Content uploaded by Khaldoon Dhou
Author content
All content in this area was uploaded by Khaldoon Dhou on Oct 08, 2020
Content may be subject to copyright.
A novel investigation of attack strategies via the
involvement of virtual humans: A user study of
Josh Waitzkin, a virtual chess grandmaster
Khaldoon Dhou
College of Business Administration
Texas A&M University-Central Texas
Abstract. A growing body of evidence suggests that attack is a signif-
icant concept that has been explored by researchers from various disci-
plines such as marketing, psychology, and computing. Additionally, there
has been substantial research undertaken on the role of attack in chess,
which brought significant contributions to different fields of research. In
this paper, the researcher investigates the attack concept in chess, as a
strategic game by exploring virtual chess players of different strategies.
In particular, the researcher explores the performance of an attacking
grandmaster against three other class-A players of different chess person-
alities that vary in controlling the center of the chessboard. To this end,
the researcher collected data from four virtual chess players: a grandmas-
ter and three class-A players. The selected grandmaster is Josh Waitzkin
who is known for his fearless attacking style and deep endgame under-
standing. The class-A players have different personalities: (1) a player
who strongly controls the center of the board; (2) a player who ignores
the center; and (3) a player who offers traps to control his opponent.
The researcher measured different dependent variables including the er-
rors of the players and the moves of the games. The findings show that
class-A players of particular chess personalities perform differently. Ad-
ditionally, the study reveals that there is a positive relationship between
the findings and some of the existing real-life scenarios in the business
domain.
Keywords: chess, chess personality, virtual humans, attack, Josh Wait-
zkin, grandmaster
1 Introduction
In the last twenty years, the chess world witnessed many interdisciplinary
endeavors from the fields of psychology, artificial intelligence, and com-
puter design. This resulted in many significant achievements including a
machine being able to defeat Gary Kasparov, the reigning world cham-
pion in 1997. Even more, current chess applications in the market are
very affordable and capable to compete at the level of a grandmaster,
the highest rank a chess player can attain. Such applications offer use-
ful features to chess players among which are providing hints, analyzing
2 Khaldoon Dhou
chess positions, and allowing a player to play against another player or
computer opponent.
Computer opponents can come in a variety of ways such as chess
engines or virtual humans. They are widely used by chess players for
training and they exist in different personalities. Throughout this paper,
the term chess personality is defined as the attitude of a chess player
during his games such as an attack, defense, or a mixture of both. The
personality of a player can shape the direction of a chess game. For
example, some grandmasters start attacking at an early stage of a game,
and this might cause their opponents to act defensively. Other players
like to get their Queen involved during the opening phase.
Investigating the personalities of virtual chess players can play an
essential role in addressing many research problems. First, there is evi-
dence that employing software loaded with virtual players with different
personalities plays a crucial role in surgical training using a virtual re-
ality simulator [5,32]. Second, existing research suggests that there is a
strong association between chess and business in many aspects such as
patience, long-term thinking, and perseverance [19, 21, 23,29, 30]. Third,
rapid developments in building new chess applications have heightened
the need for understanding chess personalities [14]. Virtual chess players
helped in investigating different playing styles by allowing researchers
to explore games between chess players of various personalities who ex-
isted in different eras [12]. Another key thing to remember is that vir-
tual humans made it possible to further examine world champions such
as Garry Kasparov and many other top grandmasters [12,14, 15]. Ad-
ditionally, relevant work is not only limited to virtual humans, but it
also shows existing studies in virtual environments simulating different
types of biological behaviors such as predator-prey ecosystems and ant
colonies [9, 11, 13, 16, 28]. All these studies showed the effectiveness of
simulated behaviors in coding binary information that is widely used in
many research activities such as perception and visualization [10, 17, 18].
In this paper, we explore four virtual players: a grandmaster and
three other class-A players. The selected grandmaster is Josh Waitzkin,
who is known for being a fearless attacker with a deep endgame un-
derstanding. The class-A personalities vary in their skills with regards
to traps and controlling the center. This paper builds on previous re-
search in virtual chess players and provides an important opportunity
to advance the understanding of chess personalities. The findings should
make important contributions to the fields of psychology and computer
science. The central question in this paper asks about the errors that
virtual players of different personalities make while playing against each
other. The main questions addressed in this paper are:
–How does Waitzkin behave while playing against class-A players who
vary in their controlling the center and trapping an opponent’s per-
sonality?
