Alea iacta est The die is cast.
Alea iacta est – The die is cast.*
*Quote Julius Caesar in reference to crossing the river Rubicon and, in doing so, starting the Roman civil war.
Abstract
Statistical analyses from more than 250 YCS Yu-Gi-Oh! matches were performed to determine whether starting a match has a beneficial effect on the outcome. Further analyses investigated format and deck type effects on the relationship between starting a match and the outcome of that match. A take home message with practical tips for duelists has been composed based on the evidence found in this research.
0) Table of Contents
1) Introduction
2) The Data
3) Statistical Terms
4) Results
4.1) General Results
4.2) Specific Results: Format Effect
4.3) Specific Results: Deck Type Effect
5) Take-Home Message
6) Confounding Variables
7) Suggestions for Further Analyses
8) Closing Notes
1) IntroductionThe game of Yu-Gi-Oh! is a turn-based game where players alternate in taking turns. During a player’s turn there are a wide array of possible actions to undertake. Some of these actions are only available during a respective player’s turn, as soon as that player forfeits his/her turn, these actions become unavailable until the turn is passed back again. Being able to perform a turn is considered more beneficial as opposed to not, since both the quantity and quality of available actions during a turn outrank the quality and quantity of available actions during an opponent’s turn. In Yu-Gi-Oh!, like in any other turn-based game, one of the players starts the match by taking the first turn. When a duelist has randomly been appointed to start the duel, the rules of the game try to compensate the opposing player by restricting the turn player (hereafter referred to as TP) in performing a subset of the actions he/she would normally be able to perform during any other turn (e.g. not being able to attack on the first turn).These rules suggest that there is an inherent advantage to starting a match as it is deemed necessary to compensate the non-turn player (hereafter referred to as NTP) for the fact that he/she has to take the game’s second turn.The purpose of this article is to call into question whether the compensation the NTP receives matches the advantage the TP receives. Therefore, this article examines whether or not starting the match has a significant effect on the outcome of that match.The hypothesis in this article is that starting a match gives a duelist a better chance to win that match.2) The DataData for this article was drawn from 272 Yu-Gi-Oh! matches that took place in YCS events in TCG areas between June 16th 2010 (YCS Washington) and April 17th 2011 (YCS Paris) and were featured on the YCS coverage websites*. Data from YCS Mexico City were unavailable and was excluded from analysis. Results from Dragon Duel events were also excluded to avoid a two-fold bias. Firstly, this type of event is only open for a specific age category. In order to avoid age-related effects, these data were excluded from analysis. Secondly, reports from this type of event are mostly limited to the final matches. In order to avoid duelist competence-related effects, these data were excluded from analysis. Matches which ended in a draw were also excluded from analysis (out of all the featured matches, only one ended in a draw).* Coverage of North American YCS events can be found at: http://www.konami.com/yugioh/blog/* Coverage of European YCS events can be found at: http://tcg.konami-europe.net/coverage/3) Statistical TermsTwo variables were defined, ‘Winning/losing the die roll’ and ‘Winning/losing the match’. Winning was coded with ‘1’, losing was coded with ‘0’. The compilation of the data resulted in a data file that displayed whether a duelist won the die roll and whether he/she won the subsequent match.The data file was used to calculate a Pearson correlation, a measure for the dependence between two variables. The Pearson correlation is a number between -1 and +1. A negative correlation implies that an increase in the first variable is accompanied by a decrease in the second variable. A positive correlation suggests that an increase in the first variable is accompanied by an increase in the second variable. A zero-correlation implies that there is no statistical relationship between the two variables.In this article, a positive correlation suggests that winning the die roll at the start of the match increased the odds of winning the subsequent match. A negative correlation suggests that winning the die roll resulted in a decreased chance of winning the subsequent match. A zero-correlation suggests that winning the die roll and winning the match were unrelated.According to the hypothesis of this article, the correlation between ‘Winning/losing the die roll’ and ‘Winning/losing the match’ should be a significant positive one.4) ResultsIn this section we will first review the general results. These results were calculated based on all available data. It provides us with an answer to the general question of whether or not starting a match leads to an increased chance of winning the subsequent match. Since the data cover multiple formats, YCS events, duelists and deck types, we can rule out most confounding effects from these variables.After studying these general results we will look into some specific results. We will check for effects from the format and deck type.4.1) General ResultsA Pearson Correlation coefficient of +0.162 was obtained for the total of 272 matches. The result was statistically significant meaning that the result differs enough from a zero-correlation to reject the hypothesis that there is no statistical relationship between the two variables. This suggests that there is indeed a relationship between winning the die roll and winning the subsequent match. If a duelist wins the die roll at the start of the match, then regardless of decktype, format, or other anticipated variables, that duelist has a better chance of winning the match then his/her opponent. Luckily for the game of Yu-Gi-Oh! the effect size is small which means that there are other factors that play a role in determining the outcome of a match.Winning the die roll puts a duelist ahead but does not imply a certain win.4.2) Specific Results: Format EffectOne of the advantages the TP gets when starting a match is the fact that he/she can set spell or trap cards without NTP interference. Since the banning of ‘Heavy Storm’, duelists do not have to fear immediate mass destruction of their spells/traps. As a consequence, the game of Yu-Gi-Oh! has seen an increase in the number of cards