1 | International Journal of Informatics Information System and Computer Engineering 1 (2020) 47-78 

 

 

 

 

 

A Paradigm Shift from Optimal Play to Mental Comfort: 

A Perspective from the Game Refinement Theory 

Hiroyuki Iida, Mohd Nor Akmal Khalid 

Japan Advanced Institute of Science and Technology, 1 Chome-1 Asahidai, Nomi,  

Ishikawa 923-1211, Jepang 

Correspondence: E-mail: iida@jaist.ac.jp 

A B S T R A C T S  A R T I C L E   I N F O 

The game refinement theory focuses on the game 
designer perspective, where its application in various 
types of games provides evidence of the occurring 
paradigm shift. Utilizing the logistical model of game 
outcome uncertainty, it provides a platform for 
incorporating gamified experience observed in games 
to be adopted in domains outside of game while 
retaining the context of the game. Making games as a 
testbed, the implications of the game refinement theory 
have been observed in the educational and business 
perspective, while further explored its utility in 
interpreting some states of the human mind. In 
addition, a holistic view of design in games and in the 
real-world environments was discussed, where the 
prospects of the game refinement theory were also 
highlighted. 
 

 Article History: 
Received 11 Nov 2020 
Revised 20 Nov 2020 
Accepted 25 Nov 2020 
Available online 26 Dec 2020 
ble online 09 Sep 2018 

___________________
 Keywords:

 Index Terms—Game refinement 
theory, 

 gamification, 

 edutainment, 

 momentum-in-mind, 

 comfort-in-mind, 

 serious game.

 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

International Journal of Informatics,  
Information System and Computer  

Engineering  
 

International Journal of Informatics Information System and Computer Engineering 1 (2020) 47-78 

 



H Iida and M N A Khalid A Paradigm Shift from Optimal...| 48 

 

1. INTRODUCTION 

Originated from the idea of the 
existence of mixed strategy equilibria in 
two-person zero-sum games (Neumann, J. 
V., 1928), game theory (GT) had been 
widely utilized as a useful tool in many 
fields such as economics, political 
science, psychology, logic and biology. 
However, the GT focuses on the 
perspective of the player’s side. Looking 
from the perspective of the designer’s 
side, the game refinement theory (GR) is 
a unique theory derived from the 
classical game theory. The GR is defined 
as the measure of attractiveness and the 
sophistication of games based on the 
game outcome uncertainty (Panumate et 
al., 2015). 

Previous works such as (Diah, et al., 
2014), (Xiong, S et al., 2014), (Xiong, S., and 
Iida, H, 2014), (Panumate et al, 2015), 
focused on various spectrum of games 
such as sports, board games and video 
games. It shows that the game 
refinement values of those popular 
games support the previous assumptions 
of a balanced range of game refinement 
value which is GR ∈ [0.07,0.08] (Xiong, S 
et al., 2014). While many research works 
have been done using GR that focuses on 
game entertainment of many game-
related domains, there had been limited 
applications to the real-world settings. 

The goal of this paper is to highlight the 
current change of paradigm in game 
design from the lens of the GR 
framework, where the shift of focus from 
making an optimal play to providing 
mental comfort has been observed from 
recent works. The organization of the 
paper is as follows. The game refinement 
theory is described in details from the 
perspective of continuous game (such as 
sport games), discrete game (turn-based 

and board games), and mixture of both 
perspectives (Section II). Then, its 
application in the context of education 
and business are investigated where GR 
theory is applied in relation to current 
concept of edutainment and gamification 
in the real-world settings (Section III). 
Next, in-depth interpretation of the GR 
theory with respect to the perceived 
nature of human mind, specifically on 
understanding the sense of curiosity and 
boredom, is investigated (Section IV). In 
addition, general discussion on the 
overall perspective of the GR theory is 
given in Section V while Section VI 
concludes the paper. 

2.   GAME REFINEMENT THEORY 

A personal decision process in mind 
typically involves considering all 
possibilities of available options which 
then are reduced to only a single 
decisive solution. This process 
commonly involves both the aspects of 
skill and chance. In a case of a board 
game, an experienced player may 
identify only a few decent moves out of 
all possible instances (Iida H., 2008).  
However, only one solution has to be 
decided as the final solution. This idea 
has been expanded to establish the 
mass-in-mind model, which being 
integrated into the game refinement 
model. Fig. 1 presents the generic 
selection process in a player’s mind. 

 
Fig. 1. The player decision selection 

process 
 

While all possible instances are 
relatively large, some of them are out of 
an experienced player’s consideration 



49 | International Journal of Informatics Information System and Computer Engineering 1 (2020) 47-78 

 

as they might lead to deficiency or 
failure. The effective branching factor b 
of a player is a subset of the branching 
factor, in which only acceptable 
solutions are concerned. Effective 
branching factor of a player is the 
number of instances, which are 
satisfyingly perceived by that player in 
a single decision. Reduction rate of 
branching factor (say α) for the 
minimax-based game tree where B and 
b (1 ≤ b ≤ B) is the average branching 
factor and the effective branching 
factor, respectively. Thus, α is defined 
by (1). The effective branching factor b 
is significantly smaller than the 
branching factor B but not underneath 
1, so 1 ≤ b ≤ B. 

 (1) 

A. A Game Progress Model 

The general game refinement model 

was proposed based on the concept of 

game information progress, where the 

gap between boardgames and sports 

games was bridged (Sutiono et al., 2014, 

Iida, H., 2018). The “game progress” can 

be one of two things. One of it is the 

game speed or scoring rate. 

Meanwhile, another can be the game 

information progress which focuses on 

the game outcome. Game information 

progress presents the degree of 

certainty of the game’s results in time 

or in steps. Having the complete 

information on the game progression 

(i.e. after its conclusion), the game 

progress x(t) will be given as a linear 

function of time t with 0 ≤ t ≤ tk and 0 

≤ x(t) ≤ x(tk), as shown in (2). 

  (2) 

Here, tk and x(tk) corresponds to the 

end of task and the goal to achieve in 

task, respectively. (2) implies that goal 

of the task under consideration must 

be achieved within the time tk, 

meanwhile it may not be shorter time 

than tk (Iida H., 2018). Under the given 

time constraint (Fig. 2) that task should 

be completed within the time t with 0 

< t < tk where x(t) = x(tk). However, the 

game information progress given by 

(2) is unknown during the in-game 

period since t < tk. The presence of 

uncertainty during the task, often until 

the final moment of the task, would 

cause the task progress to be 

exponential. Hence, a more realistic 

model of information progress of a 

given task is given by (3). 

 

 

Fig. 2. An illustration of normal 
activity becomes gamified under a 

time constraint (adapted from (Iida 
H., 2018).) 

  (3) 

Here n ∈ IR stands for a parameter 
related to the degree of difficulty of 
completing the task. In the context of 
(3), lower n implies a very boring task 
while higher n would imply higher 
difficulty of completing the task. By 
deriving the task’s information 



H Iida and M N A Khalid A Paradigm Shift from Optimal...| 50 

 

progress, when n ≥ 1, the “velocity” in 
the sense of information dynamics can 
be obtained in (4). 

  (4) 

When n ≥ 2, the second derivative of 
the task’s information progress or 
“acceleration” in the sense of 
information dynamics, which 
obtainable by deriving (3) twice. Then, 
solving it at t = tk, (5) was obtained. 

 

The game information progress 
modelled in (5) was assumed to be the 
abstraction of the information in a 
human brain. As the physics of 
information in the brain is yet to be 
discovered, it is likely that the 
acceleration of information progress is 
subjected to the forces and laws of 
physics. Too little game information 
acceleration may be trivial for human 
observers and players to compute. In 
contrast, too much game information 
acceleration would cause frustration, 
overwhelming and even 
incomprehensible to humans.  

Representing x(tk) and tk as G and T 
respectively, the GR formulation in its 
root square is given in (6). Therefore, 
increases in the value GR is expected to 
increase the excitement of the game, 
due in part to the uncertainty of game 
outcome. Application of the GR 
measure in popular sports is given in 
Table 1. 

  (6) 
 

 

 

Table 1. The gr measure for popular 

sport games (Takeuchi J., 2014, 

Ramadhan et al.,2015, Panumate, et 

al., 2017). 
Games 𝑥(𝑡𝑘) 𝑡𝑘 𝐺𝑅 

Basketball 36.38 82.01 0.073 
Soccer 2.64 22.00 0.073 

Volleyball 

(side-out: 

15pts) 

15 52.52 0.121 

Volleyball 

(rally point: 

30pts) 

30 53 0.104 

Volleyball 

(rally point: 

25pts) 

25 44 0.114 

Table tennis 

(pre-2000) 
57.87 101.53 0.075 

Table tennis 

(post-2000) 
54.86 96.47 0.077 

Badminton 

(side-out) 
30.07 45.15 0.121 

Badminton 

(current) 
46.34 79.34 0.086 

Baseball 

(major 

league) 

4.57 34.23 0.062 

 

B. A Board Game Model 

For a board game, the definition of 

branching factor is the amount of all 

possible instances in a single decision 

while the game length is the number of 

steps from the beginning to the ending 

or the resignation. A game tree is 

constructed by recursively attaching 

all possible transitions to the initial 

position (Xiong, S et al., 2014) Let B and 

D be the average branching factor and 

the average game length respectively. 

