Computer Science and Information Systems 12(4):1217–1234 DOI: 10.2298/CSIS141101054X
Attractiveness of Real Time Strategy Games
Shuo Xiong and Hiroyuki Iida
School of Information Science, Japan Advanced Institute of Science and Technology
Nomi, Ishikawa, Japan 923-1211
Abstract. Game reﬁnement idea is a unique theory that has been proposed based on
the uncertainty of game outcome. A game reﬁnement measure was derived from the
game information progress model and has been applied in the domains such as board
games and sports games. The present challenge is to apply the game reﬁnement
theory in the domain of RTS games. To do so, we use StarCraft II as a testbed
and introduce a concept of strategy tree in order to construct a game tree of a RTS
game. Then, game reﬁnement values are calculated and compared with other type
of games. It is found that StarCraft II has a zone value of game reﬁnement.
Keywords: game reﬁnement theory, StarCraft II, real time strategy game, game
progress, strategy tree.
Video games grow more popular every year and Real Time Strategy (RTS) is a sub-genre
of strategy video games which does not progress incrementally in turns . Our re-
search interest is to know a theoretical aspect of attractiveness of such popular video
games. However, any method or approach to quantify the engagement of target games is
strictly limited. In other words, no mathematical theory has been established in this di-
rection. The present study is the ﬁrst attempt to explore the attractiveness of RTS using a
new game theory which focuses on the game sophistication.
Many efforts have been devoted to the study of strategic decision making in the frame-
work of game theory with focus on mathematical models of conﬂict and cooperation be-
tween intelligent rational decision-makers or game-players. Game theory originated in the
idea regarding the existence of mixed-strategy equilibrium in two-person zero-sum games
, which has been widely recognized as a useful tool in many ﬁelds such as economics,
political science, psychology, logic and biology.
However, little is known about mathematical theory from the game creator’s point
of view. An early work in this direction has been done by Iida et al. , in which a
measure of game reﬁnement was proposed based on the concept of game outcome uncer-
tainty. A logistic model was constructed in the framework of game-reﬁnement theory and
applied to many board games including chess variants. Recently a general model of game
reﬁnement was proposed based on the concept of game progress and game information
progress . It bridges a gap between board games such as chess and sports games such
as soccer. The next challenge is to apply the game reﬁnement theory to RTS games.
In this study we have chosen the domain of StarCraft II, which is one of the most
popular RTS games. We analyze the attractiveness of StarCraft II based on the game
1218 Shuo Xiong and Hiroyuki Iida
reﬁnement theory. In typical RTS games like StarCraft II, players build armies and vie for
control of the battleﬁeld. The armies in play can be as small as a single squad of Marines
or as large as a full-blown planetary invasion force. As a commander, one observes the
battleﬁeld from a top-down perspective and issues orders to one’s own units in real time.
Strategic thinking is key to success. Players need to gather information about the oppo-
nents, anticipate their moves, outﬂank their attacks, and formulate a winning strategy.
StarCraft II features three distinct races whose armies comprise entirely unique units and
structures. Each race has its own strengths and weaknesses, and knowing their tactical
proﬁles can mean the difference between glorious victory or crushing defeat.
To our best knowledge, no one published any successful application of the game re-
ﬁnement theory to RTS games. The main reason is that a RTS game is basically time-
continuous, so any method to determine the game progress has not yet been estab-
lished. In this study we propose an idea to determine the game progress of RTS games
bases on a concept of strategy tree.
In Section 3 we present the game reﬁnement theory and in Section 2 we will in-
troduce the concept of Real Time Strategy Game. Then, a concept of strategy tree will
be described in Section 4 while showing how to apply the strategy tree to StarCraft II.
Section 5 presents an application of game reﬁnement theory to StarCraft II. Finally, con-
cluding remarks are given in Section 6.
