Tuesday, October 25, 2011

History Lesson 3: The Limit of Skill

                I have spent more time on what I am about to discuss than probably any single other subject in my entire life.  In fact, I once wrote a book on it, although the text has been lost to the ravages of a nomadic existence and several computer updates, I’m trying to pull most of the concepts and ideas back together, so we will see if I can get a solid monograph constructed at some point.

                Essentially, you can sum all 80,000 words up in one sentence:
·         Concerning any human activity not bound expressly by direct manipulation of all integral elements, there exists a point at which the outcome of random chance exceeds the ability of the actor.

As a Magic player, this relates to you because at some point, unrelated to your playtesting, theory,
or skill, luck begins to affect your results in important and unalterable ways. 
                Ashley Moray wrote an interesting article on StarCity last week that is notable for several reasons, but the issue I am writing about today involves her contention that given a large enough sample size, luck cannot explain your lack of success or your excess of it.  She is trying to suggest that if you are a skilled player, you will learn to ignore or move beyond mana screw, top-decks, or unbeatable match-ups, and enter some vaguely Elysian plane wherein your actions always dictate the outcomes of your game.

                It is my contention that the converse is actually more accurate, and in this article I want to explain why it makes sense so that next week, we can explore how we can either take advantage of the notion, or what needs to be done to minimize the damage. 

First, Ignore the Man Behind the Curtain

                Any article that suggests that luck does not factor into our game is trying to pull the wool over your eyes.  There is an anti-gambler’s fallacy at work here, known usually as the Myth of Horatio Alger.  Several notable, intelligent, and rational players fall victim to this concept.  They believe that if you work hard, practice every day, and generally lead a good life, that good things will happen to you. 
                Before we can get into anything more complicated, you need to understand that this myth is patently untrue when interpreted to mean that doing such things directly affects the outcome of such activity.  Whether it is in Magic, or life, pursuing this course of action does not guarantee anything.  One of the most important things to learn is that there is a man behind the curtain, and all you can do is maximize your opportunities to become friends with him.

Second, You Are Playing a Game of Chance, not Skill

                This is probably more misunderstood than any other issue at the basic theoretical level of Magic.  R&D has been specifically designing the game to increase the effect of random chance on the outcome of matches in order to appeal to the widest variety of players (they have even said so).

                Good players, skilled players, win more often at Magic not because they have some secret ninja ability that allows them to “make the right play” but because they recognize and understand—even subconsciously—that the game is random and they play in a certain way to minimize the impact of that randomness.

                If you haven’t figured out where I am going with this yet, I’m going to stop taking the roundabout way and arrive directly at my point:  You win games not in spite of the randomness but because of it.  A well-tuned deck and course of play is designed and executed to minimize the random elements of the game and people do not seem to understand what this means!

                For example, Kai Budde’s Morphling topdeck was widely regarded as the “luckiest” moment in Pro Tour history—until Craig Jone’s Lightning Helix, of course.  Commentators and the general public were constantly talking about the importance of how Kai was “playing for that top deck”.  Flores has said on multiple occasions that Kai knew what he had to draw in order to win, and then played in a way that “allowed him to get lucky.”  But no one ever seems to comprehend that this is the very basis of the game at every stage: pre-game, sideboarding, and post-match. 

                It flabbergasts me that people use this notion as a defense of skill, rather than as a head nod towards the reality of luck.  If Kai had not drawn the Morphling on that exact turn, there would be considerably fewer people who even know about the incident, let alone still talk about it.

Third, Do You Feel Lucky?

                I have mentioned in this column (and my other one) about how match-ups have evolved to the point that almost any two deck s are very close to 50-50, usually deviating only by a maximum of 10% either way. 
                This issue is where the name of my other column comes from, The Extra 2%.  Finding the miniscule edges, and trying to create a situation (usually by large sample sizes) where those edges allow you to eek out wins, is the fundamental guiding principle behind improving in games of chance. 
                To give the single most important example, poker professionals make money by understanding exactly when to take advantage of a situation that favors them by fractions and always making the correct decision when that choice comes up. 

                So wait, it sounds like I am agreeing with Ashley, right?  Well, yes.  But I disagree with her conclusion.  Proponents of poker love to make the statement that the game involves considerably more skill than opponents of the game perceive.  This is factually correct, but it is flawed for the same reason that Ashley’s conclusion is flawed.  Poker is a game of chance that involves skill.  By contrast, golf is a game of skill that involves chance.  By the same token, Magic is a game of chance that involves skill (more skill than poker, although not as much as people wish).  The other side would be a game like Magic, but with perfect information, and perhaps a die roll to influence the outcome of creature combat (I tried to find a game like this, but I couldn’t, and I apologize for that, I know they exist). 

                You can even simulate that game by playing with no hidden cards at all.  Try it sometime and see how you do.  Hands, libraries, everything revealed at all times.  Some players even do this while playtesting.  One thing you’ll quickly realize is that even with perfect information, sometimes you just lose.

                To conclude this section, when we look at a big tournament, say a Grand Prix, with the largest sample size possible in a single tournament setting, the difference between 8-2 and making the second day or going 7-3 by losing in the last round, is not going to be because of skill, but because of random events that happen during those last games.  The larger sample size actually works against you because it gives more opponents more opportunities to win via fluke circumstances. 

                To illustrate, let’s look at the result of a series of coin flips with a slightly weighted coin so that it comes up heads more often than tails.  If you were gambling on the outcome of 100 coin flips, you would choose heads to come up more often, and it goes without saying that you would usually be right.  In fact, because of the weight, you would win this gamble more than 55% of the time.  Again, this seems like I am agreeing with poker professionals and Ashley.  Here is where the gambler’s fallacy comes into play, because in a tournament setting, it isn’t all of the other coin flips that matter, it’s the last one.  You could win everything other flip, but if it comes down to it and the darn coin comes up tails, you are riding the pine birding the feature matches, and that is the limit of skill.


                I hope that this is a clear discussion of the concepts in play.  Remember, it took me almost 80,000 words to explain all of this before, so I understand if it isn’t making complete sense yet.  Essentially, the end result of all of this is going to be, hopefully, that you come to understand that if you are playing the game correctly, it won’t be some games that you lose to top-decks or mana screw, the ONLY games you lose will be due to top-decks or mana screw.

                This should, in turn, provide a psychological boost as well as improvement in your record, by helping you to understand that you cannot actually control the outcome of the game.  In life, as in Magic, all you can do is make it so that if you happen to wait on George Lucas’ table, he will like you enough to invite you to audition for his next sequel.  Most importantly, you’ll know that that reality is actually pretty darn ok.