A single decision can be illustrated in 

Fig. 3. By considering the geometry, 

the distance d is obtained by  

according to the Pythagorean theorem 

(Maor E., 2019). 

However, one is much smaller than 

B and left from the consideration. 



51 | International Journal of Informatics Information System and Computer Engineering 1 (2020) 47-78 

 

Hence, the distance d becomes . 

Assuming the outcome continuously 

becomes evident, the model of game 

progress x(t) is determined by the 

proportion of the d and the game 

length D. Therefore, the model of game 

progress becomes . In 

general, (7) was obtained. 

 

Fig. 3. A Generic Single Decision in a 
Game Tree 

The value of c and n(n − 1) in (5) had 

been discussed in previous works 

(Xiong et al., 2017) Following the game 

progress model, the uncertainty of the 

outcome renders the x(t) exponential. 

Therefore, the more realistic model of 

game information progress becomes 

(8).  

Then, similarly in obtaining the 

game refinement measure GR of the 

game progress model, the GR of the 

board game model is obtained by 

deriving (8) twice and taking its root 

square form, as shown in (9). 

Application of the GR measure in 

popular board games and other 

multiplayer games is given in Table 2. 

If the same model were also extended 

to the domain of the video games, then 

the B and D corresponds to the average 

number of successful attempts and 

average number of attempts per game, 

respectively. As such, the GR measure 

of some popular video games is also 

provided (Table 3). 

 (8) 

 (9) 

Table 2. The gr measure for popular 

board and other multiplayer games 

(Iida et al., 2004, Xiong et al., 2014, 

Panumate et al., 2016, Panumate et al., 

2017) 

Games x(tk) or B tk or D GR 

UNO 0.976 12.684 0.078 

RoShamBo 3 1.5 1.155 

UFO catcher 0.967 13.30 0.074 

Western Chess 35 80 0.074 

Chinese Chess 

(Xiangqi) 

38 95 0.065 

Japanese Chess 

(Shogi) 

80 115 0.078 

Go 250 208 0.076 

Mah Jong 10.10 39.56 0.078 

 

Table 3. The gr measure for popular 

video games (Xiong et al., 2014, 

Panumate et al., 2016, (Punyawee et al, 

2016, Xiong et al., 2017) 

Games x(tk) or B tk or D GR 

DoTA v6.48 69.2 110.8 0.075 

DoTA v6.64 68.4 110.4 0.075 

DoTA v6.80 68.6 106.2 0.078 

Snake AI 

(Wall) 

4.44 34.98 0.060 

Snake AI (No 

wall) 

2.18 17.03 0.087 

Starcraft 2 

(Terran) 

1.64 16 0.081 

Starcraft 2 

(Protoss) 

1.55 18 0.069 

Starcraft 2 

(Zerg) 

1.61 20 0.082 

King of 

Fighters 98 

14.6 36.7 0.104 



H Iida and M N A Khalid A Paradigm Shift from Optimal...| 52 

 

C. A Swing Model 

The game progress model supports only 

a game with uniformed scoring rate, 

e.g., Soccer. In Soccer, a successful shoot 

is particularly challenging to obtain and 

regarded as one score. Supposing that 

the gained score is multiplied, the 

measure of game progress model may 

alter, but the real essence of the game 

remains unchanged (Kananat et al., 

2016). However, SCRABBLE players 

earn several marks in turn. This incident 

happens in a case of the games with the 

non-uniformed scoring system. 

Therefore, SCRABBLE has non-

uniformed scoring rate and not directly 

compatible with the game progress 

model. 

Instead, the swing model is 

introduced by defining swing turnover 

as a state transition in mind during the 

game progress among some possible 

states. In a game with non-uniformed 

scoring rate, the average amount of 

swing turnover S is proposed as a 

measure for counting the actual 

successful shoot. Although the 

transition among possible states may 

differ for a different domain, we 

consider two cases: advantage and 

disadvantage. It is rumored that 

maximizing own profit while 

minimizing others have been the general 

principle of the intelligent decision 

maker (Harsanyi et al., 1988). Obtaining 

the highest score is the goal of playing 

SCRABBLE. 

In each step, players are taking their 

turn to attempt to have the advantage 

over the opponent, which is considered 

as the actual successful shoot G, if 

successful. Let D0 be the average turn 

that player potentially turns the swing. 

Due to difficulty in measuring D0, the 

game length D is used as its 

approximation. The game refinement 

GR of the swing model is obtained by 

(10). 

  (10) 

Swing model is an approximation of 

game progress model as an exciting 

game when there is a proper amount of 

swing turnover as opposed to a single-

sided game (Kananat et al., 2016). The 

game refinement measure reflects the 

balance between player’s strength and 

surrounding randomness in a game 

considered (Xiong et al., 2017) While a 

superior value implies that a chance 

becomes a stronger factor, a game with 

an extreme game refinement measure 

might overwhelm a player with the 

information, which results in 

frustration. As such, the GR measure 

based on (10) for SCRABBLE based on 

20,000 match records from cross-

table.com is provided (Table 4). 

Table 4. Game Refinement Value of 

Scrabble Game 

Average number of swing 

turnovers (S) 

5.096 

Average number of total 

rounds (D) 

27.145 

Total match record data 23,164 

Game refinement value 

(GR) 

0.083 

 

3. GAME REFINEMENT THEORY 

MEETS THE REAL-WORLD 

In a real-world setting, design of 

game elements is highly dependent on 

the context of interest. Incorporating 



53 | International Journal of Informatics Information System and Computer Engineering 1 (2020) 47-78 

 

game elements in education leads to an 

innovative teaching-learning 

methodology known as “edutainment”, 

which involves the mixture of 

entertainment and education or 

marriage of education with 

entertainment (Aksakal N., 2015, Agarwal 
S et al., 2019).  

Such methodology may be inclusive 

of different levels of interactions, 

motivations, experiences, and mental 

acceptance in the educational process 

through elements perceived to be 

entertaining, commonly found in 

games. The players of such games 

benefited from collaborating among 

themselves both inside the amusement 

condition (e.g. through networking on 

the web-based groups) and around it 

(e.g. through sharing game-related data 

and assets) (Agarwal S et al., 2019). 

In a broader sense, adopting game 

design elements in nongame contexts is 

a popular concept known as 

“gamification”. The concept of 

“gamification” was first launched in 

2008 in a blog post by Brett Terrill 

(Terrill, B. 2008). He described 

gamification as taking the game 

mechanics and applying them to other 

web properties to increase engagement 

(Huotari, K., and Hamari, J., 2012), which 

becomes a widespread industry use 

(Deterding, S et al., 2011). Gamification 

can be defined as adopting game design 

elements in non-game contexts, without 

changing the existing practice of that 

context, in order to improve user 

experiences in term of engagement and 

learning, employee recruitment and 

evaluation, ease of use and encourage 

physical exercise (Huotari, K., and 

Hamari, J., 2012, Huynh, D et al., 2016). 

Gamification also enhances the player’s 

ability to understand a specific domain 

of studies such as language learning or 

music. 

Although there can be many 

methods to edutainment and 

gamification, the GR theory provides an 

alternative method to both concepts 

from the educational and business 

standpoint. Note that the GR theory is 

adopted with only minor changes on 

defining the context of the “game 

progress” with respect to the 

application domain. The GR value still 

retains its original intention, which is 

the measures of attractive and 

sophistication in game design. 

A. Educational perspective 

Application of the GR measure with 

respect to educational perspective had 

seen some potentials, which 

demonstrated in two type of 

edutainment games: MindSnacks and 

Duolingo3. These games were selected 

due to several reasons. Firstly, both of 

the games were language learning 

platforms. Secondly, they shared 

similarity in term of the milestone 

technique used as part of the game 

elements in the learning process. 

Thirdly, both of them adopted learning 

methods that measurable in number 

(lessons or tasks). 

MindSnacks are specialized games 

for individual languages including 

Chinese, Japanese and several 

European languages. It spreads 

learning lessons such as vocabulary, 

spelling, and grammar across nine 

different mini-games with their own 



H Iida and M N A Khalid A Paradigm Shift from Optimal...| 54 

 

hand-drawn art. A user is first given 

three available minigames to start while 

the rest is unlocked when the user 

reaches a certain number of levels for 

each. By adopting the milestone 

technique used by game designer, there 

is a certain number of levels that require 

completion (by performing several 

tasks) before unlocking the mini-game 

in a particular milestone (Izzyann, F et al., 

2018). 

