So Many Insane Plays – Lucky? Yeah, That’s The Point

Read Stephen Menendian every Monday... at StarCityGames.com!
Monday, March 3rd – Stephen returns to the Monday slot, and talks about an argument that’s as old as the hills… is the role of Luck in Magic greater than the role of Skill? Does Luck devalue Skill in the overall scheme of the game? Strangely, Stephen believes that, far from inhibiting the skillful, Luck makes Magic a more skillful game… and he’s got the mathematical proof to back up his claim.

Owen Turtenwald startled a bystander at a StarCityGames.com Power Nine tournament in Indianapolis last year when he chided the kid by explaining that “there is no luck in Vintage.” When people complain about “luck,” my usual response is that this is the reason we play matches instead of rely on the outcome of a single game. Luck may be decisive in a game, but it is unlikely to decide an entire match.

The old luck/skill debate is a debate so old and so familiar that we seldom question its basic terms. The conventional wisdom suggests that luck tends to diminish the skillfulness of Magic as a strategy game. This point is often made with a comparison to Chess. When people talk about skill in Chess, they are fond of saying that the better player always wins because there is no chance involved, no dice, no coins… just plain smarts and know-how.

The premise of this claim is that an increase in chance/luck/randomness is a decrease in skill. It’s taken me a long time to understand why, but I no longer accept this premise. Far from decreasing skill, to an astonishing degree, chance in Magic dramatically increases the skill in the game. In short, luck makes Magic a more skill-intensive game. I hope to logically prove this by the end of the article.

Forward Thinking

In order to understand how chance makes Magic a more skillful game, we need to understand the skills that Magic tests. The only skill that Chess tests is in-game decision-making. In-game decision-making is a skill that draws upon two processes: Forward Thinking and Pattern Recognition. These are both terms of art.

Forward Thinking is a term that describes the process of evaluating decisions by the weighing the consequences of particular plays or lines of play. Typically, this type of thinking can be put in “If… then… ” terms. For example, “If I play X, then my opponent can do Y.” If I play Necropotence, my opponent can Force of Will it. If they have a Force of Will, I’d be better of Brainstorming instead to find a Duress. And so on.

The idea behind Forward Thinking is that you examine all of the possibilities lines of play and weigh their outcomes against each other. You then choose the play that maximizes your chances of winning. Forward Thinking can also be thought of as “thinking ahead” or evaluating decision trees.

Pattern Recognition captures the process of drawing upon previous experience to make decisions in lieu or in concert with Forward Thinking. The more a player plays a deck, the more familiar the pilot becomes with various situations that typically arise in the course of a game. The more familiar the player is with those situations, a better feel the player will have for the plays that will lead to a game win. The experience of having been in a situation is helpful when the situation, or one similar to it, arises in the future. For instance, if you have discovered that in a particular matchup Chalice of the Void for 1 is more likely to lead to a game win than Chalice of the Void set at 0, you can use that experience to guide your decision the next time you face that matchup.

Pattern Recognition is also analogical reasoning. It’s not simply the outcome information that is helpful, the increased familiarity and comfort with the situation will make your analysis more accurate and provide greater clarity of thought. But it’s not simply a conscious process. Many players say that they play “intuitively.” What this means is that they have so much experience with their deck through Pattern Recognition that they no longer need to engage in full throttle Forward Thinking or reason their way through a situation.

Pattern Recognition actually feeds the first process of Forward Thinking. The more familiar a pilot becomes with the outcomes of a particular line of play, the better the player will become at weighing the risks of various lines of play and arriving at the correct play. Although Forward Thinking is important, Forward Thinking becomes more accurate and more deadly when aided by a great deal of Pattern Recognition. Pattern Recognition thus enhances Forward Thinking by making your evaluative capacity more accurate, but it also can also substitute for Forward Thinking and help you play faster. Pattern Recognition is a critical skill in Chess. Chess masters have internalized not only the rote, by-the-book openings and end-games, but also the myriad mid-game scenarios that arise time and again.

Deep Blue

Although both Magic and Chess test in-game decision making, a skill that draws upon both Forward Thinking capacity and Pattern Recognition experience, Magic tests a much broader array of skills. For Chess players, the in-game decisions are everything. Chess rewards incredibly deep Forward Thinking.

Currently, humans are apparently no longer capable of beating the best computers in Chess — and for good reason, as computers are better at Forward Thinking analysis. A player can’t accurately “weigh” one line of play against another unless they are able to forecast the outcome, which is full of contingency. This is a limitation of basic computer power, whether our brains or central processors. It takes us far longer to evaluate 30+ turn lines of play than it does for a microchip. Computers have already “solved” checkers. It is only a matter of time until Chess is “solved” as well.