2. Real Time Strategy Game
Real-time strategy (RTS) is a sub-genre of strategy video games which does not progress
incrementally in turns. In an RTS, as in other wargames, the participants position and ma-
neuver units and structures under their control to secure areas of the map and/or destroy
their opponents’ assets. In a typical RTS, it is possible to create additional units and struc-
tures during the course of a game. This is generally limited by a requirement to expend
accumulated resources. These resources are in turn garnered by controlling special points
on the map and/or possessing certain types of units and structures devoted to this purpose.
More speciﬁcally, the typical game of the RTS genre features resource gathering, base
building, in-game technological development and indirect control of units.
The tasks a player must perform to succeed at an RTS can be very demanding, and
complex user interfaces have evolved to cope with the challenge. Some features have
been borrowed from desktop environments; for example, the technique of “clicking and
dragging” to select all units under a given area.
Though some game genres share conceptual and gameplay similarities with the RTS
template, recognized genres are generally not subsumed as RTS games. For instance, city-
building games, construction and management simulations, and games of the real-time
tactics variety are generally not considered to be “real-time strategy”.
In a typical real-time strategy game, the screen is divided into a map area displaying
the game world and terrain, units, and buildings, and an interface overlay containing com-
mand and production controls and often a “radar” or “minimap” overview of the entire
map. The player is usually given an isometric perspective of the world, or a free-roaming
camera from an aerial viewpoint for modern 3D games. Players mainly scroll the screen
and issue commands with the mouse, and may also use keyboard shortcuts.
Attractiveness of Real Time Strategy Games 1219
In most real-time strategy games, especially the earliest ones, the gameplay is gener-
ally fast-paced and requires very quick reﬂexes. For this reason, the amount of violence
in some games makes RTS games close to action games in terms of gameplay.
Gameplay generally consists of the player being positioned somewhere in the map
with a few units or a building that is capable of building other units/buildings. Often, but
not always, the player must build speciﬁc structures to unlock more advanced units in the
tech tree. Often, but not always, RTS games require the player to build an army (ranging
from small squads of no more than 2 units, to literally hundreds of units) and using them
to either defend themselves from a virtual form of Human wave attack or to eliminate
enemies who possess bases with unit production capacities of their own. Occasionally,
RTS games will have a preset number of units for the player to control and do not allow
building of additional ones.
Resource gathering is commonly the main focus of the RTS games, but other titles
of the genre place higher gameplay signiﬁcance to the how units are used in combat, the
extreme example of which are games of the real-time tactical genre. Some titles impose a
ceiling on the number simultaneous troops, which becomes a key gameplay consideration,
a signiﬁcant example being StarCraft, while other titles have no such unit cap.
2.1. Micromanagement and macromanagement
Micromanagement refers to when a player’s attention is directed more toward the man-
agement and maintenance of his or her own individual units and resources. This creates
an atmosphere in which the interaction of the player is constantly needed. On the other
hand, macromanagement refers to when a player’s focus is directed more toward eco-
nomic development and large-scale strategic maneuvering, allowing time to think and
consider possible solutions. Micromanagement frequently involves the use of combat tac-
tics. Macromanagement tends to look to the future of the game whereas Micromanage-
ment tends to the present.
2.2. Criticism of gameplay
Because of their generally faster-paced nature (and in some cases a smaller learning
curve), real-time strategy games have surpassed the popularity of turn-based strategy com-
puter games. In the past, a common criticism was to regard real-time strategy games as
“cheap imitations” of turn-based strategy games, arguing that real-time strategy games
had a tendency to devolve into “click-fests” in which the player who was faster with
the mouse generally won, because they could give orders to their units at a faster rate.
The common retort is that success involves not just fast clicking, but also the ability
to make sound decisions under time pressure. The “click-fests” argument is also often
voiced alongside a “button babysitting” criticism, which pointed out that a great deal of
game time is spent either waiting and watching for the next time a production button
could be clicked, or rapidly alternating between different units and buildings, clicking
their respective button.