Therefore, Lv and T is the average 

number of levels required to unlock the 

mini-games and the average number of 

tasks, respectively. To calculate the GR 

value, with reference to (6), let G and T 

equals to Lv and T, respectively, which 

corresponds to the progress model for 

MindSnacks. 

Meanwhile, Duolingo is a publicly 

available gamified free language-

learning platform since 2012 which is 

created by professor Luis Von Ahn and 

his graduate student Severin Hacker. As 

of April 2016, it offers 59 different 

language courses across 23 languages. 

Duolingo is a product of gamification, 

where game elements are utilized to 

create enjoyment in the learning 

process. In a language course, the goal is 

to complete a study by getting all 

badges in the skill-tree. To achieve a 

badge, users must complete all lessons 

in a skill. As such, the game progress of 

Duolingo language course can be 

measured by skills. Let S and L be the 

average number of skills and the 

average number of lessons in the same 

language courses, respectively. 

Therefore, with reference to (6), the S 

and L in Duolingo are equal to the G and 

T, respectively, in order to calculate its 

GR value. 

A comparison between MindSnacks 

and Duolingo on Japanese language 

course using the GR measures is given 

in Table V. Referring to the previous 

work, the Spanish language course of 

Duolingo falls onto the range of GR ∈ 

[0.020,0.026] which is reasonable for the 

serious-like game environment (Huynh, 

D et al., 2016). Similar tendency occurred 

in both platforms for the Japanese 

language course where the GR value for 

each milestone decreases gradually. 

Also, there is a big gap between GR-

value at the first milestone of both 

platforms due to the big difference of 

the average number of tasks or lessons 

needed to complete it. This difference in 

value indicates that Duolingo is much 

more attractive to beginner learner 

while MindSnacks requires learner with 

strong motivation since it’s much 

difficult to beginner. 

Table 5. Game Refinement Measures 

of Mindsnacks and Duolingo on the 

Japanese Language Course 

 

Milestone Lv T GR Milestone S L GR 

Totems 3 5 0.35 1 7 34 0.08 

Blooms 6 17 0.14 2 15 66 0.06 

Stacks 10 37 0.09 3 27 130 0.04 

Bubbler 15 85 0.05 4 40 185 0.03 

Dam 

Builder 

21 141 0.03 - - - - 

Lv: average number of levels required 

to unlock the mini-games; S: average 

number of skills; T/L: average number 

of tasks/lessons; 

The GR value for both MindSnacks 

and Duolingo started to decline in the 

  



55 | International Journal of Informatics Information System and Computer Engineering 1 (2020) 47-78 

 

subsequent milestones as the learner 

progresses, where both resulted in the 

same GR value of 0.03 at the fifth and 

fourth milestone, respectively. 

Additionally, MindSnacks has one extra 

milestone compared to Duolingo, 

making MindSnacks much more 

appealing towards serious but casual 

learners. In contrast, Duolingo may 

appeal to additional game elements 

(such as winning streaks (Huynh, D., 

and Iida, H., 2017) to retain learner’s 

motivation since only small sense of 

achievement can be elicited (from the 

small changes of the GR value between 

milestones). As such, a longer milestone 

may effect users’ feeling of achievement. 

Finally, observing the accumulated 

tasks or lessons at the end of each 

milestone, MindSnacks had a lower T 

value compared to L value of Duolingo. 

This means the enjoyment and 

motivation of finishing the tasks or 

lessons inversely proportional to its 

number. 

B. Business Perspective 

Gamification employs game design 

elements which are used in non-game 

contexts to actively improve the user’s 

engagement by applying game-based 

thinking through badges, rewards 

programs and points (Zuo, L., and Iida, 

H., 2017). There are three main 

ingredients (but not limited to) that offer 

gamification in various real-world 

application; game element, game 

design, and non-game context. 

Game elements involves building 

some form of service which utilized 

usage of bits and pieces of games (i.e. 

interactive graphical user interface) to 

improve the user experience. 

Meanwhile, game design is the inclusion 

of game playing feeling through game 

elements such as the points and tiers 

system which organized systematically 

and encourage enjoyment in such 

activity. Finally, non-game context can 

be translated to anything other than the 

game in which the objective is outside of 

the game; thus, related to their needs or 

business. With respect to the GR theory 

application and gamification in the 

business perspective, two types of 

business strategies were analyzed from 

the customer’s point-of-view; sales 

promotion and loyalty programs. 

1) “Discount” Sales Promotion: The 

money saved by the sales promotion 

‘discount’ is considered beneficial to the 

customers. This is because customers 

have little knowledge and interest about 

the cost of a product of interest (Zuo, L., 

and Iida, H., 2017). However, they 

would care more about the price of the 

product (i.e., how much money can be 

saved by the discounting). If the rate of 

discount is reasonable from the 

perspective of customers, the “game of 

discount” would have a comfortable 

zone value of game refinement, similar 

like the sophistication of the 

boardgames and sports.  

As such, the money saved by the 

sales promotion ‘discount’ is considered 

as the benefit for customers where the 

total benefit of the customer’s shopping 

activity in a certain time is measurable. 

Based on such information, the game 

progress model can be constructed by 

two factors: the total benefit of a certain 

product (G) and the total normal price 

without discount (T). Important note is 

that discount in the sales promotion 



H Iida and M N A Khalid A Paradigm Shift from Optimal...| 56 

 

typically expressed as percentage. To 

normalize the model in (6), we assume 

that the benefit of a product is ranged 

from 0 to 100 and the normal price is 100. 

Then, the model in (6) is extended to (11) 

that gets the GRc of different extent of 

discount for customers where d stands 

for the discount coefficient (i.e. 10% 

discount equals to 0.9 discount 

coefficient) (Zuo, L., and Iida, H., 2017). 

     (11) 

It is important to identify a 

reasonable discount zone for customers. 

It is expected that lower GR would be 

less attractive for customers, whereas 

higher GR would be of some concern 

about quality and hard for the 

sustainability of seller. Two data sets 

were collected for the analysis. The first 

data set is intended to optimize the 

seller’s total profit within a time frame 

using computer simulation in order to 

maximize total sales volume from the 

seller’s standpoint. The second data set 

is collected from bestsellers (Bento Boxes 

& Water Bottles4) of a popular on-line 

retailers (Amazon JP5) which 

corresponds to the customer’s 

standpoint. Then, both data set was set 

with a fictitious market demand of 

10,000 products within a year. The total 

amount sale is determined by two 

factors: quantity and price. The discount 

coefficient will be changed every week 

and range from 0 to 1.  

The demand of product follows the 

Fdistribution and the customers follow 

the Poisson distribution. Tables VI 

showed the discount rate by simulation 

and real data of Amazon JP where The 

discount rate of simulation is ranged 

from 21% off to 39% off, whereas the top 

sales product of Amazon JP is ranged 

from 42% off to 59% off. Note that the 

GRc results of simulation is best for the 

seller but considers little about 

customers. However, GRc of Amazon JP 

is ranged from 0.065 to 0.077, which is 

located in the zone value (GR ∈ 

[0.07,0.08]). Thus, under the assumption 

that the sales promotion ‘discount’ is a 

fascinating game, the simulation 

concerns about sustainability and 

Amazon JP concerns about popularity of 

the game. 

Table 6. Discount Rate and Measures of 

Game Refinement (Grc) For Simulation, 

Amazon Jp, and Recommend 

 Discount rate 

(%) 

GRc 

Simulation 42 - 59 0.065 – 0.077 

Amazon JP 21 - 39 0.046 – 0.062 

Recommended 49 - 64 0.07 – 0.08 

 

The attractiveness of games often 

comes within the approximate zone 

values (GR ∈ [0.07,0.08]) where its 

corresponding discount zone is ranged 

from 49% to 64% off (Tables 6). The 

essence of game refinement theory is to 

find a comfortable acceleration (the 

sense of thrill) for game players (or 

customers). Hence, the discount rate 

should not be too high. For example, too 

high GRc may also cause some concern 

such as quality of a product of interest.  

This is why some shopping 

festivals, like “Black Friday” in America 

and “1111 Shopping Festival” in China, 

set their discount rate 50% off since this 

discount rate falls on the comfortable 



57 | International Journal of Informatics Information System and Computer Engineering 1 (2020) 47-78 

 

zone. Higher GRc means higher 

entertainment impact and more popular 

which would be able to motivate 

customers to buy more. The essential 

idea is to offer an appropriate discount 

zone based on the previous knowledge 

of the GR theory where benefits of game 

thinking (such as discounting) can be 

adopted in the business domain. 

