Thursday, July 18, 2013

X's and O's. Scissors cut Paper.



By Lana Kang
lkang01@syr.edu

Do you have 10 seconds? Even a quick game can teach you something new or improve your social skills, memory, and mood.

Take some easy games from your childhood like Tic-Tac-Toe and Rock Paper Scissors. These can have surprising educational value and significantly contribute to skill and strategic development. 

Tic-Tac-Toe 

So how does one play Tic-Tac-Toe? It is often played on a 3x3 grid with two players using x’s and o’s as respectively. The players take turns putting (or drawing in) their icon in the grid. The object of the game is to get 3 in a row before your opponent. It is also possible for the game to end in a tie (no winner).

If you analyze the game, it becomes a game of reactions. Player 1 initiates, Player 2 reacts, Player 1 reacts, etc. But if you break it down further, how does Player 1 choose where to place their chip? Oftentimes, they analyze the board and which location would give them the best chance for winning.


  (from “The Educational Value of Tic-Tac-Toe for Four-to Six-Year-Olds” by Constance Kamii and Mariko Nagahiro)
 

When Player 2 reacts, do they react by initiating their own attack or choose to take a more defensive stance (blocking your opponent) right off the bat?

This cost/gain analysis on whether to take a more risky and aggressive stance or a more defensive position can be applied to fields such as business, economics and the stock market, or even to war strategies. For example (if we take a storytelling view of it), say the grid represents a country and the goal of the players (generals) is to make it across the country with their armies before the other. Each X and O represents a supply train and the supply train must stretch across the board for the armies to cross successfully. 


While tic-tac-toe has been played by all ages and all around the world for centuries, it can be the base of some very interesting and in-depth study. It has been applied by Kamii and Nagahiro (2008) to measure development in 4-6 year olds “because it encourages children to make many kinds of logico-mathematical relations a) in an inter-related way and b) in a hierarchical way” (pg. 3).  The inter-related relationships come from Piaget and include classification, serial, numerical, spatial, and temporal while the hierarchical aspect shows that the development in the inter-related relationships becomes more sophisticated with age and practice (Kamii and Nagahiro 2008). Another study focused on tic-tac-toe with a mathematical analysis in a probabilistic neural network context (Grim, Somol, and Pudil 2005).   

Rock Paper Scissors (RPS)


RPS is a well-known game, like Tic-Tac-Toe, used by people of all ages and throughout the world. 



Often used for minor decisions such as who gets to go first, ride shotgun, get the last piece of pie, the rules are simple. Two or more people can play. The players count or say, “Rock, Paper, Scissors Shoot! And put out their hand in the shape of one of the three objects (see above). Rock crushes scissors, scissors cut paper, paper covers rock. 




While on the outside, it seems like a game of random chance, RPS requires a choice by the player. You analyze your opponent. You remember what they have already thrown down and you decide which choice will give you the best odds of winning. There are also several strategies and gambits one can use to win, confuse your opponent, or to learn your opponent (Eyler, Shalla, Doumaux, & and McDevitt, 2009 and The Washington Times, 2004). Reading your opponent is the most important strategy point for RPS since it, like Poker, can give a player the competitive edge. 

In a New York Times article interviewing two RPS Champions, Bob Cooper (World Champion) and Bryan Bennett (N. America Champion) the social aspect is stressed by both. In particular, they stress reading opponents. According to Cooper, “It is not about predicting what your opponent will throw; it is about predicting what your opponent predicts you will throw.” Bennett adds, “Jocks and meatheads like to start with rock. Women are often partial to scissors. More ethereal types prefer paper.” He prefers playing against men since he finds women harder to read and his strategies include using body language tells and reading playing patterns such as gambits (Applebome 2006).  

Another opinion was given by Douglas Walker, co-founder of the World RPS Society in an interview with The Washington Times. He believed that the hands used in play reveal characteristics about a player. “Paper is subtle, the choice of intellectual, passive-aggressive types. Scissors are devious, a tool of controlled malice. Rock is between-the-eyes intimidation, preferred by beginners and players who have been backed into a corner.” (The Washington Times, 2004)

For more about RPS gambits and patterns, go to the World RPS Society’s web page. http://www.worldrps.com/gambits.html

For more on mathematical analyses and strategies for winning in RPS, please read “Winning at Rock-Paper-Scissors” by Derek Eyler, Zachary Shalla, Andrew Doumaux and Tim McDevitt or “Rock Paper Scissors” by Bryan McCannon. 

References



Applebome, P. (2006, November 26). A Winning Hand, and a Zen Master. New York Times. Retrieved from http://www.nytimes.com/2006/11/26/nyregion/26towns.html?_r=1&

Eyler, D., Shalla, Z., Doumaux, A., & and McDevitt, T. (2009). Winning at Rock-Paper-Scissors. Mathematical Association of America, 125-1285. Retrieved from http://www.jstor.org/stable/25653686

Grim, J., Somol, P., & Pavel, P. (2005, September). Probabilistic neural network playing and learning Tic-Tac-Toe. Pattern Recognition Letters, 26(12), 1866-1873. doi:http://dx.doi.org/10.1016/j.patrec.2005.03.008

Kamii, C., & Nagahiro, M. (2008, May). The Educational Value of Tic-Tac-Tow for Four- to Six-Year-Olds. Teaching Children Mathematics, 14(9), 523-527. Retrieved from http://www.jstor.org/stable/41199962

McCannon, B. (2007). Rock Paper Scissors. Journal of Economics, 92(1), pp. 67-88. doi:http://dx.doi.org/10.1007/s00712-007-0263-5

The Washington Times. (2004, December 10). Fists Fly in Game of Strategy. The Washington Times. Retrieved from http://www.washingtontimes.com/news/2004/dec/10/20041210-120729-4008r/?page=all#pagebreak

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