A third common criticism is that real-time gameplay often degenerates into “rushes”
where the players try to gain the advantage and subsequently defeat the opponent as
quickly in the game as possible, preferably before the opposition is capable of successfully
1220 Shuo Xiong and Hiroyuki Iida
reacting. For example, the original Command & Conquer gave birth to the now-common
“tank rush” tactic, where the game outcome is often decided very early on by one player
gaining an initial advantage in resources and producing large amounts of a relatively pow-
erful but still quite cheap unitłwhich is thrown at the opposition before they have had time
to establish defenses or production. Although this strategy has been criticized for encour-
aging overwhelming force over strategy and tactics, defenders of the strategy argue that
they are simply taking advantage of the strategies utilized, and some argue that it is a
realistic representation of warfare. One of the most infamous versions of a rush is the
“zergling rush” from the real-time strategy game StarCraft; in fact, the term “zerging” has
become synonymous with rushing.
2.3. Tactics vs. strategy
Real-time strategy games have been criticized for an overabundance of tactical considera-
tions when compared to the amount of strategic gameplay found in such games. In general
terms, military strategy refers to the use of a broad arsenal of weapons including diplo-
matic, informational, military, and economic resources, whereas military tactics is more
concerned with short-term goals such as winning an individual battle. In the context of
strategy video games, however, the difference is often reduced to the more limited criteria
of either a presence or absence of base building and unit production.
2.4. The introduction of research object– StarCraft II
Our research mainly focus on StarCraft II: Heart of the Swarm(A expansion of StarCraft
II). It is a most outstanding and popular real time strategy game where the players goal
is to destroy their enemys base by developing their own base and an army. Players can
choose from three different races (Terran, Zerg, Protoss) to play, each of which plays very
differently. To construct buildings and produce army units, a player needs minerals and
gas. During the game, players unlock new options by constructing particular buildings.
The game revolves around three species: the Terrans, human exiles from Earth; the
Zerg, a super-species of assimilated life forms; and the Protoss, a technologically ad-
vanced species with vast mental powers. In macroscopic view, three races are the same
strength, however in microcosmic view every race has their own advantage and disad-
vantage what is quietly related with game reﬁnement. In the Table 1 have introduced the
character of three races.
3. Game Reﬁnement Theory
We give a short sketch of the basic idea of game reﬁnement theory from . The “game
progress” is twofold. One is game speed or scoring rate, while another one is game in-
formation progress with focus on the game outcome. In sports games such as soccer and
basketball, the scoring rate is calculated by two factors: (1) goal, i.e., total score and (2)
time or steps to achieve the goal. Thus, the game speed is given by average number of
successful shoots divided by average number of shoot attempts. For other score-limited
sports games such as Volleyball and Tennis in which the goal (i.e., score to win) is set
Attractiveness of Real Time Strategy Games 1221
Table 1. The features of three races
Terran 1. Excellent defensive ability in Opening
2. The are many strategies in Opening, however with
the time past, that will decline
3. Endurance is weak
4. From quantitative change to qualitative change
5. Observe weakly in Opening, however with the
time past, that will develop
Zerg 1. Strength in numbers
2. The opening strategy is less than Terran and Pro-
toss, but with the time past, that will develop fast
3. Endurance is strong
4. Observe is normal in any time
Protoss 1. High quality of soldiers
2. The are many strategies in Opening, however with
the time past, the number of strategy will decline
3. Observe is very weak in Opening, however with
the time past, that will develop up to normal level
4. Endurance is normal
in advance, the average number of total points per game may correspond to the steps to
achieve the goal .
Game information progress presents the degree of certainty of a game’s results in
time or in steps. Let Gand Tbe the average number of successful shots and the average
number of shots per game, respectively. Having full information of the game progress, i.e.
after its conclusion, game progress x(t)will be given as a linear function of time twith
0≤t≤Tand 0≤x(t)≤G, as shown in Equation (1).
x(t) = G
However, the game information progress given by Equation (1) is unknown during
the in-game period. The presence of uncertainty during the game, often until the ﬁnal
moments of a game, reasonably renders game progress as exponential. Hence, a realistic
model of game information progress is given by Equation (2).
