Exploring Four-ball and Creativity
Stephen Choi
Georgia Institute of Technology
Atlanta GA 30332-0155 USA
[email protected]
ABSTRACT
In this paper, we describe how four-ball and its rule affect
the players’ activity. We have conducted two experiments
to explore players’ thoughts processes; one in real billiard
table, the other using on-line game simulator,
BilliardsMania. The focus was to find out whether
experience level and absence of physical challenge affect
players’ decision of shot making. We conclude that rule of
physics precedes all of players’ decision and sport is limited
in creative activity due to the physical challenge.
Author Keywords
Ellen Do
Georgia Institute of Technology
Atlanta GA 30332-0155 USA
[email protected]
process involved in playing four-ball.
FOUR-BALL
Four-ball is a type of carom billiards game, which is the
overarching title of a family of billiards games generally
played on cloth-covered, 5 by 10 feet (approximately 1.5 ×
3 m) pocketless tables, which often feature heated slate
beds [1]. Three-cushion carom or three-cushion billiards is
a similar type of carom billiards game, but much more
difficult than four-ball. Therefore, four-ball is preferred by
the amateurs and remains popular, despite its absence in the
official international billiards event.
Billiards, four-ball, creativity.
Rules
ACM Classification Keywords
H5.m. Information interfaces and presentation (e.g., HCI):
Miscellaneous.
INTRODUCTION
Creativity can have all kinds of different meanings. Some
say it is an ability to make things, some say it is thinking
outside the box, and so on. In sports, however, we often
hear commentators yelling “What a creative play!” or
“Jordan with a creative pass.” such as in basketball or
soccer. What does creative mean in this context? Do games
in general develop or promote creativity?
Rand stated that without rules there is no motivation, test of
skill, or ultimate reward—no game [2]. Furthermore
without rules, there is no creativity. Sports do have
motivation (to win) and rules, and therefore it must involve
creativity. To find a creative activity in sports, I tried to
explore with a billiard game called four-ball. In billiards,
each and every play is different despite the same table, the
same number of balls, and the same starting positions. Here
we describe the rules of four-ball, physics behind billiards,
and show the result of experiments to explore thinking
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A variant of four-ball is the East Asian game yotsudama
(Japanese for "four balls") or sagu (Korean for "four balls").
The game is played with two red object balls, one white cue
ball and one yellow cue ball (or sometimes both cue balls
are white, one having a red spot). Each of the two players is
assigned his or her own cue ball. A point is scored when the
shooter caroms on both red balls. The shooter is penalized a
point for failure to carom on either red ball or if the shooter
causes his cue ball to carom off the opponent's cue ball.
Thus, the shooter must avoid any carom or kiss off of the
opponent's ball while striving to carom on the two red
object balls. A carom on only one red ball results in no
points but ends the shooter's inning. In the Korean version,
the players work their way down from their respective
handicaps. After having scored the final point a win is
secured by doing a three-cushion shot. In this paper, we
only follow Korean (sagu) rule due to its limited
accessibility around Georgia Tech.
Physics and Movement
To better understand how ball movements are determined,
we briefly describe rule of physics behind the billiards balls.
First, cue position affects how the cue ball moves after it
hits either the rail or the first red ball. The vertical axis of
the cue ball induces the forward and backward move after
the hit because of the spin it’s giving towards the direction
of the movement and vice versa. Similarly, the horizontal
axis controls the cue ball’s movement to the left and right
because of clockwise or counter-clockwise spin. For
example, if the ball was hit on 11 o’clock position, it will
move towards left and front. When it is hit in the center,
there is no spin; therefore, no movements are made after
hitting the red ball. (See figure 1).
Secondly, the rule of an angle of incidence and angle of
reflection applies. If the cue ball is hit with no spin and
incidence angle is 0° (or 180°; straight), its reflection angle
is also 0°. Intuitively, the amount of spin, or cue position on
the horizontal axis, affects the reflection of angle. See
figure 1 for more detail.
Figure 2. Angle of separation.
(center, 1/4, 1/2, 3/4 from left to right)
EXPERIMENT
Figure 1. Cue points induce different ball movements
Lastly, the angle of separation is determined by angle
between the cue ball and the red ball and power of the
impact. Without a deep understanding of physics, we know
that if a moving object hits a stationary object slightly off
the center, they would move against each other forming the
same separation angle. This is precisely what happens in
four-ball. If the cue ball hits the half of the red ball, it will
move 45° off from the surface. If it was hit “thin”, degree
gets bigger, and if it was hit “thick”, degree gets smaller.
Another factor is the power of the impact on the cue ball. If
it was hit hard, the forward movement reduces at the
moment of impact; therefore falling short. (See figure 2)
There are some calculations that can be performed for
finding the right angle; however we will not discuss about it
as it is beyond the scope of the paper.