2) Customer Loyalty Program: In today 

highly competitive marketplace, 

customer retention is an important 

factor for the success of businesses 

because the cost of finding a new 

customer is about 5 to 10 times more 

than to keep the existing one. Customer 

retention is defined as the activities and 

actions of companies and organizations 

to reduce the number of customer 

defections (Xin, O et al., 2017). Loyal 

customers tend to spend more (67% 

more than new customers) and often 

know exactly what they want when 

purchasing from a certain brand. 

Unfortunately, companies tend to lose 

around 13% of their customers every 5 

years (Kumar, K., 2016). 

Therefore, loyalty of a customer is 

critical to the sustainability of a business. 

Generally, loyalty program refers to a 

reward program offered by a business to 

customers who frequently make 

purchases (Xin, O et al., 2017). Loyalty 

program typically requires customers to 

register with their information and 

customers will be given a unique 

membership ID or physical membership 

card to be used when making purchases. 

The business owner can track behavior 

and history of their customer purchase 

in order to recognize the loyal customers 

and hence reward them. Meanwhile, 

customer engagement is further 

improved when the feeling of 

appreciation by the company is 

established with the customer. As such, 

three case studies of the customer 

loyalty program are analyzed using the 

GR theory; Starbucks loyalty program, 

hotel loyalty program, and frequent 

flyer program (FFP). 

Starbucks is a fast growing coffee 

shop business with 7% annual growth 

rate (Xin, O et al., 2018). According to 

statistic in 2016, there is increase of 26% 

in profit and 11% total revenue when 

Starbucks introduced the “My Starbucks 

Rewards” program (Fisher, E., 2016). 

“My Starbucks Rewards” is a free 

loyalty program that gives exclusive 

member offers and allow customers to 

earn rewards (such as free drinks, foods 

and refills). Customers simply need to 

pay for any Starbucks product with a 

registered Starbucks card to earn a 

reward. Each time a purchase is made, 

customer will earn a specific amount of 

stars that can be redeemed for free 

Starbucks treat. The terms and 

conditions of “My Starbucks Rewards” 

varies according to different countries. 

As of 2016, the number of Starbucks 

licensed stores globally is ranked by 

Unites States (US) as the first with 5,292 

stores and followed by China with a 

total of 1,110 stores (Xin, O et al., 2017). 

In order to calculate the GR value based 

on (6), the number of free items 

redeemed and total number of items 

consumed is represented by G and T, 

respectively. The evolution of “My 

Starbucks Rewards” since 2009, 

Starbucks US had continuously made 

minor changes on the rules in redeeming 

free items (assuming the average price 



H Iida and M N A Khalid A Paradigm Shift from Optimal...| 58 

 

of a cup of Starbucks coffee which is $4 

and RMB27 in US and China, 

respectively). Hence, the GR value of 

different versions of “My Starbucks 

Rewards” from the perspective of point 

system in Gold Level is analyzed (Table 

VII). 

Table 7. Differences of “My Starbucks 

Rewards” In Us and China and Gr 

Values of Starbucks Loyalty Program 

(Point System) In Earning a Free Item 

in Gold Level Based On Versions 

Country US  China 

Levels 2  3 

Req. to reach/stay (Gold 

level) 

38  47 

Req. to get 1 free item 

(Gold level) 

16  10 

Year Version G T GR 

2009 Visit-based 1 15 0.067 

2012 Visit-based 1 12 0.083 

2016 Spend-based 1 16 0.063 

Req.: Purchase requirement in number of 

cups per customer 

From 2009 to 2012, changes in “My 

Starbucks Rewards” rules increased the 

GR value. This means that customers in 

Gold Level are required to spend less for 

a free item redemption. On the other 

hand, comparing the visit-based in 2012 

with the spending-based in 2016 of "My 

Starbucks Rewards", the GR values 

decreased from 0.083 to 0.063. This 

result may be explained by the fact that 

Starbucks requires its customers to 

spend more in order to get a free item. 

Before introducing the spending-based 

reward, customer can spend less than $4 

(the average price of a cup of Starbucks 

 
1 All company names, loyalty rewards names, trademarks, and 

pictures are properties of their respective owners. 

coffee in 12 transactions) to earn a free 

item. Since Starbucks values its loyal 

and high-spending customer, the 

reward rules change so that star is 

earned based on amount of spending. 

These changes are less entertaining and 

more challenging for the customers 

whom spend minimum amount to earn 

stars or free items. In addition, it was 

found that the requirement for a 

customer to reach or stay in Gold Level 

in US is lower than in China. However, 

the requirement for a customer to get 

one free item in Gold Level is higher in 

US as compared to China. 

Another customer loyalty program, 

called the hotel loyalty program, 

involves enticing frequent hotel guests 

or other business travelers to favor that 

particular brand or group of hotels over 

others when selecting a hotel (Zuo, L et 

al., 2018). The world’s largest hotel 

chains, including Marriott, Starwood, 

Hyatt, Hilton, IHG (InterContinental) 

and others, all operate reward 

programs1. Hotel loyalty program 

usually adopted tiers system (up to four 

tiers) and point system (point 

accumulation). A newly joined 

customer has several benefits, such as 

the complimentary inroom internet 

access and the guarantee of the lowest 

rate to encourage retention in the loyalty 

program. Joining the scheme and 

staying nights in a hotel will typically 

accumulate points where it can be 

redeemed for free nights in hotels (Zuo, 

L et al., 2018). 

Higher levels in the scheme will 

generally offer a combination of benefits 



59 | International Journal of Informatics Information System and Computer Engineering 1 (2020) 47-78 

 

(i.e. complimentary room upgrades, 

bonus points and hotel’s amenities such 

as conference room, lounge and other 

privileges). An elite status is typically 

reached by staying a certain number of 

nights say 60 or more during the 

membership year. The two mechanics 

(tiers and points) seem to be irrelevant, 

however, when looking back to the 

whole structure of the hotel loyalty 

program since it was found that the two 

mechanics are correlated with each 

other. The elite member could 

accumulate their points much faster 

with the additional points policy which 

also means that they could get more free 

nights (Zuo, L et al., 2017). 

To calculate the GR value for hotel 

loyalty program of a tier system, the 

number of successful qualifying nights 

corresponds to the G and the total 

number of days within a year (365 days) 

corresponds to the T, where the result is 

given in Table 8. Basically, each hotel has 

almost the same strategy of membership 

management and tiers. However, 

Marriott hotel has a higher requirement 

for the silver status. It means that 

Marriott requires customers to spend 

more on its loyalty program. By 

observing the GR values, we may 

conclude that the GR value between 

0.000 (become a member) to 0.027 

(Platinum level) would be the activity 

zone for the hotel loyalty program. This 

means that a customer can enjoy much 

more only when they becomes the elite 

status membership. Thus, the hotel 

loyalty program may be recognized as a 

kind of skill-based games. 

 

Table 8. Gr Measures for Hotel 

Loyalty Program with Focus on 

Qualifying Nights: Five Hotel Groups 

Compared 

Hotel 

Groups 

GR 

Silver Gold Platinum 

IHG 0.009 0.017 0.024 

Hilton 0.009 0.017 0.021 

Starwood 0.009 0.019 0.027 

Marriott 0.014 0.019 0.024 

Hyatt 0.009 0.015 0.021 

 

Meanwhile, the points for 

redeeming free nights dramatically 

differ from the location and brands, 

which highlights the consideration of 

hotel location when applying the GR 

measure to different cities. Thus, three 

big cities were chosen: Shanghai, Tokyo, 

and Paris. In addition, as the GR 

measure requires the highest level 

(skillful player) to make the result more 

objective, the most senior membership 

was taken as the sample to calculate the 

GR value. As such, each member would 

be playing the same game. As such, the 

number of redeemable free nights (G) 

and the number of successful qualifying 

nights (T) is considered for the point 

system (Table IX). The results showed 

that the average price and redeem points 

differ based on location. However, IHG 

and Hilton have the same GR values 

regardless of the location which implies 

that these two hotel groups have the 

same strategy when dealing with the 

free nights. The GR value of Starwood 

and Hyatt slightly vary with the 

location. On the other hand, the result of 

Marriott greatly differs in location. Also, 

both Starwood and Marriott provide a 

higher game element for Shanghai 



H Iida and M N A Khalid A Paradigm Shift from Optimal...| 60 

 

location; thus, showing that Marriott is 

dedicating its resources in China 

location by providing a more enjoyable 

experience in Shanghai. 