x(t) = G(t
Here nstands for a constant parameter which is given based on the perspective of an
observer in the game considered. Then acceleration of game information progress is ob-
tained by deriving Equation (2) twice. Solving it at t=T, the equation becomes
x′′(T) = Gn(n−1)
It is assumed in the current model that game information progress in any type of
game is encoded and transported in our brains. We do not yet know about the physics of
information in the brain, but it is likely that the acceleration of information progress is
1222 Shuo Xiong and Hiroyuki Iida
related to the forces and laws of physics. Hence, it is reasonably expected that the larger
the value G
T2is, the more the game becomes exciting due to the uncertainty of game
outcome. Thus, we use its root square, √G
T, as a game reﬁnement measure for the game
under consideration. We can call it Rvalue for short.
Here we consider the gap between board games and sports games by deriving a for-
mula to calculate the game information progress of board games. Let Band Dbe average
branching factor (number of possible options) and game length (depth of whole game
tree), respectively. One round in board games can be illustrated as decision tree. At each
depth of the game tree, one will choose a move and the game will progress. Figure 1 il-
lustrates one level of game tree. The distance d, which has been shown in Figure 1, can
be found by using simple Pythagoras theorem, thus resulting in d=√∆l2+ 1.
Fig. 1. Illustration of one level of game tree
Assuming that the approximate value of horizontal difference between nodes is B
then we can make a substitution and get d=(B
2)2+ 1. The game progress for one
game is the total level of game tree times d. For the meantime, we do not consider ∆t2
because the value (∆t2= 1) is assumed to be much smaller compared to B. The game
length will be normalized by the average game length D, then the game progress x(t)is
given by x(t) = t
2D. Then, in general we have, x(t) = cB
cis a different constant which depends on the game considered. However, we manage
to explain how to obtain the game information progress value itself. The game progress
in the domain of board games forms a linear graph with the maximum value x(t)of B.
Assuming c= 1, then we have a realistic game progress model for board games, which
is given by
x(t) = B(t
Equation (3) shows that the game progress in board games corresponds to that of sports
games as shown in Equation (2).
To support the effectiveness of proposed game reﬁnement measures, some data of
games such as Chess and Go  from board games and two sports games  are com-
pared. We show, in Table 2, a comparison of game reﬁnement measures for various type
Attractiveness of Real Time Strategy Games 1223
of games. From Table 2, we see that sophisticated games have a common factor (i.e., same
degree of acceleration value) to feel engagement or excitement regardless of different type
Table 2. Measures of game reﬁnement for board games and sports games
Game B or G D or T R
Chess 35 80 0.074
Go 250 208 0.076
Basketball 36.38 82.01 0.073
Soccer 2.64 22 0.073
4. Strategy Tree in RTS
Our present study focuses on StarCraft II which is a RTS game where the player’s goal is
to destroy their enemy’s base by developing their own base and an army. In StarCraft II
players cannot see their opponent’s situation and they have the same power, StarCraft II
does not rely on any chance. Therefore, in a sense this game is similar with board games
such as chess. It means that we can use some similar tools or methods to analyze the game
of StarCraft II.
4.1. Basic Idea of Strategy Tree
Minimax strategy is a decision rule used in decision theory, game theory, statistics and
philosophy for minimizing the possible loss for a worst case (maximum loss) scenario
. Alternatively, it can be thought of as maximizing the minimum gain (maximin or
MaxMin). Originally formulated for two-player zero-sum game theory, covering both the
cases where players take alternate moves and those where they make simultaneous moves.
It has also been extended to more complex games and to general decision making in the
presence of uncertainty. The traditional minimax tree is illustrated in Figure 2.
Fig. 2. The traditional minimax tree
As we know, while players want to execute one strategy, some premises are needed.
