This essay will examine theoretical and experimental probability in relation to the Korean card game called Sut-Da. First, a definition of probability and how it is used in general life will be examined. Each hand of Sut-Da provides the theore

Authors Avatar

ABSTRACT

This essay will examine theoretical and experimental probability in relation to the Korean card game called ‘Sut-Da’. First, a definition of probability and how it is used in general life will be examined. Each hand of ‘Sut-Da’ provides the theoretical probability for a player to win the game. It is clear however, that the theoretical value of winning in ‘Sut-Da’ does not always apply in real life games. Secondly, the experimental probability of winning for each hand is examined. To find out the probability of winning with each hand, I am using permutation & combination, theoretical probability and experimental probability. Experimental probability data was gained from my friend and I playing the game. Finally, within my evaluation, I looked at experimental probability using excel spread sheets and also using calculations that were compared with the experimental probability data gained from actually playing the game. The theory of probability has been covered in a number of textbooks and I used these textbooks to help me get used to the formula. I have then worked out all the possibilities of hands and their probabilities for winning, performing all the calculations myself and using my own numbers in presenting my data for the experimental probability data.

Introduction

        It all began when I started to watch a Korean drama called “Ta-JJa”. I decided to watch this drama as one of my favourite actor was the main character in the drama. This drama was about this man getting into the world of gambling in order to be successful in his life. This drama was only based on the tricks that could have been used while playing the game “Sut-Da”. Then the drama made me to wonder whether this game plays under the concept of probability and also questioned me if the game was a fair game or not. Hence came to decision to make this as my extended essay topic.

         I will first introduce what is probability and the game called “Sut-Da”. Everyone has different definition for probability and it depends on which perspective the people looks from, but generally, probability is the measure of how likely for an event to occur.

        Throughout this essay, these two games will be set under few conditions. These conditions are;

        1. Number of players are 2

2. The deck is shuffled 10 times after the game in order to create a fair deck every round

My research question becomes:

What are the possibilities of winning in “Sut-Da” and how does the theoretical value compare with the experimental value?

        I will start by giving brief idea on what is probability and how it relates to the real life world situations. I will then start examining the chances of getting each hand with “Sut-Da” then compare with the experimental value. I will be using the probability theory and combination theory to calculate each hand for the “Sut-Da” game and use trial and error for experimental value. I will then investigate similar concepts that are being used in different parts in the world.

Understanding the Concepts

        1. Probability

1. What is Probability?

There are number of different definitions of mathematical probability which have been proposed by various authors. The scientific definition of a ‘fundamental’ concept such as “the concept of probability is merely the refinement and logical processing of a series of very simple observations and practical methods that have proved their value by successful use over a long period of time”. (GendenkoB., SecklerB.) Also, it could be written as a quantitative measure of the degree of certainty of the observer or the relative frequency of occurrence of the even in a large number of trials or it could be defined as mathematical method to describe the ‘chance’ or ‘likelihood’ of an event happening. (UrbanPaul, MartinDavid, HaeseRobert)

2. History of Probability  

It is known that the development of probability theory was begun in 17th century; however, it was firstly performed by Girocardano (1501-1576) an Italian mathematician, physician and gambler. He created a manual discussing many of the basic concepts of probability. However, his work did not get revealed until 1663 and received little attention.

The development of modern probability theory began in 1653. It started when one gambler made a contact with the mathematician, ‘Blaise Pascal’, with a problem on how to divide the stacks when the gambling game has been interrupted. Pascal involved ‘Pierre de Fermat’ and together solved the problem. During this process, they created the foundation of the laws of probability.

        

3. Experimental Probability

        The number of trial is the total number of times the experiment is repeated.

        The outcomes are the different results possible for one trial of the experiment

The frequency of a particular outcome is the number of times that this outcome is observed.

The relative frequency of an outcome is the frequency of that outcome expressed as a percentage of the total number of trials.

For example, when a wooden cone was thrown 200 times it fell on its side 123 times and on its base 77 times.

The relative frequency of side and base are;

        123/200 = 61.5%        and        77/200 = 38.5%

        4. Theoretical Probability

Theoretical probability is based on what we theoretically predict to occur. It measures the chance of that event occurring in any trials of an experiment.

Probability =

For example, when a dice was thrown chance of getting a ‘6’ is 1/6 and when a dice was thrown chance of getting ‘2’ and ‘3’ is 1/2.

        2. Game

        “Sut-Da”

                The game is called "Sut-Da", this game uses cards called "Hwa Too"                         which was originated from Japanese cards called “Danafuda”. Cards were                 spread around early 19th century, when Japanese merchants visited                         Korea frequently. The cards are made up of 48 cards, 4 cards each                         represent each month of the year.
                Each month has different names; January is Song-Hak, February is Mae-                        Jo, March is But-Ggot, April is Huk-Ssa-Ri, May is Nan-Cho, June is Mo-                        Ran, July is Hong-Ssa-Ri, August is Gong-San, September is Kook-Jun,                         October is Dan-Feng, November is Oh-Dong and December is Bi.
                This game "Sut-Da" does not use all these 48 cards but only uses 20                         cards. This game can hold two to ten people in one game, however in this                         essay, there will be 2 people playing the game.
                There are two ways of dealing; first one is each player receive two cards                         each and then reveal the cards to see who has the highest hand. Second                         one is each player receive three cards, create a highest hand possible                         with using only two cards from three and burn the unused card. The word                         ‘burn’ in previous sentence means to throw away and not use the card in                         the game. But in this essay, the first dealing type will be used.

                These 20 cards are 2 cards from each month, except for November and                         December.

                Diagram 1. Cards Used to Play Sut-Da

                                

                        1                2                       3                      4                    5

                
                        6                7                       8                      9                   10

        
                There are total of, 12 types of hands from highest to lowest; 3-8 Guang-                        Ddaeng, Guang-Ddaeng, Ddaeng, Ali, Dok-sa, Gu-Bbing, Jang-Bbing,                         Jang-Sa, Sae-Luk, Gab-Oh, Gget, Mang-Tong.


                3-8 Guang-Ddaeng is when a player gets March and August card with                         光.This Chinese character光 locates in right bottom corner of January and                 left bottom corners for March and August. Different types of cards may                         have different Chinese characters replacing the original character光.

Join now!

                Diagram 2. Example of 3-8 Guang-Ddaeng
                

                Guang-Ddaeng is when a player gets January and March or January and                         August card with 光.

                Diagram 3,4. Examples of Guang-Ddaeng
                                             

                Ddaeng is when a player gets any same months, October is highest and                         January is lowest.

                Diagram 5. Examples of Each Ddaeng
                

                Ali is when a player gets two cards formed from January and February.

                Diagram 6. Examples of Ali
                

                Dok-sa is when a player gets two cards formed from January and April.

                Diagram 7. Examples of Dok-Sa
                

                Gu-Bbing is when a player gets two cards formed from January and                         September.

                Diagram 8. ...

This is a preview of the whole essay