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June 1, 2005

The Great Yu-Gi-Oh! Simulation Study

One of the greatest aspects of any game is the discussion that centers around the best way to handle things.  This could be as abstract as deciding a national championship in football, the validity of the trap system in hockey, or the best kind of deck to use in Yu-gi-oh. Yu-gi-oh, in fact, is responsible for a number of interesting discussions which one can find on the internet, particularly in the discussion boards on this site.

In a discussion on one of Napay’s first articles, regarding the probability of a win on the first turn for a duellist using an Exodia deck, it occurred to me that many of these questions can be answered using a technique called simulation, which allows us to examine situations empirically.

So, what does that all mean? I’m glad you asked! See, games like chess and poker are easy to program into a computer. Chess pieces have rules they have to follow, poker hands are fixed in value – generally there is not much decision-making going on.  However, a game like Yu-gi-oh is very difficult to program.  Each card has a different effect, and there is no specific set of rules on how to play each card, other than a set of basic rules for types of cards (chaining, and so on).  Even those basic rules are malleable, in that some traps are chainable, and some are not.  You get the idea…

So, how do we simulate the game without the use of a computer?  Another great question, and the answer lies in the same place we look for all these great questions: the Pojo Discussion Boards. Thanks to the great response, more than thirty duellists have volunteered to be a part of the first Yu-gi-oh Simulation Study in history. While you read this, duellists are preparing the experimental deck for the first phase of this scientific endeavor. Each participant will be randomized to one of two groups (experiment and control) and each pair will duel a fixed number of times.  Using a specific deck, we can look at the effects we want to measure by controlling for various other factors. Duellists from all over the world, representing various age groups and experience levels, have all volunteered to be part of this massive project.

PHASE I: Optimal Deck Size

Our first set of experiments will center around the optimal number of cards in a deck.  We will look at the effect of adding a single card to a pre-approved experimental deck containing forty cards.  Forty is the minimum size allowed by the rules, but no maximum card limit is enforced.  However, many people who play this game insist that more than 40 cards is detrimental to the success of the deck.  We will test this by having two opponents play each other.  The deck played by the experimental opponent will have 41 cards, while the control opponent’s deck will have 40.  Our null hypothesis is that, if the extra card has no effect at all, the control opponent should win about half of all games played.  We are testing against an alternative that the proportion of wins is something else (although we should say something larger than 0.5, we will use the two-tailed approach for more statistical power). Further examination for this phase will include addition of more than one card as well, in an effort to answer three basic questions:

1. Is the additional of a single card as detrimental as everyone says?
2. Is there a upper limit to deck size where the addition of cards severely hurts your chances for victory?
3. Is there an optimal deck size which serves to maximize your chances for victory?

We can do a simple significance test to look at the win proportion for the control deck, but to really know if we have a significant difference, we will need to look at our analysis after adjusting for confounding variables like age and years of experience with Yu-gi-oh.  In addition, we will also adjust for the round of play, as people tend to play better with a deck after multiple games.  Adjusting for this may tease out any learning effect.

FOLLOW-UP PHASES

The application of simulation to Yu-gi-oh allows us to explore a number of various questions.  We are not limited to deck size.  We can investigate deck types, strength of structure decks, the effect of going first in a duel, the win rate when cards like Pot of Greed, Graceful Charity and/or Delinquent Duo are played on the first turn, and so on.  I am sure that, after having read this, you have ideas for other experiments, or may be interested in participating.  Find my threads on the discussion boards or send me an e-mail at ygoprofessor@bellsouth.net . Thanks for reading, and look forward to future articles on this ground-breaking study.