For any graph structure as Shogi(Japanese Chess) shown in Figure 3 are all deﬁned
1224 Shuo Xiong and Hiroyuki Iida
as strategy tree. While player choose node1.1 , the next strategy must execute follow
Fig. 3. The basic strategy tree in Shogi(Japanese Chess)
node1.1 and player hardly go back to choose node1.2 again. Structurally analyze, node2.1
“Yagura” is one child node of node1.1 “Ibisha”, also it is the premise of node 3.1 and
Because StarCraft II is an incomplete information game, neither player A nor player B
do not know opponent’s condition, so they only consider about their own tree. the player
Astepiand player B stepishould be happened in the same time and shown in Figure 4.
Fig. 4. Strategy tree model for two players
Our idea is to combine the search tree of both players. Then we can establish a strategy
tree of StarCraft II.
4.2. Strategy Tree of StarCraft II
StarCraft II is a RTS game where players have the goal to destroy their enemy by build-
ing a base and an army. Players can choose 1 out of 3 races to play with. These races are:
Terran, Protoss, and Zerg. Terran are humans, Protoss are alien humanoids with highly ad-
vanced technology, and Zerg are a collection of assimilated creatures who use biological
adaptation instead of technology .
For anything a player builds, he needs to gather 2 types of resources: minerals and
gas. These resources are used to construct buildings which in turn can be used to produce
units. At the start of the game, not all units and buildings are available. New construction
options can be unlocked by making certain buildings. This means that some units and
buildings are available at the start of the game while others become available later in the
game. This is also called tier: the point in time that certain units and buildings become
Attractiveness of Real Time Strategy Games 1225
In order to play the game well, one must engage in strategy, macro-management and
micro-operation. Strategy determines whether player can establish the strategic superior-
ity. Macro-management determines the economic strength of a player. This is determined
by the construction of buildings, the gathering of resources and the composition of units.
Micro-operation determines how well a player is able to locally control small groups and
individual units. It includes movements and attacks that are issued by the player .
Macro-management of a player heavily depends on the strategy the player has chosen
to follow. For example, if a player chooses to rush his opponent by making ﬁghting units
at the very early stage in the game, his economy will suffer. On the other hand, if a player
chooses to focus on having a strong economy before building an adequate-size army, he
would take the risk of being overrun by his opponent.
Opening stage of StarCraft II According to the game features of StarCraft II, we should
divide the game into four parts: Opening, Mid-prophase, Mid-anaphase and Endgame.
The game could ﬁnish in any time domain. For example, while players choose supervise
attack or extremely rush strategy, the game must ﬁnish in 7 or 8 minutes or before; Nor-
mally, the average game time is 15 to 20 minutes (it means that most games will not enter
into Mid-anaphase or Endgame time domain). As our experience, we ﬁnd the game in
different time domain, the main elements are completely disparate.
Table 3. Feature of Starcraft II in every process
Domain Timing Character
Opening 0 to 10 minutes Strategy
Mid-prophase 10 to 20 minutes Economy and Management
Mid-anaphase 20 to 30 minutes Economy and Operation
Endgame Over 30 minutes operation
In the opening, the StarCraft II is similar to real war or traditional board games. In
other words, only in the opening time domain, StarCraft II is an intellectual game. While
a game enters into Mid-prophase or Mid-anaphase, the main elements are economy, man-
agement and operation. It means that in mid-game, the StarCraft II is similar to the sim-
ulation game. As we know, a good chess player can not always be a good manager, a
strategy genius does not mean that he could be a nice executive.
For the endgame, the operation element will be more and more important, even occupy
all the StarCraft II process. It means that on that time StarCraft II is similar to Super
Mario. When we watch somebody playing Super Mario, we only focus on whether or not
his operation skill is proﬁcient. In this situation, StarCraft II is like sports games such as
soccer and basketball.
According to the above, only in the opening stage, we have the strategy tree, and then
ﬁnd the Band D. Also in the opening stage, the game is highly similar to traditional
board games or brain sports, we can take example by game tree model to establish new
mathematical model. If we want to research mid-game or end game, we must ﬁnd other
model or method. At least, the meaning of Band Dmust be changed. Actually, the
1226 Shuo Xiong and Hiroyuki Iida
Fig. 5. Feature of StarCraft II
completion between profession players, the most exciting and wonderful part is mid-
game. It is likely that body sports are more suitable than brain sports to watch. However
for AI research, apparently opening part seems more valuable. Also the opening stage is
worth to establish opening book or do other related research in the future. So these are the
reasons why we only focus on the opening stage.