–How are class-A players of various chess personalities related to traps
and controlling the center influenced while competing against Wait-
zkin?
–How is the length of the games played against Waitzkin influenced
by the different class-A players employed in the experiment?
An exploration of attack strategies via the utilization of virtual humans 3
The overall structure of this paper takes the form of six sections in-
cluding this section. Section 2 begins with exploring the related studies
and identifying the gaps where further research is needed; Section 3 is
concerned with the study design; Section 4 analyzes the results of the
experiment and presents the findings; Section 5 provides a general dis-
cussion of the research findings based on the existing literature; finally,
section 6 concludes the paper, and offers suggestions for future research.
2 Related work
A large and growing body of the literature has investigated the psychol-
ogy of chess players. Models were developed over the years to understand
a chess player’s mind. The first model was offered by Cleveland [7] and it
incorporates the most vital aspects in modern chess theory and focuses
on chess development. In 1965, de Groot [8] investigated chess players’
thinking and memory and how they solve chess problems. De Groot
exposed chess players to meaningful chess patterns and asked them to
reconstruct them from memory. He found that masters outperformed
novice chess players. This was followed up by the study of Chase and Si-
mon [6] who did a similar experiment with random chess positions. They
found that chess players of various skills failed to reconstruct them. The
previous two experiments show the importance of chess patterns in a
chess player’s skill.
Chess players vary in their ability and are ranked according to a rat-
ing, which is a number that provides an estimation of a chess player’s
skill measured against other players in the chess community. Many orga-
nizations provide chess ratings such as the World Chess Federation and
the United States Chess Federation (USCF). For example, according to
the USCF [34], the highest title is a Senior Master, which is awarded to
a chess player who maintains a rating of 2400 and above. Below that is
a Master, for a player who maintains a rating between 2200 and 2399;
Expert between 2000 to 2199; class A between 1800 to 1999 and so on.
Chess players are not only characterized by their ratings, but they
can also be described by their chess personalities. These personalities are
reflected by the playing style of a player during different game phases.
For example, Marshall (1942-2017) is a risk-taker who offers sacrifices to
gain an advantage during his games [33]. Exploring chess personalities
has its roots in psychoanalysis and numerous studies have attempted
to investigate it from different angles. For example, Jones [24] explored
the personality of grandmaster Paul Murphy and identified many as-
pects in his playing styles such as attack and piece sacrifice. Similarly,
Karpman [25] explored the topic of chess personalities and the condi-
tions at which certain players play the best. He also identified contrasts
in personalities among chess grandmasters and the reasons behind some
game results. In the same vein, Haran [22] identified five chess personal-
ities depending on the opening variation: normal personality, aggressive
personality, defensive personality, semi-open personality, and positional
personality.
4 Khaldoon Dhou
The rapid developments in Artificial Intelligence and Computing
Technology made it possible to include new modern features that en-
able further exploration of chess personalities. Among these features are
the virtual chess players, which are defined as computer programs that
simulate real chess players of different levels from beginners to top-rank
grandmasters. Virtual humans opened new research horizons and offered
alternative prospects on how to analyze chess games and explore the psy-
chology of different players. This began with a study that investigated
virtual grandmasters and class-B players that represent actual human
chess players [12]. In the study, the author explored the personalities of
attacking and defending grandmasters and the outcomes while they com-
pete against less skilled players. They found that an attacker grandmas-
ter tends to have fewer errors than a defensive grandmaster. Similarly, the
author found that the class-B players in the study perform better while
competing against an attacker grandmaster. These findings have grounds
in social sciences as research showed that people instinctively seek to per-
ceive the reasons behind challenging events and how they influence their
existence when they face them [36]. This view is also supported by the
study conducted in [15] showing that an attacker grandmaster performs
better as opposed to a defensive grandmaster while competing against
class-A players. What’s more, these are not the only studies that investi-
gated virtual chess players. A recent study explored the chess personality
of Garry Kasparov and how he is influenced by and influencing class-A
players of different personalities [14]. All these studies have emphasized
the importance of virtual humans and how they are used to explore
the personalities of chess players. It is also important to mention that
emulating real chess players is a major area of interest within the game
industry. One example is Virtual Kasparov [2], developed by Titus, which
incorporates simulated chess players of different personalities. Similarly,
Ubisoft developed the Chessmaster and it offers many virtual players
representing real players including top grandmasters such as Kasparov
and Polgar [33].
