# 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

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Introduction

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”.

Middle

Probability of winning with April (Ddaeng-4) is split into eight different possibilities

Graph 7. Tree Diagram of Ddang-4

= 4.9545604 x 10-3

Probability of winning with March (Ddaeng-3) is split into nine different possibilities.

Graph 8. Tree Diagram of Ddang-3

For Ddaeng-3, it is slightly different than other hands. This is because Ddaeng-3 includes a card that has 光. As this hand requires光card to complete the hand, 3-8 Guang-Ddaeng and 1-3 Guang-Ddaeng cannot be created. Hence these two hands were eliminated from the probability of opponent winning.

= 4.9879601 x 10-3

Probability of winning with February (Ddaeng-2) is split into ten different possibilities.

Graph 9. Tree Diagram of Ddang-2

= 4.8847609 x 10-3

Probability of winning with January (Ddaeng-1) is split into eleven different possibilities.

Graph 10. Tree Diagram of Ddang-1

For this hand, it is similar with Ddaeng-3. Because this hand requires 光card, 1-3 Guang-Ddaeng and 1-8 Guang-Ddaeng cannot be created. Hence these two hands were eliminated from the probability of opponent winning.

= 4.9191606 x 10-3

Ali

Probability for player 1 to get Ali is 2/20C2. Ali could be formed using one January and one February card; hence there are four combinations and 20C2 represents getting two cards from a deck of 20 cards. However, this needs to be split into two different ways where the January card may be 光card or not. Hence, the probability for player 1 to win with Ali is (1/2) x (2/20C2) x (1 – (10/18C2) – (12/18C2). (10/18C2) is the sum of probabilities where player 2 will win when player 1 has Ali with January 光card. (12/18C2) is the sum of probabilities where player 2 will win then player 1 has Ali with normal January card.

Hence, by subtracting from 1, 2nd bracket represents the sum of probabilities of player 2 receiving a lower hand than player 1.

P(player 1 win with Ali) =

= 9.76952185 x 10-3

Dok-Sa

Probability for player 1 to get Dok-Sa is 2/20C2.

Conclusion

However, considering that the game is limited, a game where the player has limited information, there are not many situations in different parts of the world that undergoes similar concepts. However, this could be seen similarly in combats between two groups. For example, when there is a debate between two parties, then both sides are going through the same concept compared to ‘Sut-Da’. Since they lack in information, they are handicapped in preparing for the discussion, however, they do have choice in what they will do in order to win the discussion.

To conclude, it was obtained by the calculations that the percentage difference between the theoretical probability and the experimental probability is similar for some hands but also have huge difference in other hands. To fix this problem, when the number of trials were increased, then the probability would be more spread out than by just having 1000 trials. Also, this concept of ‘Sut-Da’ could be seen in the combat between two groups such as debating.

Appendices

Appendix 1. Photos of My Friend and I Playing ‘Sut-Da’

## Bibliography

Chaudhri, Vivek. "Game Theory and Business Applications." Economic Record (2005): 88+.

"Game Theory." The Wilson Quarterly (2005): 92+.

Gendenko, B. V. and B. D. Seckler. The Theory of Probability. New York: Chelsea Publishing Company, 1962.

Hanafuda The Japanese Flowercard Game. 2010. 10 October 2009 <http://www.hanafuda.com/>.

Henry E. Kyburg, Jr. Probability Theory. Englewood Cliffs: Prentice-Hall, 1969.

Kneale, William. Probability and Induction. Oxford: Clarendon Press, 1949.

Leonard, Graham. Sutda. 26 04 2004. 12 December 2009 <http://hanafubuki.org/sutda.html>.

Urban, Paul, et al. Mathematics for the international students Mathematics HL (Core). Adelaide: Haese & Harris, 2008.

Wilson, Matthew C. "Uncertainty and Probability in Institutional Economics." Journal of Economic Issues (2007): 1087+.

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