that are set in the back row during a match. Since this can be done freely by the duelist taking the first turn in a match, it seems to be expected that duelists gain more advantage from taking the first turn in a match since the banning of ‘Heavy Storm’ then before. To test this hypothesis, data from before and after the banning of ‘Heavy Storm’ were compared.Analysis revealed remarkable effects. The general results were confirmed in the post-banning of ‘Heavy Storm’ (significant Pearson correlation of +0.245) but not in the pre-banning of ‘Heavy Storm’ (non-significant Pearson correlation of -0.133). These results signal that before the banning of ‘Heavy Storm’, there was no positive relationship between ‘Winning/losing the die roll’ and ‘Winning /losing the match’. However, since the banning of ‘Heavy Storm’, this relationship is in fact present, implying that a duelist playing in the post-banning of ‘Heavy Storm’ gains more advantage from going first in a match than a duelist going first during the pre-banning of ‘Heavy Storm’.This can be interpreted as: Being able to set (more) cards, unhindered by the opponent, during the first turn of a match has a significant outcome on the result of said match with the duelist going first having advantage.4.3) Specific Results: Deck Type EffectSome deck types in the game of Yu-Gi-Oh! revolve more around explosive combo’s than others. Being able to perform an explosive combo during the first turn of a duel, while the TP is almost entirely unhindered by the NTP, should lead to a significant advantage for such deck types when they are able to take the first turn. Conversely, these decks should suffer more when they are not able to perform their explosive combo during the first turn of a match.In order to investigate this hypothesis, we will look into the results set by Legendary Six Samurai decks. These decks revolve, among other things, around the synchro summon of ‘The Legendary Six - Samurai Shi-En’. Since this play can be made relatively unhindered during the first turn of a match, this deck type qualifies as a valid test subject for our hypothesis.The data used for this analysis are drawn from every match that involved at least one Legendary Six Samurai deck in the YCS’s held since the release of the archetype. These YCS’s involve YCS Dallas, Charlotte, Anaheim and Paris respectively.Results show a confirmation of the hypothesis. When Six Samurai are allowed to take the first turn, there is a positive correlation (+0.259) between winning the die roll and winning the match. When Six Samurai are not allowed to take the first turn, there is also a positive correlation (+0.400) between winning the die roll and winning the match. This means that when a Six Samurai player is allowed to take the first turn, chances of winning the match rise for that player. When the Six Samurai player is not allowed to take the first turn in the match, chances of winning the match rise for the opponent of the Six Samurai player. Due to the small sample sizes of these analyses, the effects that are reported border on non-significant.5) Take Home MessageA) Winning the die roll puts a duelist ahead but does not imply a certain win.-> When you win the die roll and get to choose which duelist goes first, pick yourself to go first. Your chances of winning the match will increase.B) Being able to set (more) cards during the first turn of a match, unhindered by your opponent, has a significant outcome on the result of said match with the duelist going first having the advantage.-> Going second in a match? Don’t play into the opponent’s Spells/Traps but wait for your own set Spells/Traps to come into play. This does not imply that it is best to avoid summoning a monster and trying to attack with that monster. It merely means that a duelist should hold off any large explosive play if possible.C) When a Six Samurai deck is allowed to take the first turn, chances of winning the match rise for the Six Samurai player. When the Six Samurai player is not allowed to take the first turn in the match, chances of winning the match rise for the opponent of the Six Samurai deck.-> Playing versus Six Samurais? Maindeck cards like ‘Effect Veiler’ so that you are able to interfere with the Six Samurai player’s first turn. By doing so you can partly compensate for the advantage the Six Samurai player has when starting the match.6) Confounding variablesYCS coverage features matches during the entire course of a tournament. Part of these matches take place during the Swiss rounds of the main event. Another part of the covered matches take place during the knock-out portion of the tournament wherein only the very best players remain. Since coverage is fixed on two feature matches per round, a disproportionately large amount of coverage goes to the relatively smaller knock-out portion of the YCS events. This may bias the results away from the average Yu-Gi-Oh! match during the Swiss rounds towards the high-profile Yu-Gi-Oh! matches played near the end of a YCS event.7) Suggestions for further analysesInstead of looking at the correlation between ‘Winning/losing the die roll’ and ‘Winning/losing the match’, it would be interesting to look at the correlation between ‘Winning/losing the die roll’ and ‘Winning/losing the duel’. This would lead to a larger sample size since every match consists of at least two duels wherein at least two different players start the duel.It would also be interesting to look at the correlations between both aforementioned variables for matches held in the Swiss portion of the YCS events and the knock-out portions of the YCS events.Further statistical analyses could be carried out to more firmly prove causation between the studied variables.8) Closing notesThis article was written by €-C on 19/04/2011 for Yugiohforums.com ‘s article section. I have written this to the best of my ability and with the best of intentions. Writing this has given me the chance to combine and learn more of two of my interests, my studies in Psychology (and the statistics that go with it) and the game I like so much, Yu-Gi-Oh!.Special thanks go to Perseus_Stoned, Dragondudea6 and my girlfriend for proofreading initial drafts of this article and providing me with help to correct errors and make it better.I’m open to any critiques and they can be posted here or pm’ed to my account on Yugiohforums.com.Feel free to copy/paste this article to other message boards, no permission is required. Do however be so kind to provide people with a link to the original article. Many thanks.
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