Overall, all the studies reviewed here and the tremendous industrial
advancements in virtual humans highlight the need to further investigate
this field of research. These studies clearly indicate that there is a strong
relationship between virtual humans, personalities, and existing real-life
scenarios in different fields of research including marketing, management,
and psychology. However, there remain several aspects of virtual chess
players about which relatively little is known.
3 Method
3.1 Participants
Participants in this study were virtual chess players of different chess per-
sonalities. The data for the study was collected from the games between
the virtual players participating in the experiment. The virtual players
that were chosen for the study simulate Waitzkin, and three other class-
A players of different personalities. Below is the description of each of
the virtual players in the experiment, as provided by Ubisoft [33]:
An exploration of attack strategies via the utilization of virtual humans 5
–Waitzkin: a well-known chess grandmaster and author who is char-
acterized by being a courageous attacker with a deep comprehension
of the endgame.
–Buck: a player who favors openings that include a significant por-
tion of captured pieces. His vulnerability is his almost negligence of
dominating the center of the chessboard. His USCF rating is 2355.
–J.T.: he plays specific openings that are outlined to attract his op-
ponent to fall into a prepared trap. His USCF rating is 2330.
–Lili: a player with a comprehensive opening knowledge, however,
she favors particular lines of play that can be insignificantly disad-
vantageous. As opposed to Buck, she has excellent control over the
chessboard. Her USCF rating is 2394.
The selection of these players that represent different personalities
is influenced by the categories of moves offered by Chase and Simon
[6, p. 259] such as opening, exchange, defense, and attack. Additionally,
Chase and Simon [6] explored five chess relations between pieces: attack,
defense, proximity, color, and type. It is essential to note that the ratings
of the class-A players utilized in the experiment were almost identical.
3.2 Materials
The simulations were run using the Chessmaster software offered by
Ubisoft [33]. The software is highly praised in the chess community, it
plays at the same level as a top-rank grandmaster, and is used in different
research projects [12, 14, 15].
In the design of the current experiment, the researcher manipulated
two independent variables: the color of the grandmaster’s pieces, and
the class-A player’s personality. Each class-A player played 78 games
against Waitzkin, where half of the games played by each player were
with the white pieces and the other half was with the black pieces. The
class-A player’s personality independent variable has three levels: the
personalities of Buck, J.T., and Lili. The description of their personalities
was provided in the previous subsection.
The researcher used the Chessmaster for analyzing the games and
used the data in the analysis. That is to say, the design involves three
dependent variables:
–The agreement percentage of the moves made by the grandmaster
–The agreement percentage of the moves made by a class-A player
–The number of moves in the game: a move is defined as the White
player’s move followed by the Black player’s move
3.3 Procedure
Waitzkin played 78 games against each class-A player utilized in the
study. To reduce the chance that the player’s color influences the design,
each player plays half of the games in the experiment with white color
and the other half with black.
6 Khaldoon Dhou
4 Results
The researcher conducted a two-way ANOVA to examine the effect of
two independent variables (grandmaster’s color and class-A player’s chess
personality) on each of the dependent variables. All the effects were con-
sidered statistically significant at p < 0.05. There was a significant main
effect of the class-A player personality on the number of moves in the
games, F(2,228) = 5.607, p= 0.004. Pairwise comparisons indicate that
the significant main effect reflects a significant difference (p= 0.003)
between J.T. (M= 68.410) and Lili (M= 57.372).
There was a significant main effect of the color of the grandmaster on
the agreement percentage of the moves made by Waitzkin, F(1,228) =
5.919, p= 0.016. This indicates that the Chessmaster agrees more with
Waitzkin when he plays with black pieces (M= 98.111%) than when
he plays with white pieces (M= 97.385%). Additionally, there was a
significant main effect of the color of the grandmaster on the agreement
percentage of the moves made by the class-A players, F(1,228) = 11.132,
p= 0.001. More specifically, the Chessmaster agrees more with the class-
A players when Waitzkin plays with the black pieces (M= 94.410%)
than white pieces (92.487%). Similarly, there was a significant main ef-
fect of a class-A player’s personality on the agreement percentage of
the moves made by class-A players participating in the experiment,
F(2,228) = 3.529, p= 0.031. Pairwise comparisons indicate that the
significant main effect reflects significant differences (p= 0.039) between
Buck (M= 92.744%) and Lili (M= 94.513%). Fig. 1 shows the Chess-
master’s agreement percentages on the moves made by Waitzkin and the
other class-A players employed in this study.
