Page 225 - The-5th-MCAIT2021-eProceeding

2. Game Refinement Theory, Variable Ratio Schedule, and Application in Animation

Quantifying entertainment impacts in games have been previously conducted through the game refinement
(GR) theory (Iida et al. 2004). According to the GR theory, it is assumed that every game's progress was encoded
and transported in the minds. Although the behavior of the physics of information in the brain is unknown, the
acceleration of information progress is likely subject to physics’ forces and laws. The GR theory has been
applied to many different games for quantifying their entertainment impacts (Iida and Khalid, 2020). From a
player’s perspective, the game outcome is a function of time (i.e., number of possible moves or successful
score) and the game process as solving game outcome uncertainty ′( ), 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.
Equation (1) 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 games, the game's total length is significantly different for players with different levels. Assuming
that the solved information ( ) is twice derivable at ∈ [0, ], then the second derivative of (2) indicates
the accelerated velocity of the solved uncertainty along with the game progress. It has been found that
sophisticated games have a similar GR value located at the zone of ∈ [0.07, 0.08]. It is expected that
such sophistication also existed in the domain of animation.
It is essential to convey enough information to the viewer to catch people’s attention before losing interest.
Moreover, the later episodes’ development and pace depend on effective information delivery speed; too fast
or too slow can lead to many problems. After a continuous climactic or depressing plot, the plot’s transition
should give the viewer some time to rest and adjust. Continuous high emotion or depression will also make the
viewer feel tired and less receptive to the information.
Engaging and attractive episodes were loved and discussed by everyone in terms of content and graphics
quality. When an attractive episode was perceived, the “bullet curtain” was sent by viewers to entice interactions
with other viewers. Alternatively, viewers can also leave comments to express their feelings or donate coins to
show their support. With different climax, trough, and transition, the plot development curve can be qualified
as an elegant plot or storyline. Hence, GR's measure in animation can be roughly formulated as (3).
√ √
= = (3)

Adopting the principles of the VR schedules, the parameter N shows the average reward frequency, where 1
< N∈ R. The animation initially consisted of moments that attract viewers (i.e., settings, atmosphere,
placements, to name a few) associated with high-energy and appealing after the plot's development and buildup
(Xiaohan, et al., 2020). In this study, these moments were thought of as the rewards that viewers receive during
the viewing process. Based on the above principles, given N equals the number of episodes, then the velocity V
is formulated as (4). Such velocity measure is utilized as the total perceived entertainment of the viewers for
each animation which can be roughly associated with the average “reward” felt by the viewers.
1
= (4)

3. Data Collection and Analysis

In this paper, the data of their “bullet curtain,” comments, and coins of each episode of 14 popular animations
on the Bilibili website were collected, where the fourth column of Table 1 gave its combined average for each
episode. By adopting a boxplot, the attractive episodes can be determined by finding the episode that exceeded
the third quartiles value of the combined average episode data (Figure 1). Then, GR and velocity measures was
adopted to analyze further each animation’s sophistication and entertainment aspects.

E- Proceedings of The 5th International Multi-Conference on Artificial Intelligence Technology (MCAIT 2021) [210]
Artificial Intelligence in the 4th Industrial Revolution