Page 234 - The-5th-MCAIT2021-eProceeding

2. Game Refinement Theory Meets Rhythm Games

Game refinement (GR) theory (Iida, 2004) is used to measure the sophistication (i.e., the balance between
luck and skill) of a game. It provides an innovative game dynamic view by evaluating the process of a game,
simulating the game outcome's uncertainty as a kind of force in mind (Sutiono, 2014), which corresponds to
force in nature based on Newton's second law.
From the perspective of players, information of the game outcome is a function of time (in board games
would be the number of possible moves). By considering the process of game as a process of solving game
outcome uncertainty (or obtained certainty) ′( ), then (1) is obtained.

′( ) = ( ) (1)

The parameter (1 ≤ ∈ ) is the number of possible options, and (0) = 0 and ( ) = 1. Here
( ) stands for the normalized amount of solved uncertainty. Note that 0 ≤ ≤ , 0 ≤ ( ) ≤ 1. Eq. (1)
equation implies that the rate of increase in the solved information ′( ) is proportional to ′( ) and inverse
proportional to ( ) and inverse proportional to . Then, (2) is obtained by solving (1).

( ) = ( ) (2)

In most board and continuous movement video games, the game's total length is significantly different for
players with different levels. We assume that the solved information ( ) is twice derivable at ∈ [0, ]. The
second derivative here indicates the accelerated velocity of the solved uncertainty along with the game progress.
After the second derivative, GR's measure can be formulated in its root square form, as given by (3). It has been
found that sophisticated games have a similar GR value located at the zone of ∈ [0.07, 0.08] as shown in
Table 1. The game progress pattern or its difficulty is essential concerning the player's engagement.

√ ( −1)
= (3)

Table 1. Various popular games with measurement of game refinement theory
Game GR
Chess 0.074
Shogi 0.078
Go 0.076
Basketball 0.073
Soccer 0.073

While we play a song of the rhythm game, we should adjust the finger for the next hit in all time. Therefore,
this study considers that every time we touch the button or prepare for the next hit as the decision progress. The
gameplay depends on the song, one song finished, and the player is achieving an exact condition that means a
clear stage. A player should concern the hit time for every button. Hence, according to the rule, the parameter
in rhythm game progress can be given by possible options of each step, and game length is given by the
average touch time of one game. Therefore, the measure of GR is calculated as Equation (4).

√ ℎ ∗ ℎ ℎ ℎ ℎ
= (4)
ℎ ℎ

This study focuses on six popular rhythm games (Table 2). The rule of the game is similar. When you play
a song, music bricks fall towards each of the judging areas on the screen in time with the song's rhythm. The
players should hit the point as they highlight each judging area. The condition of the button and clear condition
are different among each game.

E- Proceedings of The 5th International Multi-Conference on Artificial Intelligence Technology (MCAIT 2021) [219]
Artificial Intelligence in the 4th Industrial Revolution