Strategy Tree – The Tree with Unbalanced Children Nodes In StarCraft II, there are
three races. Every race has their own particular strategy tree. Here we analyze the Pro-
toss strategy tree. We enumerate all the opening strategies existed, which are commonly
used in High Ladder system. Professional players have validated their rationality through
experience and experiments.
In the following strategy tree, the content is denoted as “4BG” or “BF” which means
a strategy name or code name. These strategies would be used in the opening stage, i.e.,
within 10 minutes after starting a game. Then we get the strategy tree as shown in Figure 6.
Fig. 6. The opening strategy tree of Protoss
In traditional turn-base board game, any length of one depth should always equal to
1. Since StarCraft II is a RTS game, its minimax tree cannot be built in a normal way. For
Attractiveness of Real Time Strategy Games 1227
example, the depth of tree is deﬁned by each step or turn, while in StarCraft II, the depth
might be given by time evolution. In Figure 7, we notice that the child node “BCrush”
and “BF 2BN” have the different depth. This situation would never happen in traditional
board games to build a minimax search tree. So we consider one method to solve it, while
changing an unbalance depth tree into a balance tree.
Fig. 7. An example of strategy tree with two unbalanced child nodes
Here is an interesting example in our life. Now we assume a professor X who have two
conference in the same day, one will be held in Tokyo and other will be held in Shanghai.
Prof. X live in Osaka, of course he only can attend one conference on that day. From
Osaka to Tokyo will cost 1 hour, and From Osaka to Shanghai will cost 2 hours, then he
has a strategy tree with time as Figure 8 shows.
Fig. 8. The travel strategy tree of Prof.X
From Osaka to Shanghai, just consider about one thing. After one hour past, the air-
plane will arrive Fukuoka. However, Prof. X cannot leave the airplane or airport to enter
in Fukuoka city (he must go to Shanghai, and he cannot order aircraft commander to stop
the airplane), so the strategy tree will completely equal to Figure 9. We call Fukuoka is a
According to this method, while adding the temporary node, then we get another
strategy tree of Protoss as shown in Figure 10.
1228 Shuo Xiong and Hiroyuki Iida
Fig. 9. Temporary node in unbalance strategy tree
Fig. 10. The new opening strategy tree of Protoss with temporary node
Attractiveness of Real Time Strategy Games 1229
5. Analysis of Attractiveness of StarCraft II
5.1. Applying Game Reﬁnement Measure
The game of StarCraft II can be divided into four parts. For the artiﬁcial intelligence, the
most important part is the opening domain where players have to focus on their strategies.
In this area, the weaker player would have a little chance to win. Now we can draw the
ﬁgure of Terran and Zerg as follows.
Fig. 11. The opening strategy tree of Terran
Fig. 12. The opening strategy tree of Zerg
In Figure 10, the Protoss tree’s depth is 9. In this tree, the total branching factor is 116
and we have 74 parent nodes, so average branching factor is B=116
74 = 1.57. However,
until now we cannot calculate the game reﬁnement value directly. Because in the real
game, two players cannot maintain playing game independently at anytime. Sometimes,
they will use spy and predict their opponent’s choice to modify their strategy. So we can
combine two trees into one tree, as shown in the following ﬁgure.
For the combined strategy tree, player A’s choice and Player B’s choice are all hap-
pened in the same time. No matter player A choose A1 or A2, it will not affect player B
to decide B1, B2 or B3, combine the two trees together, can analyze the game reﬁnement
value more accurately. While player A uses spy then realize player B will choose “some
strategy”, he can modify his next path based on player B’s parent node.