Path
As demonstrated, there are three things to be considered
when hitting the cue ball: cue position, angle (or thickness),
and power. Of course, there are some easy shots, and tough
shots. In many cases, some shapes or patterns appear
frequently, and therefore players seem to learn paths for
certain set. The most basic sets are those which do not
require cushion.
In many cases, player’s only need to hit cue ball adjusting
the thickness to hit the first red ball. Some sets may require
cushions such as back-door rotation, front-door rotation,
side- rotation, two-round rotation, and so on (see figure 3).
In this paper, we wanted to explore how players’ thinking
processes differ, though there are some familiar shapes or
patterns.
In the first experiment, we introduced them with premade
sets to find the difference between experience levels. In the
second experiment, we let players to free-play, and
recorded their cue positions, thickness, and power of the
shot.
First Experiment
We recruited two experienced (handicap over 100) and two
novice (handicap less than 100) players for the first
experiment. In this experiment, we were interested if the
level of experienced made differences in their behavior. To
test this, we gave each person the same set and recorded
how they shot. For novice players they were given three
trials whereas the experienced were given only twice.
The sets were divided into two parts. One was the basic set,
which does not involve cushion. The other was the ones
that involve a cushion or more by either blocking the first
red ball with opponent’s ball or placing the second red ball
into a position where using cushion might benefit.
The results of the basic test showed that, people who
participated in this study knew and followed the
conventional path no matter what their level of experience
was. In another words, they all shot quite the same. Though
this was considered to be a “basic” set, the experienced
group did not feel much comfortable. This is due to its
difficulty of making a shot with perfect angle and power.
Surprisingly, the one of the experienced group participant
expressed that it is easier to make a shot with cushion
because it could make an angle with a higher chance of
hitting the second red ball.
The result of advanced sets which include cushion shots
came out to be the same as the basic sets. There were some
differences in the rate of success between those groups, but
the chosen paths were uniform. For novice group
participants, they had some shots thinner or thicker, hit
harder or softer than the experienced group, or cue points
were not hit as he wanted to. This may indicate that the
difference between two groups is not the way of their
thinking but a physical one.
you would actually do at the real four-ball game. First you
choose the angle, then the cue position, and then select the
power by releasing the mouse button at the power level you
want. (See figure 4)
This game allowed us to look at it from different angle as
physical part becomes negligible and let user to be creative
in their decision of making shots. Also, there is a 30seconds time limit for each shot to play, which forces the
players to come up with best shot under pressure. To
observe users behavior, the experimenter played in the
“practice room,” which doesn’t require any money and
allows playing with any level of users, with other users. The
experimenter spent an extensive amount of time to analyze
and conclude their behavior.
As we have hypothesized that the absence of physical
challenge would encourage players’ creativity, this turned
out with the positive results. Players were making what are
known to be almost impossible or very tough shots many
times. Further, unlike the experienced group from the first
experiment told us, most of the users were making direct
shots or one cushion shots. For example, in case of Figure
3b (front-door rotation routine), many of them actually shot
straight ahead with cue position towards bottom, so that it
will create backward movement after hitting the first red
ball and come back straight. This is a very tough shot in
reality, and requires superb control of the cue.
We believe this is mainly because of the time limit and
ability to make tough shots without worrying about their
physical contact. Another reason for this might be because
of the lack of actual game experience. Many of the users in
BilliardMaina are young who doesn’t have financial
capabilities to go to billiards place and tend to avoid going
to place as billiards is not considered as a healthy recreation
in Korean culture.
Figure 3. Examples of cushion shots.
back-door rotation, front-door rotation, side-rotation, and
two-round rotation (from top to bottom)
Second Experiment
To see how others do and choose their shots, we wanted to
look at many people playing. Due to its time and cost limits,
we looked at the on-line four-ball simulation game as an
alternative method. The procedure is quite similar to what
Figure 4 Screenshot of Hangame BilliardsMania
CONCLUSION
In this paper, we introduced a billiard game called four-ball
and its rules. We conducted two experiments; one in reality
with different level of players, and another using on-line
game simulator. Two experiments showed widely different
results and we believe this is due to the difference or the
lack difficulty of making physical shots. In short, in reality
ability to make good shot determines the path, and if there
were no constraints in physical aspect, people came up with
different shots.
It may be too radical to generalize the result of this
experiment to other sports; however, in reality being
creative playing sports would mean one can create a tough
play look easy because it is unthinkable to begin with. In
short, sport is a physical game and creativity comes after.
ACKNOWLEDGMENTS
I would like to thank Dr. Ellen Do for leading Creativity
Design and Cognition class, friends who played four-balls
with me.
REFERENCES
1. Froeshcle, Robert (1971). Official Rule Book for All
Pocket & Carom Billiard Games. Billiard Congress of
America.
2. Rand, P, 1965 Design and the Play Instinct, in
Education of Vision, ed. Gyorgy Kepes (George
Braziller. 1965) (pp154-173)
3. BilliardsMania, Hangame
http://game1.hangame.com/billmania.nhn