5 General discussion
This study set out with the aim of assessing the importance of chess per-
sonality in the errors made by virtual chess players of different personal-
ities. The results of this study indicate that a chess player can perform
differently depending on the personality of his opponent. Surprisingly, the
findings showed that Waitzkin performed better with black pieces as op-
posed to when he had white pieces. Likewise, the virtual class-A players
performed better with the black pieces than when they had white pieces.
It is interesting to note that previous research indicated that the per-
formance of less-skilled chess players, measured by the errors they make
is consistent with the performance of their grandmaster opponent. For
example, in a former study exploring two groups of chess players: grand-
masters and class-B players, the researcher found that class-B players
had fewer errors when they played against Anderssen (i.e. an attacker
grandmaster), as opposed to when they played against Leko (i.e. defen-
sive grandmaster). Similarly, the same study showed that Anderssen had
fewer errors than Leko when they both played against the same class-B
players. One possible explanation of why Waitzkin in this experiment
performed better with black pieces is related to chess opening. A chess
An exploration of attack strategies via the utilization of virtual humans 7
Fig. 1. The Chessmaster’s agreement percentages on the moves made by Waitzkin
and the other class-A players utilized in the study. As shown in the figure, Waitzkin
performed the best while competing against Lili as opposed to the other class-A players.
Likewise, Lili did the best among the other class-A players employed in the study.
player sometimes tends to perform better when he encounters an opening
he is familiar with [14].
Openings are not just important in chess, but existing research in the
marketing domain showed the importance of carefulness in handling a
new product. One example is the purchase of Snapple by Quaker, which
owned Gatorade at that time. On the day of declaring that Quaker would
purchase Snapple for 1.7 billion dollars, their stock price decreased by
about 10%, and three years later, after several attempts to merge Snapple
into their environment with Gatorade, Triarc purchased Snapple for 300
million dollars [26]. The example shows that Snapple and Gatorade are
different brands and should not be treated as equals without carefulness.
Likewise, in chess, openings are different, and not being familiar with
a particular opening can result in making more mistakes and probably
losing a game. This is further evidenced by the outcomes of the analysis
showing that the games against J.T. last the longest (Fig. 2), although
8 Khaldoon Dhou
he has almost the same rating as the other class-A players utilized in
this experiment. However, J.T. utilizes opening traps while playing, and
these can probably make his opponent further resist, especially if not
aware of particular opening lines.
Fig. 2. The average number of moves in the study while competing against Waitzkin.
The figure shows that on average, the games involving J.T., a players who considers
traps in the openings were the longest
Another important finding was that, although having almost the
same rating, the class-A players in the study performed differently while
competing against Waitzkin. The experimental results revealed that the
Chessmaster significantly agrees more on the moves made by Lili than
the moves made by Buck. Controlling the center is an essential chess
strategy and for some chess openings, a player sacrifices material to gain
more control of the center of the board [4, 20, 27]. Interestingly, existing
research shows that controlling the center, and other activities encoun-
tered by students while playing a chess game are analogous to some
management principles [4]. In his research, students learn the concept
of controlling the center of the board, which leads to controlling the
game. Additionally, his research shows that such a concept is compara-
ble to winning the domination in the industry and developing into the
performing standard [4].
An exploration of attack strategies via the utilization of virtual humans 9
The findings in this study further support the idea of exploring the
personalities of chess players and how players perform while competing
against other players. That is to say, the findings of this study are con-
sistent with the findings of other studies involving virtual chess players
confirming that players of the same rating perform differently depend-
ing on the personalities of the opponents they are competing with. For
example, in a previous study that investigates the personality of Garry
Kasparov, the findings show that the performance of Kasparov varied
while competing against other less-skilled players [14].
6 Conclusion
The purpose of the current study was to determine how a chess grand-
master who considers attacking strategies performs while playing against
class-A players of different personalities. For this purpose, the researcher
employs virtual players that simulate Waitzkin, as an attacker grand-
master, and other class-A players. Like real players, virtual players have
certain characteristics and they follow different game strategies such as
attack, defense, and controlling the center. The three class-A players
vary in their personalities: a player who tends to capture the opponent’s
pieces, a player who considers offering traps in the opening phase, and a
player with solid center control and comprehensive opening knowledge.
This study has shown that a grandmaster performs differently de-
pending on his opponent’s strategy. Likewise, players of the same rat-
ing perform differently while competing against the same grandmaster.