In Magic, Forward Thinking is not nearly as important. In Chess, there is no unknown or unknowable information. The only limitation on your ability to foresee plays is your own smarts. Since information is hidden in Magic, there is only so far you can reasonably ‘calculate’ lines of play. You fan open a hand that wins on turn 1 but loses if your opponent starts with Force of Will or Leyline of the Void. You have no idea what your opponent is playing. Calculate the odds of your opponent having one of those cards. You just don’t have enough information or the time to do that. And even if you could, that wouldn’t answer the question of what to do. Let’s say that your hand can win on turn 2, but then you have to calculate the risk of getting Duressed, Thoughtseized, Sphere of Resistanced, Unmasked, Chalice of the Voided, etc, etc on turn 1. You have to weigh the risk of Force or Leylined on turn zero versus the risk of getting shut out even harder if your opponent gets a turn.

To take a more complicated example, suppose you are piloting Aggro MUD against a UB Control deck. It is turn 7. Your opponent is at three life. Unfortunately, they’ve managed to deal with all of your threats and they’ve just resolved Tinker, which has found Darksteel Colossus. You are at twenty life.

In your hand you are holding Triskelion and Chalice of the Void. Your opponent has two cards in hand. They have played two Force of Wills and two Mana Drains so far this game. They have six lands in play, three of which are tapped and they’ve seen about 25 cards from their library.

You can play Triskelion right now, and if it resolves, you will win the game. Alternatively, you can play Chalice of the Void for 2 and cut them off of Mana Drain so that you don’t have to worry about getting Mana Drained when you go to play Trike next turn. However, next turn they’ll be able to hardcast Force of Will and they’ll see another card. What do you do? To come to the correct conclusion, you’d have to calculate the odds of them being able to Mana Drain your Trike. Then you have to calculate the odds that they will be able to utilize that mana and will be able to Force of Will your Trike next turn if you play Chalice instead. Finally, you need to calculate the odds of both your chances of winning increasing if you just wait longer versus the chances that your opponent will combo kill you first. Calculating any single one of these is basically impossible to do on the fly, let alone all five, which is necessary to determine the “best” line of play.

Given the mathematical challenge of making complex (or even simple) mathematical probability calculations within a “reasonable time” and then weighing them against each other, it’s just not possible to conduct full bore Forward Thinking analysis to make decisions. In Chess, it’s not only possible, that’s what Chess computers are designed to do. They are incredible at Forward Thinking.

Magical Skills Inventory

Magic rewards a wide array of skills that Chess does not: the ability to analogize effectively and efficiently under incredible time pressure with incomplete and hidden information, to properly anticipate metagames, to understand effective and ineffective sideboard plans, to design metagaming solutions, and so on. The possibility of chance is what makes these skills possible.

In Chess, you may only play one of two colors: black or white. Chess would be like Elves versus Goblins holiday theme pack except that you can only play Goblins versus Goblins or Elves versus Elves. There is only one deck you can ever play. In Magic, you can play not just black or white, but magenta, purple, blue, orange, etc. You can literally play hundreds and thousands of decks with a rainbow of color combinations. If you make decks more uniform and remove chance, you eliminate the skill of deck selection, perhaps one of the crucial skills in Magic. If anything, the chance of getting “screwed” is far more likely to occur through bad deck selection than in-game decision making. In Vintage (and Magic), the deck you play is the most important factor that goes into your success (hand Jon Finkel 60 Mountains and see what happens). When playing among the absolute best players, deck selection becomes almost centrally important.

Imperfect information is what makes this a skill. If you had perfect information about what people were going to play, it would be an easy thing to design a solution. In fact, if you had perfect information about the metagame, that would mean that they would have perfect information about you. Everyone would be playing the same deck, much as in Chess everyone has the same pieces. In Chess, there is no “metagame” in the sense of deck variety. Unknown information, chance, makes choice possible. And whenever there is choice, there is the possibility of skill. The fact of imperfect information means that people who are familiar with the metagame, familiar with the general “tastes” of people in their environment, and are good at figuring out where to position themselves in an uncertain metagame are rewarded. Similarly, sideboard plans and sideboard decision-making is another skill that is often based upon the same metagame assumptions. The “Ichorid gambit” of showing up without sideboard hate for Dredge is a great example.

You can apply these principles to deck construction itself. Decks have strengths and weaknesses that are only a part of the game because of chance. Players are allowed to select decks that exist on a strategic and tactical spectrum due to variety made possible by chance. Players can select decks that have varying degrees of power, consistency, speed, and resilience. Legacy Belcher, for example, has extreme opening hands. Some hands are unstoppable and some are terrible. You can build your deck to be more inconsistent (but more explosive) by decreasing mana and vice versa.