Another customer loyalty program, 

called the frequent-flyer program or 

FFP, is a loyalty program offered by 

airlines. From a historical perspective, 

FFP is considered to be the world’s 

largest gamified service (Zuo, L et al., 

2017). Many airlines have FFPs designed 

to encourage customers to accumulate 

points (also called miles or segments) 

that redeemable for air travel or other 

benefits travelers can receive from the 

program (Zuo, L et al., 2017). The FFP 

first started with the “Advantage” 

program which was characterized by a 

series of inventions that improved 

airlines’ revenue streams, increased 

customer recognition, reward customers 

for using the airline, and to promote 

future customer loyalty (De Boer, E. R., 

and Gudmundsson, S. V., 2012). 

Gamification of the FFP leverages the 

intrinsic human motivations of 

accumulating rewards or miles and 

build up the users’ motivation while 

ensuring the engagement is continuous 

(Zuo, L et al., 2017). It can be defined as 

a service quality attribute that consists of 

two systems: tiers system and points 

system. 

The tiers system is commonly 

represented by four levels: member, 

silver, gold and platinum. The tiers 

system is an application of progression 

levels or difficulty levels just as in video 

games. Depending on the airline’s 

regulations, different statuses enjoy 

different levels of rewards, additional 

points, priority check-in and lounge 

access. The membership requirement of 

tiers system of four Chinese FFPs is 

given in Table X. Meanwhile, the points 

system (or miles) is a type of virtual 

currency used predominantly within 

the game world (Zuo, L et al., 2018). As 

a new player, one is offered a 

“Qualifying Segment” by the system 

which allows them to get fast bonus-

point earnings; thus, instant 

gratification. Most, if not all, programs 

award bonus earnings to premium-

cabin passengers and their elitestatus 

members based on tier status. A 

common bonus for these passengers is 

to earn an extra 15%–55% of the miles 

flown on a given flight. Points can be 

redeemed for air travel, other goods or 

services, class upgrades and airport 

lounge access. For the tier system, the 

game progress model of a FFPs can be 

determined based on the action of 

qualifying segments of membership 

tiers, which defined by the number of 

successful qualifying segments G and 

the total number of segments within a 

year T (365 days). Here, we consider the 

normalized model that the customer can 

usually get one segment in one day 

(Table 11). For the point system, data is 

collected by considering the flight 

distance. As game refinement requires 

the highest level (corresponding to the 

skillful player) to make the result more 

objective, only the most senior 

membership was used as a sample. 

Since the higher status of the customers, 

the more miles/points they obtain. 

However, the points for redeeming free 

segments differ dramatically from the 

distance. There are three kinds of free 

segments considered: short, medium 

and long. Thus, the impact of a free 



61 | International Journal of Informatics Information System and Computer Engineering 1 (2020) 47-78 

 

segment for the highest membership of 

Fortune Wings Club and the distance 

within a year to illustrate game 

sophistication and game experience. 

The total points one can earn within a 

year with considering the 80 segments 

(XIY-PVG) of the domestic travels with 

the point bonus are about 170,000. Then, 

the data can be collected from the 

official website to check the points 

required for a free flight7, where the 

results is given in Table 12. From Table 

11, every airline company has almost 

the same strategy of membership 

management composed of four tiers, 

except Sky Pearl Club that excludes the 

platinum tier. Maintaining or 

promoting the tier corresponds to 

overcoming a challenge in a game. The 

trend of these four FFPs increases the 

GR value with the tier promotion, 

implying that the tiers system is offering 

a fun-game experience. This leads to a 

winwin scenario: customers improve 

their loyalty and companies increase 

their revenues (Zuo, L et al., 2018). One 

dimension is the tiers system involving 

the sustainability of the frequent 

customer, while another is the 

profitability of points system which 

indicates the popularity of the gamified 

service since profit may encourage more 

customers involvement. Meanwhile, 

Table 12 shows that the highest GR 

value is 0.045. It is important to note that 

the more free segments is redeemed, the 

less challenge is met. This implies that 

the points system offers a serious-game 

experience. The points system concerns 

about the benefit for customers who 

may feel serious-game experience (a 

good balance between customer’s 

capacity and challenge) but related to 

the popularity. The free ticket is so 

compelling as everyone.  

 

Table 9. Gr Measures for Hotel Loyalty Program in Shanghai/Tokyo/Paris with 

Focus on Free Nights: Five Hotel Groups Compared 

Hotel Groups Ave. Price ($) Ave. Redeem Points Free Nights GR 

IHG 75/208/148 18421//50000/34778 6/6/6 0.033/0.033/0.033 

Hilton 125/190/190 31400/55400/55000 3/3/3 0.029/0.029/0.029 

Starwood 115/247/335 6900/16000/19769 12/10/10 0.035/0.032/0.032 

Marriott 143/208/285 13026/36250/32800 15/7/10 0.052/0.035/0.042 

Hyatt 146/336/233 13285/20667/18000 4/6/51 0.033/0.040/0.037 

4. GAME REFINEMENT AND THE 
PERCEIVED NATURE OF MIND 
 

Game has existed since 2600 BC and 

has been the primary conditions of 

human culture and cultivated various 

complex activities of the human society 

such organization, languages, 

philosophies, war, and art (Huizinga J., 

2014). In the beginning, the game was 

just for relaxation after a busy work or 

making a simple decision. With the 

development of society, the game 

process becomes more complex and 

meaningful. 



H Iida and M N A Khalid A Paradigm Shift from Optimal...| 62 

 

Table 10. Tier Membership Levels Based on Four Frequent-Flyers Programs 

Membership Tier Miles/Segments Extra Bonus (%) 

Eastern Miles 

Silver 40,000/25 15 

Gold 80,000/40 30 

Platinum 160,000/90 50 

Phoenix Mile 

Silver 40,000/25 25 

Gold 80,000/40 30 

Platinum 160,000/90 50 

Fortune Wings Club 

Silver 30,000/20 25 

Gold 50,000/40 50 

Platinum 100,000/80 55 

Sky Pearl Club 

Silver 40,000/20 15 

Gold 80,000/40 30 
 

Table 11. Gr Measures for Tiers System from Four Ffps 

Membership 
Tier 

GR 

Eastren Miles Phoenix Miles Sky Pearl Club Fortune Wing Club 

Silver 0.014 0.014 0.012 0.012 

Gold 0.017 0.017 0.017 0.017 

Platinum 0.026 0.026 - 0.024 

 
desires to enjoy a flight without 

payment as well as highlevel services. 
Thus, these two gamified services 

organized systematically is to create a 
program to maintain customer loyalty. 

 
 

Table 12. Gr Measures for Points System in Fortune Wings Club 

Segment Point Free Qualifying GR 

 req. flights segment GR 

Short (XIY-PVG) 13 13 80 0.045 

Medium (XIY-NRT) 28 6 80 0.031 

Long (XIY-CDG) 45 3 80 0.022 

   req.: point requirement ×103 

 
 
 
 
 

 
 
 



63 | International Journal of Informatics Information System and Computer Engineering 1 (2020) 47-78 

 

Historically, harnessing the power 

of play had been attempted to serve the 

purpose which is beyond entertainment. 

Game designers are constantly working 

on stronger AI players to compete 

against human or other AI champions. 

Similarly, there are human society 

constantly searching for ways to 

effectively disseminate ideas, educators 

constantly seeking appealing learning 

process, and companies constantly 

seeking to engage their customers (Gino, 

F., 2018). The key factor to human 

conscience that triggers learning is 

curiosity, which observable from both 

entertainment and educational 

perspectives.  

Although a mechanical definition of 

curiosity is unknown, the perceived 

curiosity from the learning process is 

measurable from the development of 

edutainment game. In most cases, 

edutainment game design tends to favor 

either extremes (entertainment or 

education), but not both. Similarly, 

online learning games (such as the login 

system) that typically involved 

monotonous and repetitive action, tend 

to prioritize either the feeling of 

attractiveness (i.e. reward) or experience 

of engagement (i.e. loyalty program), 

but not both.  

Due to aforementioned situations, 

the perceived curiosity are modelled in 

two distinct form that corresponds to the 

player’s state of mind: (a) by the growth 

rate of learning; and (b) the diminishing 

rate of engagement. The former is 

named as the momentum-in-mind while 

the latter is named as comfort-in-mind. 

Note that, up to this point, the usage of 

GR value provides a very different 

interpretation to game design, which is 

highly dependent on the context of 

interest. 

A. Momentum-In-Mind 

Corresponding to the perceived 

“curiosity” of the player when playing a 

game, the momentum-in-mind is 

defined as the growth rate of mind of the 

player while moving from one level to 

another by acquiring a set of 

information from each level

 (Agarwal, S et al., 2019). In the context of 

edutainment, momentum is required to 

be maintained relatively with the time, 

because curiosity triggers increases the 

activity in the brain. This helps us 

identify the perfect combination of 

education and entertainment in games. 

As such, the proposed momentum-

inmind (p~) is formulated as (12). Here, 

the t is the time taken to acquire 

information to reach a higher level in the 

game. It can be measured as the 

difference in the levels or in the unit of 

time. 