These findings are consistent with the previous findings exploring grand-
masters and less skilled players [12,14, 15]. For example, class-B players
of almost the same ratings and different chess personalities had different
reactions while competing with two grandmasters of different styles [12].
Likewise, the same study showed that Anderssen, an aggressive grand-
master performed better than Leko while competing against less skilled
players of the same rating category.
The findings in this study suggest that in general, chess personality
is a crucial factor to consider when evaluating the outcomes of chess
games between different players. In other words, although chess players
are evaluated based on their chess ratings, this does not seem to be the
only way to assess their performance. Additionally, since chess is a fun-
damentally strategic game, these findings can be extended to be explored
in other domains such as psychology, business, and computing. The find-
ings reported here shed new light on the psychology of competition and
how the personalities of virtual humans are related to many aspects in
domains exploring many attitudes such as aggressiveness and defense.
That is to say, the researcher believes that the present study lays the
groundwork for future research into exploring how virtual humans can
aid in understanding new elements in business strategies. To develop a
full picture of the personalities of chess players, additional studies will
be needed that explore different aspects of personalities. For example,
further studies, which take personality traits into account, will need to
be undertaken [1, 3, 31, 35].
10 Khaldoon Dhou
References
1. Al-Samarraie, H., Sarsam, S.M., Alzahrani, A.I., Alalwan, N., Ma-
sood, M.: The role of personality characteristics in informing our
preference for visual presentation: An eye movement study. Jour-
nal of Ambient Intelligence and Smart Environments 8(6), 709–719
(2016)
2. Butts, S.: Virtaul kasparov. Online (April 2002), http://www.ign.
com/articles/2002/04/19/virtual-kasparov, retrieved on March
20, 2017
3. Caci, B., Cardaci, M., Miceli, S.: Autobiographical memory, per-
sonality, and facebook mementos. Europe’s Journal of Psychology
15(3), 614–636 (Sep 2019), https://ejop.psychopen.eu/index.
php/ejop/article/view/1713
4. Cannice, M.V.: The right moves: Creating experiential management
learning with chess. The International Journal of Management Ed-
ucation 11(1), 25 – 33 (2013), http://www.sciencedirect.com/
science/article/pii/S1472811712000535
5. Chalhoub, E., Tanos, V., Campo, R., Kesrouani, A., El Rassy, E.,
Rizkallah, J., Chalhoub, D., Walter, C., Sleiman, Z.: The role of video
games in facilitating the psychomotor skills training in laparoscopic
surgery. Gynecological Surgery 13(4), 419–424 (2016)
6. Chase, W.G., Simon, H.A.: The mind’s eye in chess. (1973)
7. Cleveland, A.A.: The psychology of chess and of learning to play it.
The American Journal of Psychology 18(3), 269–308 (1907)
8. De Groot, A.: Thought and choice in chess (1965)
9. Dhou, K., Cruzen, C.: An innovative chain coding technique for com-
pression based on the concept of biological reproduction: An agent-
based modeling approach. IEEE Internet of Things Journal 6(6),
9308–9315 (2019)
10. Dhou, K.: Toward a Better Understanding of Viewers’ Perceptions
of Tag Clouds: Relative Size Judgment. Ph.D. thesis, The University
of North Carolina at Charlotte, USA (2013)
11. Dhou, K.: A novel agent-based modeling approach for image coding
and lossless compression based on the wolf-sheep predation model.
In: Shi, Y., Fu, H., Tian, Y., Krzhizhanovskaya, V.V., Lees, M.H.,
Dongarra, J., Sloot, P.M.A. (eds.) Computational Science – ICCS
2018. pp. 117–128. Springer International Publishing, Cham (2018)
12. Dhou, K.: Towards a better understanding of chess players’ person-
alities: A study using virtual chess players. In: Kurosu, M. (ed.)
Human-Computer Interaction. Interaction Technologies. pp. 435–
446. Springer International Publishing, Cham (2018)
13. Dhou, K.: An innovative design of a hybrid chain coding algorithm
for bi-level image compression using an agent-based modeling ap-
proach. Applied Soft Computing 79, 94 – 110 (2019), http://www.
sciencedirect.com/science/article/pii/S1568494619301425
14. Dhou, K.: An innovative employment of virtual humans to explore
the chess personalities of Garry Kasparov and other class-A players.