In minimax tree, the whole tree size is estimated by BD, and the game reﬁnement
formula equal to √B
D, while in the combined strategy tree, the tree size is (B2)D, so the
game reﬁnement value should be given by √B
2D. Then the game reﬁnement value of Protoss
in the opening time domain is given by
1230 Shuo Xiong and Hiroyuki Iida
Fig. 13. Combination of two strategy trees
Similarly, race Terran and Zerg also have their own strategy tree, then the game re-
ﬁnement value is calculated, as shown in Table 4. In this table, we notice that Zerg has
two game reﬁnement values.
Table 4. Measure of game reﬁnement for three races in StarCraft II
Race all nodes all parent nodes B D R-value
Terran 126 76 1.64 16 0.0805
Zerg 219 141 1.54 18 0.0692
Zerg* 564 210 1.61 20 0.0819
Protoss 116 74 1.55 18 0.0691
The R-value not only means the property of every race, but also means the competi-
tion between same race such as Terran versus Terran or Zerg versus Zerg. We evolve the
mathematical formula in Equation (4).
AllB ranchF act1
AllF atherN ode1∗All BranchF act2
AllF atherN ode2
logAvg.depth (depth1∗depth2)∗Avg.depth (4)
Then we have the full data of every race’s competition in Table 5:
Table 5. Measure of game reﬁnement for every competition in Starcraft II
Terran Zerg Zerg* Protoss Average
Terran 0.0805 0.0746 0.0809 0.0747 0.07675
Zerg 0.0746 0.0692 None 0.0694 0.07107
Zerg* 0.0809 None 0.0819 0.0754 0.07940
Protoss 0.0747 0.0694 0.0754 0.0691 0.72150
Compared with other traditional board games, the result are closed, as Table 6 shows:
Attractiveness of Real Time Strategy Games 1231
Table 6. Game reﬁnement values for StarCraft II and board games
Zerg 0.07107 to 0.07940
As shown in Figure 11 and Figure 12, strategy trees of Terran and Zerg are more complex
than Protoss. In particular Zerg’s strategy tree has critical points, as shown in Figure 12.
This means that game reﬁnement value will change after crossing the critical point .
Below we show the illustration of tech tree structures of three different races. Fig-
ure 14 shows that Protoss tech tree is a branch tree. Terran tech tree is basic divergence
linear, as shown in Figure 15. Moreover, Zerg tech tree is a disperse tree, as shown in
Figure 16. Thus the different structures determine that Zerg has a strategy critical point in
the opening stage, but Terran and Protoss have no such point.
Fig. 14. Protoss’s tech tree structure
Fig. 15. Terran’s tech tree structure
Compared with the StarCraft II ladder race ratio in Table 7, it is found that the race
Zerg has been selected with highest percentage in every local server. Behind that, the
second popular race is Protoss. Consider the operation difﬁculty, the results mainly ﬁt
the research result. In addition, as shown in Figure 17 , we notice that the wining
percentage of Terran is lower than Protoss. Actually, Protoss is much easier to control,
while Terran and Protoss’s player has the same APM(Actions Per Minute), Terran’s player
1232 Shuo Xiong and Hiroyuki Iida
Fig. 16. Zerg’s tech tree structure
Table 7. StarCraft II ladder race ratio of grandmaster group
Server Terran Zerg Protoss Random
US 23.5% 38% 36.5% 2%
EU 23.8% 40.5% 34.7% 1%
China 25.5% 35.8% 34.3% 4.4%
Korea & Taiwan 30.1% 32.5% 32.5% 4.9%
has less chance to win. According to the nature of StarCraft II, many players play the
game not only for fun, but also for winning the competition, even though Terran is more
interesting than Protoss, they prefer to choose the latter.
Fig. 17. wining percentage of three races
While introducing the concept of strategy tree, the game reﬁnement measure has been
calculated for three different races in the opening game of StarCraft II. Thus, it is possible
to compare the degree of game reﬁnement or engagement of RTS games with other type
of gamers such as board games and sports games. We conclude that the resulting game
reﬁnement values of StarCraft II, as measured by game reﬁnement theory, support the
Attractiveness of Real Time Strategy Games 1233
previous assumptions of a balanced window of game sophistication around 0.07-0.08.