Even in-game decision making is somewhat more skillful in at least one respect due to chance. In Chess, skill is purely a function of the correct evaluation of lines of play (aside from the psychology of being ability to think clearly under pressure, etc.) In Magic, in-game decision making is based upon imperfect information. The ability to read the opponent, to guess at their plays, to bluff and tell – these skills are possible because of chance, because of hidden information. Experience and intuition count in Magic in ways that they do not in Chess. Relative to Chess, Magic tests a broader array of skills and that the only reason and difference for this is chance.

Logical Proof

Let’s divide all Magical skills into two categories: in-game decision-making and everything else. Everything else is a product of chance in Magic. In-game decision-making is merely accentuated (in some ways) by randomness, but also diminished by randomness. For instance, we all acknowledge that if you can accurately calculate a 90% chance of winning by making a certain play and you lose because you were in the 10%, then that does not reward skill. This is what people mean when they complain about a lucky topdeck.

For purposes of this inductive proof:

skill = a discreet, individual skill
SKILL = the sum/net effect of the collection of multiple skills
TS = Technical Playskill, meaning in-game decision-making skills

Outcomes in Chess = SKILL(Chess)= skill(TS) There are no other variables. There is no coin flip, no draws, no dice.

So, for Magic:

SKILL (without chance) = Skill (TS)


SKILL (with chance) = [W * (skill(TS) + enhanced (TS)) — chance losses caused by proper TS)] + [A * skill(archetype selection)] + [B* skill(deck tuning)] + [C* skill(sideboard design] + [D*skill(mulliganing)] + [E*skill(bluffing)] + [F*skill(all other skills)]

W, A, B, C, etc are the modifiers that describe the difference in terms / importance / significance / weight that we might ascribe to each of these skills.

My equation is part of an inductive argument that shows that it is improbable that chance decreases the SKILL in Magic. Many of you are familiar with deductive arguments. In logic, a deductive argument is an argument where it is impossible for the premises to be true and the conclusion false. Inductive arguments are far more common. For inductive arguments, it is improbable for the premises to be true and the conclusion false. For example:

Premise: If the rainfall in Seattle has been more than 15 inches every year for the past thirty years.
Conclusion: Therefore, the rainfall over the next year will probably be more than 15 inches.

That’s a classic inductive form of argument.

Given the equation, it is simply improbable that chance doesn’t increase the skill of Magic. In order for SKILL (without chance) to be greater than SKILL (with chance), what would have to be true?

First of all, you’d have to show that the “enhanced (TS)” that results from chance is less than the “chance losses caused by proper TS.” Second, even if you could make that showing, you’d have to show that the term “Chance losses caused by proper TS” weighted by (W) is greater than all of the other weighted terms combined. In essence, you’d be saying that the importance of technical playskill is far greater than the importance of any other skill or combination of skills. Since we can prove through counter-example that deck selection is just as important to winning as technical skill, this is a virtually impossible showing to make.

In addition, the term “chance losses…” could not make the sum of this term negative: [W * (skill(TS) + enhanced skill(TS) — chance losses caused by proper TS)] . If that whole term were to become negative, we would in effect be saying that technical playskill is useless in a world of chance, even though there are other skills that are relevant. I doubt that anyone would argue that TS has no positive utility in current Magic.

Given the sheer number of conditions that would have to be met for there not to be a net increase in Skill in the condition SKILL(with chance), and the virtual impossibility of making that showing, it is improbable that there is not a net increase in SKILL through the provision of chance in Magic.. If you’re a Bayesian, I think you’d find my argument even more compelling.

Magic is Young

The fact that Magic has chance does not make it a less skillful game than Chess. Tic Tac Toe is a game of 100% skill and no chance. It doesn’t matter who goes first. It doesn’t matter who goes second. The better player will win or tie 100% of the time. I’m not saying that Magic is a more skillful game than Chess, but I do claim that it tests a much broader array of skills than Chess.

Since Magic actually tests a broader range of skills, why isn’t Magic considered a higher art of competitive gaming?

Chess has been around for nearly a millennia in its current form. It has been played by kings, queens, emperors, and popes. It is a game with a history of great players that can be measured in centuries. Its traditions, praxis, and theory have been developed over generations.

Magic, in contrast, is a card game that has existed for little more than a decade. In some ways we are still beginning to understand what Magic is even all about. Only in the last five years has design in magic really become consistent and better understood. Patrick Chapin described the incredible skill differences that existed in Magic in 2002 to today… Imagine what Magic will look like in 2012!

People who play Chess have often been playing it for decades in many cases. You couldn’t be playing Magic for decades even if you wanted. Most Magic players are young. They are young because Magic is a game that was targeted to adolescents and young adults, if not children. Those children who learned the game are not yet old enough to give the game stature. That day will come. Someday a 60 year old will be able to look back on 40 years of Magic. I’m sure I’ll be there to see it.

Until next time…

Stephen Menendian