In: Stephanidis, C. (ed.) HCI International 2019 – Late Breaking Pa-
pers. pp. 306–319. Springer International Publishing, Cham (2019)
An exploration of attack strategies via the utilization of virtual humans 11
15. Dhou, K.: An exploration of chess personalities in grandmasters and
class-a players using virtual humans. International Journal of Enter-
tainment Technology and Management (2020)
16. Dhou, K.: A new chain coding mechanism for compression stimu-
lated by a virtual environment of a predator-prey ecosystem. Future
Generation Computer Systems 102, 650 – 669 (2020), http://www.
sciencedirect.com/science/article/pii/S0167739X1832630X
17. Dhou, K., Hadzikadic, M., Faust, M.: Typeface size and weight
and word location influence on relative size judgments in tag
clouds. Journal of Visual Languages & Computing 44, 97
– 105 (2018), http://www.sciencedirect.com/science/article/
pii/S1045926X16300210
18. Dhou, K.K., Kosara, R., Hadzikadic, M., Faust, M.: Size judgment
and comparison in tag clouds. IEEE Visualization Poster Proceed-
ings (2013)
19. Dilmaghani, M.: Gender differences in performance under time
constraint: Evidence from chess tournaments. Journal of Behav-
ioral and Experimental Economics p. 101505 (2019), http://www.
sciencedirect.com/science/article/pii/S2214804319303052
20. Fischer, R.: A bust to the king’s gambit. American Chess Quarterly
pp. 3–9 (2015)
21. Graber, R.S.: Business lessons from chess: A discussion of parallels
between chess strategy and business strategy, and how chess can
have applications for business education. Academy of Educational
Leadership Journal 13(1), 79 (2009)
22. Haran, A.: Collaborative computer personalities in the game of chess.
Ph.D. thesis, Dublin City University (2002)
23. Hunt, S., Cangemi, J.: Want to improve your leadership skills? play
chess! Education 134(3), 359–368 (2014)
24. Jones, E.: The problem of paul morphy: a contribution to the psycho-
analysis of chess. The International Journal of Psycho-Analysis 12,
1 (1931)
25. Karpman, B.: The psychology of chess:(richard reti). The Psychoan-
alytic Review (1913-1957) 24, 54 (1937)
26. Lehn, K.M., Zhao, M.: Ceo turnover after acquisitions: are bad bid-
ders fired? The Journal of Finance 61(4), 1759–1811 (2006)
27. Montero, B., Evans, C.: Intuitions without concepts lose the game:
mindedness in the art of chess. Phenomenology and the Cognitive
Sciences 10(2), 175–194 (2011)
28. Mouring, M., Dhou, K., Hadzikadic, M.: A novel algorithm for bi-
level image coding and lossless compression based on virtual ant
colonies. In: Proceedings of the 3rd International Conference on
Complexity, Future Information Systems and Risk - Volume 1: COM-
PLEXIS. pp. 72–78 (2018)
29. Nielsen, C.: The global chess game ... or is it go? market-entry
strategies for emerging markets. Thunderbird International Business
Review 47(4), 397–427 (2005), https://onlinelibrary.wiley.com/
doi/abs/10.1002/tie.20060
30. Rice, B.: Three moves ahead: What chess can teach you about busi-
ness. John Wiley & Sons (2010)
12 Khaldoon Dhou
31. Sarsam, S.M., Al-Samarraie, H.: Towards incorporating personality
into the design of an interface: a method for facilitating users’ inter-
action with the display. User Modeling and User-Adapted Interaction
28(1), 75–96 (2018)
32. Schlickum, M.K., Hedman, L., Enochsson, L., Kjellin, A., Fell¨ander-
Tsai, L.: Systematic video game training in surgical novices im-
proves performance in virtual reality endoscopic surgical simulators:
a prospective randomized study. World journal of surgery 33(11),
2360–2367 (2009)
33. Ubisoft: Chessmaster grandmaster edition, http://chessmaster.
uk.ubi.com/xi/index.php
34. US Chess Federation: USCF Ratings Distribu-
tion Charts. Online (October 2015), retrieved from:
http://archive.uschess.org/ratings/ratedist.php
35. Vollst¨adt-Klein, S., Grimm, O., Kirsch, P., Bilali´c, M.: Person-
ality of elite male and female chess players and its relation
to chess skill. Learning and Individual Differences 20(5), 517
– 521 (2010), http://www.sciencedirect.com/science/article/
pii/S1041608010000403
36. Wise, D.M., Rosqvist, J.: Explanatory style and well-being. Compre-
hensive handbook of personality and psychopathology p. 285 (2006)