Particularly, our research was based on the July, 2014 year. After that, some parameter
in StarCraft II had been changed and player’s tactics had been updated. However, base
on our achievements, game reﬁnement theory can successfully be used in various of Real
Time Strategy game, it can be a good tool to help game designer to make rules or set the
Acknowledge. This research is funded by a grant from the Japan Society for the Promotion of
Science, in the framework of the Grant-in-Aid for Challenging Exploratory Research (grant number
1. T. Avontuur. (2012). Modeling player skill in Starcraft II, HAIT Master Thesis series nr. 12-
004, Tilburg University.
2. C. Chambers, W.Feng, W.Feng, and D.Saha. (2005). Mitigating information exposure to
cheaters in real-time strategy games, In Proceeding of NOSSDAV’05 Proceedings of the in-
ternational workshop on Network and operating systems support for digital audio and video,
3. D.Cheng, R.Thawonmas. (2004). Case-based plan recognition for real-time strategy games. In
Proceedings of the 5th Game-On International Conference, pp.36–40.
4. H. Iida, N. Takeshita, and J. Yoshimura. (2003). A metric for entertainment of boardgames:
Its implication for evolution of chess variants. Entertainment Computing Technologies and
5. H. Iida, K. Takahara, J. Nagashima, Y. Kajihara and T. Hashimoto. (2004). An application of
game-reﬁnement theory to Mah Jong. In Entertainment Computing–ICEC2004, pp. 333–338.
6. J. Neumann. (1928). Zur theorie der gesellschaftsspiele. Mathematische Annalen, 100(1):295–
7. R.L.Rivest.(1987). Game tree searching by min/max approximation. Artiﬁcial Intelligence,
8. A. P. Sutiono, A. Purwarianti, and H. Iida. (2014). A mathematical model of game reﬁnement,
in D. Reidsma et al. (Eds.): INTETAIN 2014, LNICST 136, pp.148–151.
9. J. Takeuchi, R. Ramadan, and H. Iida. (2014). Game reﬁnement theory and its application to
Volleyball, Research Report 2014-GI-31(3), Information Processing Society of Japan, pp.1–6.
10. Abuhamdeh, S., & Csikszentmihalyi, M. (2012). The importance of challenge for the enjoy-
ment of intrinsically motivated, goal-directed activities. Personality and Social Psychology Bul-
letin, 38(3), 317-330.
11. Abuhamdeh, S., Csikszentmihalyi, M., & Jalal, B. (2015). Enjoying the possibility of defeat:
Outcome uncertainty, suspense, and intrinsic motivation. Motivation and Emotion, 39(1), 1-10.
12. Langer, R., Hancock, M., & Scott, S. D. (2014). Suspenseful design: Engaging emotionally
with complex applications through compelling narratives (pp. 1-8). IEEE.
13. StarCraft II Game guide. 2014 BLIZZARD ENTERTAINMENT, INC. ALL RIGHTS RE-
SERVED. url: http://us.battle.net/sc2/en/game/
14. Statistics of winning percentage. 2013 SGAMER, Copyright 2002-2011. url:
15. Real-time strategy. (2014, August 10). url: http://en.wikipedia.org/w/ index.php?title=Real-
1234 Shuo Xiong and Hiroyuki Iida
Shuo Xiong is a Ph.D student of the School of Information Science, at the Japan Ad-
vanced Institute of Science and Technology. S. Xiong been an enthusiasm researcher in
the domains such as computer and video games, game design, Asian game industry and
Hiroyuki Iida is a full professor of the School of Information Science, at the Japan Ad-
vanced Institute of Science and Technology. Dr. Hiroyuki Iida has been an enthusiasm
researcher in the domains such as computer games and entertainment computing, while
acting as important roles of international activities such as conference chair, program chair
and journal editor.
Received: November 1, 2014; Accepted: July 11, 2015.