  (12) 

Table 13 summarizes the 

mathematical model of game progress 

using momentum. If the time is reduced, 

momentum increases and vice versa. 

Thus, momentum is inversely 

proportional to time if the progress (h/l) 

is kept constant. In the context of the 

board game, the growth is not 

continuous and mostly redundant. As 

such, the momentum-in-mind is 

obtained by (13). B is the information of 

the game or game progress which the 

player learns actively while playing the 

game and t is the time for the player to 

acquire that information. 



H Iida and M N A Khalid A Paradigm Shift from Optimal...| 64 

 

Table 13. Momentum-in-mind 

Notation Game progress model 

h Game information at 

higher level 

l Game information at 

lower level 

t Time taken between 

the levels 

p~ = (ln h) · 1 l t Momentum (p~) 

acquired 

  

(13) 

1) Game play stages: It is supposed 
that most player in games proceed in the 
manner of two stages, called the ‘skill 
acquiring’ stage and ‘competitive’ stage. 
The skill acquiring stage is the stage 
when the player internalizes the skill 
required for the game (learning). As 
such, the competition is usually with 
oneself. At this stage, the goal is set 
against oneself and that goal becomes 
the ‘mental’ barrier (or ‘inertial’ level) 
that requires to gain enough 
momentum. As such, the momentum is 
expected to be low which implies high 
learning experience. Another stage is 
called the competitive stage where the 
player starts to compete with other 
players (and get better at it). Since 
competing with other player involved 
some level of skill and chance. The 
uncertainty would become higher 
which implies high sense of excitement 
and enjoyment. Most edutainment 
games lack this stage where very 
minimal competition existed. Therefore, 
the learning growth during this period 
is very low while the momentum is 
high. 

2) Application to competitive games: 

Several examples of sport games include 

Table tennis, Basketball, Soccer, 

Badminton, and so on, while example of 

board games are Go, Shogi, Chess, 

Baghchal, and so on. Based on the 

previous work by (Panumate, C et al., 

2017), the branching factor B and the 

game length D were taken where the GR 

value were calculated by using 

(6) and (9), while the momentum p~ 

were calculated by using (13), where D 

is considered as the length t for 

calculating the momentum for the 

aforementioned sports and board games 

(Table 14). Based on the calculated p~ 

and GR values, similar pattern was 

observed where increase in the GR also 

increases the p~, and vice versa. This 

aligns with current understanding of the 

game play stages where the considered 

games only reflected the competitive 

stage of an entertaining games where 

little learning had occurred. 

Table 14. Sports Games: Game 

Refinement and Momentum 

Game B D p~ GR 

Table tennis 

(post-2000) 

54.86 96.47 0.01802898 0.077 

Basketball 36.38 82.01 0.01903259 0.073 

Soccer 2.64 22 0.01916382 0.073 

Badminton 

(current) 

46.34 79.34 0.02099768 0.086 

Tic-tac-toe 9 9 0.10602695 0.333 

Western Chess 35 80 0.01930085 0.074 

Japanese Chess 

(Shogi) 

80 115 0.01654861 0.078 

Go 250 208 0.01152868 0.076 

Baghchal 242 26 0.09342471 0.075 

 

3) Application to edutainment games: 

Educational games are played for 

educational purposes where the 

intention of the game may be to acquire 

a new skill (such as a language in 



65 | International Journal of Informatics Information System and Computer Engineering 1 (2020) 47-78 

 

DUOLINGO and MEMRISE) or to check 

an already acquired skill (such as 

SCRABBLE)2. Players in the educational 

games grow actively throughout the 

game. As such, information at lower 

level and at higher level are taken as the 

game information. Although 

SCRABBLE is considered to be a board 

game, this study considered it as an 

educational games since its primary 

purpose is education. As such, the p~ 

value is obtained by (12) in the 

educational games. 

Three educational games were 

considered in this study. The first one is 

Duolingo, a language learning platform 

which has pre-structured course and 

‘Spanish for English Speakers course’ is 

considered in this study. Memrise is also 

language learning platform which does 

not have structured courses where the 

user can create the course according to 

their convenience but a pre-structured 

course is also available. Only the 

language learning perspective is 

considered for Memrise. where 

‘Japanese for English speakers’ is used 

for this study. Lastly, Scrabble is an 

educational game designed to test one’s 

skills where the English language 

version is considered. These games were 

chosen for their popularity and step by 

step progress method which assisted in 

the analysis of growth rate. 

In spite of the fact that Duolingo has 

utilized many game components in their 

stage, the badges and winning streak are 

explicitly examined because the critical 

piece of effective gamification is the 

substance and learning material itself 

(Boskic, N., and Hu, S., 2015). Also, the 

primary reason for players interested in 

Duolingo involves taking in a second 

language, while the badges and winning 

streak are utilized to lift up the player 

motivation. With respect to the work in 

(Huynh, D et al., 2016), the growth rate 

of learning and quantifying entertaining 

experience utilizes formulation (6). As 

such, the GR and p~ values for each 

milestone in the badge and winning 

streak systems are given in Table 15. 

According to previous studies (Huynh, 

D et al., 2016), (Huynh, D., & Iida, H., 

2017), the GR value implies the 

significant of the winning streak to 

users’ motivation compared to the 

badges. The momentum in both badge 

and winning streak scenarios decreases 

to eventually become almost equal after 

certain milestones. This implies that 

Duolingo is more of an educational but 

entertaining game as well as better for 

beginner level of learners but not very 

attractive to learners of advanced level. 

While winning streak element of 

Duolingo successfully maintains 

uncertainty, it does not solve the 

problem of falling curiosity. 

 

 

 
2 To maintain the fairness, all the three games are considered 

as language learning educational game. Since the comparison is 
not between skill acquisition and testing knowledge, it does not 
make the difference in the results. 
The games are tested on an individual basis and not categorical. 



H Iida and M N A Khalid A Paradigm Shift from Optimal...| 66 

 

Table 15. Duolingo Badge And Winning Streak: Game Refinement (Gr) And 

Momentum (P~) 

Milestone  Badge  Lk →
𝒑 

GR 

1 6 21 0.03706 0.1166 

2 16 67 0.01797 0.0597 

3 29 160 0.0914 0.0337 

4 61 317 0.00563 0.0246 

Milestone Winning Streak Lk →
𝒑 

GR 

1 2.2 21 0.01631 0.0047 

2 6.4 67 0.01203 0.0053 

3 21.9 160 0.00838 0.0127 

4 47.8 317 0.00530 0.0260 

        Lk : average number of lessons learned; 

In Memrise, users are required to 
accumulate experience point (XP) to 
cross a particular level. This mechanism 
works similar to the milestone 
technique in the Duolingo game. 
Similarly, the GR and the p~ are 
calculated where the XP refers to the 
required XP accumulation to reach a 
particular level. As evident from Table 
XVI, p~ value is building up while the 
GR value is rapidly declines. From such 
observation, even though the user’s 
learning growth is maintained for a 
period of time and increases in another, 
limited game element makes it difficult 
to keep the user entertained. In 
addition, in term of catching up with the 
course structure, it is better for the user 
when the learning growth gradually 
increases. Nevertheless, a sudden jump 
in p~ in Memrise implies that the 
learning growth suddenly become too 
large which become difficult to catch up 
(i.e. Level 8 to 9 and Level 14 to 15). This 
explains the reason for the declining GR 

value since acquiring XP point becomes 
a burden instead of enjoyment which 
make the game lose its attractiveness for 
the user (especially when trying to reach 
level 13). Thus, having diverse game 
elements during the game play may 
enhance the game progress and 
rejuvenate the curiosity of users.  

Finally, Scrabble may be considered 
as another board game but differ 
because of its scoring mechanism. As 
such, the scoring rate, the branching 
factor, and the game length can be 
observed. Since those information are 
fundamental for applying the game 
progress model, the GR value can be 
computed utilizing the board game 
model, as in (9). Then, the momentum 
(p~ value) are calculated by simulating 
selfplay of an open source game of 
Scrabble called Quackle Version 1.0.3. 
The data includes the average of 100 
game plays between various levels of AI 
players. Based on the results of obtained 
in Scrabble (Fig. 4), the momentum is 



67 | International Journal of Informatics Information System and Computer Engineering 1 (2020) 47-78 

 

highest when the dictionary size is the 
highest and the game length is the 
lowest.  

