perhaps we can call this “meta”-physics.

Force is something which makes things move, e.g. to push/pull a car, one needs to exerts the equal force. Force is denoted by:

$F = ma$

therefore

$F = m\frac{d^2s}{dt^2}$

where:

 $F$ : Force $m$ : Mass $a$ : Acceleration $t$ : Time

That’s the Isaac Newton’s force equation applied to object. In Game Information Dynamics, force is analogous with how much impact that the players will receive when they play games. Impact here is not the difference of momentum between time ($\Delta{}p$), but rather the impact to mind, e.g. thrill, engagement, pleasure, pressure, fear, etc. Of course game impact can’t be quantified, yet the equation to calculate the mind impact can be developed. In this research we define the value of game progress information over time $x(t)$ denoted by this Equation:

$x(t) = B(\frac{t}{D})^n$ (for board games) or $x(t) = G(\frac{t}{T})^n$ (for sport games)

where:

 $x(t)$ : Degree of information at time $t$ $B$ : Breadth or number of possible moves $D$ : Depth or length of game $t$ : Time $t$ $G$ : Goals or successful scoring attempts $T$ : Total scoring attempts (including failures and goals) $n$ : Power factor, differs from each person

and assume that

$F \cong x(t)$

therefore the factor acceleration $a$ which makes the force apparent is analogous with $\frac{d^2G}{dT^2}$ with the $n \geq 2$. In other words:

$a \cong \frac{G}{T^2} n (n-2)$

This $a \cong \frac{G}{T^2} n (n-2)$ is what we call Game Refinement Value ($R$), which denotes the degree of game sophistication. For most of the part, however, we use its root square model, which is:

$R = \frac{\sqrt{G}}{T}$

The study shown that a sophisticated board games have value $0.07 \leq R \leq 0.08$. What is this about? To simply put, it talks about how gameplay progress have effect to player’s mind.

## My Research

Well, FYI, this research has no relation to my thesis AT ALL. Say, I do this as an Ex-Gratia Research. My research was relating this equation to many things e.g. the gameplay progression of games, the relevant variables for each type of games, etc. I still don’t even understand how this topic emerge, but this research is an attempt to break the Nash Equilibrium in Game Theory [3] so that we can quantify the game progress and its attractiveness, not just via its information entropy value.

P.S.: This post is a dedicated as a practice to write a scientific paper via $\LaTeX$. It’s a very powerful tool.

### References:

 1 H. Iida, H. Takahara, J. Nagashima, Y. Kajihara, and Y. Hashimoto. (2004). An application of game-re nement theory to mah jong. In International Conference on Entertainment Computing (ICEC):333-338. 2 Iida, H., Nakagawa, T., Spoerer, K., Information dynamic models based on fluid mechanics. Entertainment and Computing, 2012. 3 Nash, J. (1950). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences 36(1):48-49.