 

 

This actually aligned with the 
findings by (Kananat, S et al., 2016) 
where that study claimed that Scrabble 
is most enjoyable 

 

Table 16. Memrise Experience Point (Xp): Game Refinement (Gr) And Momentum 

(P~) 

Level X P Lw 
→
𝒑 

GR 

1 500 11 0.69314718 2,033 

2 1,000 22 0.69314718 1,437 

3 2,000 44 0.69314718 1,016 

4 4,000 88 0.69314718 0,719 

5 8,000 177 0.69314718 0,505 

6 16,000 355 0.69314718 0,356 

7 32.000 711 0.69314718 0,252 

8 64,000 1422 0.69314718 0,178 

9 128,000 2844 0,91629073 0,126 

10 320.000 7111 0,91629073 0,080 

11 800,000 17777 0,91629073 0,050 

12 2,000,000 44444 0,91629073 0,032 

13 5,000,000 111111 0,91629073 0,020 

14 12,500,000 277777 0,91629073 0,013 

15 31,250,000 694444 1,16315081 0,008 

XP : experience points; Lw : learned words; 

when the dictionary size of the AI player 

is the highest. In contrast, smaller 

dictionary size and higher game length 

results in decrease in the value of 

momentum which implies that high 

learning growth (due to high p~ value) 

would occur when experienced players 

(corresponds to high dictionary size or 

maximum game information) compete 

within a short period of time. 

 



H Iida and M N A Khalid A Paradigm Shift from Optimal...| 68 

 

 

Fig. 4. Momentum in Scrabble. It Can Be Seen That Momentum Is Highest When 

The Game Length Is Short And Game Information Is Maximum. 

B. Comfort-In-Mind 

Looking from another perspective, 

the GR measure provides the whole 

game playing situation through a single 

constant value. In other word, both the 

game element (such as reward) and the 

total process are constant as well as the 

attractiveness of the whole process 

remain the same. However, if the game 

element along the process changes, how 

can the measure of attractiveness be 

determined in any time or step of the 

process? By focusing on the change of 

the GR value throughout the game 

process, its “attractive” tendency can be 

determined using the third derivatives 

of (3), resulting in (14). This process 

gravitates towards increase in 

attractiveness which represents an 

addictive-like situation or strong feeling 

of engagement, namely as the AD value 

given by (15). 

  
 

This value can be perceived as the 

“force” in the human mind, where the 

present of “inertia” makes it difficult to 

persist along the total process. In other 

word, a timely reward change is an 

appropriate stimulation to help users 

continue to overcome the difficult uphill 

process (potentially caused by 

boredom). As such, a relation between 

the bio-mechanical effects and 

psychological attractiveness can be 

established. For example, when we take 

the roller coaster, not only we can feel 

the gravity, but also we can feel the 

“attraction” in our mind. As such, the 

relationship between the change of 

gravity (phenomenon known as 

“weightlessness”) and the change of 

attractiveness (in this context, called 

“addiction”) is investigated. 

A ‘login system’ is widely used and 

relevant in many fields, especially in the 

domain of online learning games such as 



69 | International Journal of Informatics Information System and Computer Engineering 1 (2020) 47-78 

 

DouDizhu3, BaiCizhan4 and Duolingo11. 

A login system is a typical monotonous 

repetitive action. As such, the system 

designers are expected to set some 

rewards to motivate the users to log in 

more often. From user’s point-of-view, 

such reward in the login system can be 

regarded as some form of entertainment. 

However, maintaining engagement in 

this type of game is not an easy feat, 

especially with the rise of free-toplay 

business model of games (Castro, E. G., 

and Tsuzuki, M. S., 2015) and rising 

popularity of elearning as an 

educational medium (Shabihi, N et 

al.,2016). Some game elements had been 

adopted to increase motivation and 

improve retention of the users on such 

system. Such feats can be achieved by 

careful attention to the relations 

between the attractiveness or the loyalty 

of the users and the game elements 

(Huotari, K., and Hamari, J., 2012). This 

is especially true for an online learning 

system such as login system, where 

several tiers and different reward rules 

can be applied. Previous study had 

provide evidence that “tiers system” is 

better than the “equal reward” because 

the process provides smoother decrease 

of user’s attractiveness throughout 

longer time span (months to years). 

Based on this aspects, two popular 

application named “we are primary 

school students” and “War poetry” were 

adopted for this purpose. The first 

application regulation involves user 

receiving one reward per day through 

application login which described by 

two factors: the number of reward 

 
3 http://www.auway.net/Games/play/Dou-Dizhu.htm 

obtained from “continuous login days” 

and the number of “login days” that 

corresponds to the G and T, respectively. 

The focus is on making more gentle and 

smooth loss of the user’s attractiveness 

based on the reward rule. As such, 5 

different reward rules are defined as in 

Table 17 which represents an 

incremental reward system. 

Table 17. Five Different Reward 

Schedules and Rules. 

Rule # Period∗ Reward 

Distribution 

1 365 days 1.00 

2 365 days/2 0.50, 1.50 

3 365 days/3 0.50, 1.00, 1.50 

4 365 days/4 0.25, 0.75, 1.25, 1.75 

5 365 days/5 0.25, 0.75, 1.00, 1.25, 

1.75 
            ∗: divided into equal parts; 

By applying the five rules in Table 

17, the curves of the GR value and AD 

value are depicted in Fig. 5. Since the 

login application is a repeated action, 

losing attractiveness from the users 

quickly is typical and should be 

avoided. Fig. 5 (top) shows the change of 

GR value over time based on the regular 

reward rule which rapidly declining at 

the beginning. This implies that the 

users will lose their attractiveness and 

feel boring in a short time. However, the 

decrease of GR values is the least for 

Rule 5, which indicates a smoother 

“attractiveness decrease” process. 

Although Rule 1 to 3 provide better GR 

value in the beginning, the rapid 

decrease of the GR value over time 

would cause the inability of the user to 

4 https://www.baicizhan.com 
11https://www.duolingo.com/ 

http://www.auway.net/Games/play/Dou-Dizhu.htm
https://www.baicizhan.com/
https://www.baicizhan.com/
https://www.duolingo.com/


H Iida and M N A Khalid A Paradigm Shift from Optimal...| 70 

 

retain engagement. In addition, the 

change of AD values over time (see Fig. 

5(bottom)) also showed similar 

tendency of reducing smoothly, 

especially on Rule 5 which implies 

gentle losses on users’ attractiveness. 

Imagine the “weightlessness” of the 

roller coaster, the change of the AD 

values corresponds to the degree of 

“attractiveness-less” where it is more 

acceptable to be experienced by the 

users little by little. In other words, 

although “attractiveness-less” can be 

viewed as a negative experience, it still 

retains user’s sense of enjoyment, which 

reduces smoothly over a long period of 

time. As such, “attractiveness-less” that 

barely noticeable to the users who can 

make their engagement to be retained 

longer.  

Another example application is the 

War poetry which adopted similar 

reward rules and schedules is given in 

Table 18. This enables the player to 

obtain login rewards that grows over 

time, rather than remain constant every 

day. If the number of rewards and the 

login days in War poetry is regarded as 

the G and T, respectively, the changes of 

the GR and AD values (Fig. 6) can be 

obtained. The differences of the GR 

values and AD values, at the beginning 

and the ending for each login systems is 

summarized in Table XIX. When the 

reward system is smoother towards 

losing user’s “attractiveness”, the value 

of ∆GR × ∆AD is lower. This implies that 

changes in GR and AD values are 

important factors to retain the 

engagement of the users. As such, it is 

important for the system designers to set 

different reward rules in different time 

stages. Based on the value of ∆GR×∆AD, 

both the incremental reward (Rule 4 and 

Rule 5) and tiers system is the most 

effective in gently reducing the 

“attractiveness” and prolonging the 

engagement of the user. 

Although the total reward is a constant, 

the rate of change of 

 

 
 

Fig. 5. The Change of Gr and Ad 

Values over Time: Five Different 

Reward Rules Compared 

 

 

 



71 | International Journal of Informatics Information System and Computer Engineering 1 (2020) 47-78 

 

Table 18. Different Reward Schedules of “War Poetry” From First to the Seventh 

Day 

Reward rule War poetry rewards 

Point system Tier system 

Day 1 1.77 1.00 

Day 2 1.77 1.10 

Day 3 1.77 1.30 

Day 4 1.77 1.50 

Day 5 1.77 2.00 

Day 6 1.77 2.50 

Day 7 1.77 3.00 

Total 12.40 12.40 

 

 

 
Fig. 6. The Change of Gr and Ad Values over Time: Different Reward Rules of 

“War Poetry” Compared 

Table 19. The analysis of gr value and add value based on login system 

Login system GRb GRe ADb ADe ∆GR × ∆AD 

Rule1 1.0000 0.0523 1.0000 0.0027 0.94514 

Rule2 0.7071 0.0523 0.7071 0.0027 0.46124 

Rule3 0.7071 0.0523 0.7071 0.0027 0.46124 

Rule4 0.5000 0.0523 0.5000 0.0027 0.22264 

Rule5 0.5000 0.0523 0.5000 0.0027 0.22264 

Point system 1.3310 0.5031 1.3310 0.1901 0.94455 

Tiers system 1.0000 0.5031 1.0000 0.1901 0.40244 

    b: begin; e: end



H Iida and M N A Khalid A Paradigm Shift from Optimal...| 72 

 

The GR value had demonstrated some 

successful cases for the designers to set 

different reward rules in different 

stages in two example login 

applications, “we are primary school 

student” and “War poetry”. 

Maximizing the user’s attractiveness 

and making them more loyal are 

achieved by dividing the process to 

many stages in order to optimize the 

reward rule (Zuo, L., et al, 2017). 

Looking from another perspective, the 

interpretation of the rate of change of 

the GR values and AD values can be 

related to the bio-mechanical processes 

of the roller coaster (Eager, D et al., 

2016). ∆GR means the interval of the 

attractiveness of users in the total 

process, which implies the range of 

maximum and minimum “attraction”, 

just like the height of the roller coaster. 

The AD value is similar with the feeling 

of “weightlessness” (or related to the 

force of gravity) where ∆AD implies the 

interval of the degree of 

“weightlessness” (changing rate of the 

GR value). Making both ∆GR and ∆AD 

smaller would also make the 

“attractiveness” to decline smoothly. 

Similarly, the tiers system which 

corresponds to the value of ∆GR×∆AD, 

also indicates smooth and progressive 

reduction of the GR value; thus, 

corresponds to the acceptability of the 

user.  

 

5. GENERAL DISCUSSION 

Applications of the GR theory have 

seen much success in quantifying the 

attractiveness and sophistication of 

almost all well-known competitive 

games such sports (Fig. 7), board games 

(Fig. 8), and video games (Fig. 9). 

Games that highly depend on luck 

(shorter game length, high branching 

factor) are situated in area greater than 

GR = 0.08 while games that highly 

depend on skill (longer game length, 

high branching factor) are situated in 

area lesser than GR = 0.07.  

These so called “comfortable” zone 

(GR ∈ [0.07,0.08]) was identified based 

on a shared patterns of games that 

found to be enjoyable and attractive to 

both beginner and advance level 

players. The zone provides a harmonic 

balance between the level of challenge 

and luck imposed on the player when 

playing the game. For the games that 

situated area GR < 0.07, it is largely 

dependent on skill that can be made 

known (or controlled) in order to 

influence the game outcome (i.e. the 

precision of hitting on the baseball bat 

and level of knowledge of a chess 

player). In contrast, games situated in 

area GR > 0.08 are highly dependent on 

luck/chance where any small external 

factors may not be visible 

(uncontrollable), but nevertheless 

influence the game outcome (i.e. the 



73 | International Journal of Informatics Information System and Computer Engineering 1 (2020) 47-78 

 

probability of encountering rock for 

three consecutive time in RoShamBo 

and change of pace or direction of the 

shuttle in Badminton). 

 

Fig. 7. Comparison of Various Sports 

Relative To The The Game 

Refinement Curves of gr ∈ [0.07,0.08]. 

Gr = 0.07 and gr = 0.08 is the Lower 
Bound and Upper Bound of Game 

“Comfortable” Zone, Respectively. 

While these “comfortable” zone 

provide evidence the state of mind of 

players in the competitive 

environment, such zone needed to be 

generalized in much broader context. 

Based on the application of the GR 

measure in educational standpoint, a 

gamified learning experience provides 

user with better appeal to the overall 

learning process where technique such 

as learning milestone had improved the 

learning experience by making learning 

session shorter and more engaging (see 

SectionIII-A). In addition, GR measure 

also provides indication for users to 

approach the educational materials in a 

more sensible manner (i.e. user with 

motivation). Meanwhile, from the 

business standpoint, the GR measure 

provides insights to both the customer 

and the business owner with respect to 

their own interests and benefits (see 

Section III-B). For example, the GR 

measure for the sales promotion 

‘discount’ provides insights on product 

popularity and business sustainability, 

where the zone value balances these 

two factors so that it becomes beneficial 

to both customer and the business 

owner.  

In addition, the GR measure of the 

Starbucks customer loyalty program 

indicates the need for the customer to 

spend and the free items the Starbucks 

willing to give to their loyal customer. 

Similarly, the GR measure of the 

gamified services for hotel and airlines 

loyalty programs also showed that 

“skillful” customer (becoming loyal 

customer) will likely enjoy the benefits 

of their services while the companies 

systematically improve their revenues. 

In-depth analysis of the GR measures 

and its derivatives may also provide a 

different perspective to the state of 

mind of users or players. While 

competition in game may be related to 

enjoyment and entertaining state-of-

mind, little was known to what 

perceived to happen in our mind when 

stimulated (such as curiosity during 

learning) and boredom (such as 

retention of engagement).  

Application of GR measure showed 

that some of the gamified elements of 

an edutainment game may entice 

certain learner curiosity (such as 

Duolingo entices beginner level learner 

due to its being an entertaining 

edutainment game) while impedes 

learner curiosity when lacks content 

diversity (see Section IV-A). In 

addition, skillful or experienced player 

that compete within a short session 

would also encourage growth of 



H Iida and M N A Khalid A Paradigm Shift from Optimal...| 74 

 

learning (i.e. high curiosity). On the 

other hand, application of GR measure 

and its derivative (AD value) also 

provide insights on dealing with 

boredom. Making a long and repetitive 

tasks engaging can be difficult, but 

possible when the sense of enjoyment is 

incrementally injected in-between tasks 

(see Section IV-B). Although repetitive 

tasks can be viewed as negative 

experience and reduce users 

engagement, reducing it smoothly and 

gradually may prolong the sense of 

engagement as much as possible while 

avoiding user rejection (or frustration).  

By avoiding abrupt and sudden 

change in the user experience, the bio-

mechanical equivalent known as 

“weightlessness” is imitated from the 

perspective of the psychological 

attractiveness, where the force of 

acceleration (thrills or excitement of 

accumulating rewards) cancelled out 

by the inertia (rejection or frustration of 

repeating the repetitive tasks). Such 

situation can be perceived as reaching 

the state of “attractiveness-less”, which 

approximately correlates with 

“addiction”12. In essence, the findings 

from the successful application of the 

GR measure and its derivative have 

provided evidence on the current 

paradigm shifts where the state of 

design for the users or players have 

shifted from optimizing play 

experience through various aspect of 

the game (or their environment) into 

state of design for the users or players 

that prioritized comfortable 

psychological state of mind in various 

aspects of the game (or their 

environment). As such, game designer 

not only needs to design an optimal 

play experience, but also a comfortable 

state of mind to provide a holistic 

approach in game development as well 

as other related ind ustries; thus, 

blurring the line between work and 

play (Iida H., 2018). 

 

Fig. 8. Comparison of various 

board games relative to the the game 

refinement curves of gr ∈ [0.07,0.08]. 
Gr = 0.07 and gr = 0.08 is the lower 

bound and upper bound of game 

“comfortable” zone, respectively. 

 

Fig. 9. Comparison of various 
video games relative to the the game 

refinement curves of GR ∈ [0.07,0.08]. 
GR = 0.07 and GR = 0.08 is the lower 

bound and upper bound of game 

“comfortable” zone, respectively. 

 

 



75 | International Journal of Informatics Information System and Computer Engineering 1 (2020) 47-78 

 

6. CONCLUSION AND FUTURE 
PROSPECTS 

This paper highlights evidences of 
the occurring paradigm shifts that were 
observed from the application of the 
game refinement theory and its 
derivative in the educational and 
business perspective, while further 
explored its utility in understanding 
and mapping the stimulation and 
ultimatum of the state of human mind, 
through the lens of games. 
Nevertheless, there are still plenty of 
open problems concerning the current 
research that requires further 
exploration. 

Since the recent debut of AlphaGo 
and AlphaZero, fair play becomes an 
important issue in game (Aung, H. P. P 
et al., 2019). Mechanically define the 
term “fairness” from the framework of 
game refinement theory provide a 
fascinating prospects in the future. On 
the other hand, with the recent 
development of accessible and widely 
available brain-computer interface 
technology such as Muse13,  

exploring the correlations of the 
measured brain waves with respect to 
the game refinement theory, where 
actual emotional and psychological 
state of mind can be mapped to distinct 
labels for better understanding of our 
brain and how it work, would be an 
interesting direction for future 
research. Finally, similar to the work in 
(Browne, C., 2020).  

Which focuses on the physical 
evolution of games, further exploration 
from the psychological footprints of 
game evolution through the framework 
of the game refinement theory (see 
preliminary works by (Yicong, W., 
2019) can be ventured in the future. 

ACKNOWLEDGMENT 

This research is funded by a grant from 
the Japan Society for the Promotion of 
Science, within the framework of the 
Grant-in-Aid for Challenging 
Exploratory Research. 

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