Understanding Variance in Magic: An Introduction

“Oh man I was so unlucky, I got crushed game one and game two I mulled to five and I lost.”

“I was at 3 and he was dead on board but he drew lightning bolt for the win, such luck!”

How many of you have ever heard at least once this kind of sentence? Blaming bad luck for your losses is typical for an inexperienced player. What I want to talk you about today in my first article is what I believe is one of the centerpieces of being a great Magic player: understanding the role of variance.

What is Variance

It’s probably better to start with some mathematical concepts. Quoting Wikipedia: “In probability, theory, and statistics, variance measures how far a set of numbers is spread out.” This means that for every event, there’s an expected value called “mean,” and how the values are spread around the average value is measured by variance. For instance, an average value of 6 is reachable with two 4 and two 8 but also with two 1, one 3 and one 19. Variance in these cases will be different.

That’s all we really need to know to define variance. The problem, rather than being mathematical, is how this concept affects our mental state. Magic is a game closely related to probability and to explain it better I will provide an example using the most hated permanents in the game, land.

The number of lands that a deck plays is strictly in correlation with what it wants to accomplish and with how many lands it can operate (aka its mana curve). The magical number in limited, for instance, is 17 lands. We usually take this number for granted because our fathers taught us that we want to play that many lands and that’s what we will teach to our children, but have you ever considered why?

17 is the minimum number that guarantees you a reasonable chance of getting 4-5 lands around turn 5. Of course we could use 18, 19 or even 20 to have a better chance to hit land drops but that will cost us in terms of a higher chance of flooding out.

Let’s put down some numbers to explain better what I mean. Let’s assume a limited deck of 40 cards with 17 lands. We are in our fifth turn on the play which means we have already drawn 11 cards. I made a graph of the chance of getting from 1 to 11 lands in our 11 cards.


As predicted 4,5,6 lands are the most likely cases but the sum of those is not over 70% which means in the remaining 30% (3 games out of out ten) we are or screwing or flooding out on turn five. Of course 0,1, 9, 10, 11 lands are really remote cases (<1%) but remember, in the long run this is going to happen. Statistically speaking in a hundred or a thousand games you will face cases like that.

How our mental state is influenced

Have you ever felt anger, frustration, or sadness for your bad draws / opponent’s good draws? Well I’m here to tell you that a good understanding of this article may bring you a better peace of mind. In a perfect world, the perfect player that has no emotions and deals with variance in an objective way would be perfectly fine with losing to a mull to four G1 and G2 of a match, even 5 matches straight. The perfect player probably would like to play chess rather than Magic, though. A part of why we love the game is variance itself, the thrill of topdecking. The chance of defeating a better player is something difficult to find somewhere else.

Variance is both love and hate.

In the end I’m not saying that we should become robots and I’m not claiming to be perfectly fine when something bad happens to me, but I trained myself to be less influenced by dark thoughts that might be detrimental for my future games. Just understand that bad things happen, to you, to me, and to everybody. On this matter we are equally lucky so more or less we will screw or flood or get topdecked in the same way and we will lose as many games due to our flood as we will win games because our opponent is flooding out.

What getting angry does is take away our focus from two things: what we could have done differently to give us better chances to win, and; what we have to do in order to win the next game.

I saw dozen of players tilting badly after they got unlucky and literally throwing away games because in their mind the only thing they could think of was, “Why I’m so damn unlucky.” I also saw them keeping bad hands because, “It’s already the Xth mulligan today.” I played hundreds of competitive matches in my life, I took mulligans countless of times. I’m proud to say though that I never lose hope, I usually stay sharp, keep going, and I can remember happily winning with even 4 card hands. If you can wash away those negative thoughts you are putting yourself in the best position to win.

There’s a saying: “If life gives you lemons, make lemonade” (and don’t get mad because they are not oranges). The importance must be in doing good with what you have, not throwing out blame that you are not in the best spot possible to win. You will face screw, flood, better players than you, and bad matchups, but you have to keep playing. Blame is simple and is easier than focusing and fighting your way back into the game.

A helpful mindset is changing your goal: if your goal is just to win, and it doesn’t happen, you are going to blame bad luck. If instead you set the goal as “doing the best that I can,” it doesn’t matter if you are under bad circumstances, if you know at the end of the game that you did your best despite what happened in terms of variance you will still be happy for the loss, or at least not sad nor frustrated nor angry. Winning for you will become a consequence of doing the best you can do and losing won’t be about being unlucky.

Achieveing such a Zen condition can be pretty hard but also very rewarding in terms of self improvement and inner peace, and I will give you some examples to better understand that variance is a part of the game and that we have to embrace it as it is.

Understanding the role of Variance

Thinking in terms of the long run. I can’t say I’ve been frequently to casinos but what I got from watching people playing roulette is invaluable. Electronic roulettes are amazing because they provide you all a bunch of useful data such as last 100 spins. Once I saw a streak of 8 reds, roughly 0.4% chance that this might happen (without considering the 0). If you are betting on black numbers you simply end up in a bad streak, but statistically speaking considering a high pool sample, what’s going on is legitimate. The spins are like your matches, the more you play the more you will face weird things, like mulligan streaks or continuous floods / screws. It’s part of the game, we have to face it at some point.

“But you have to be in a position to be lucky.” -Kai Budde

This is one of the most important sentences in building you mindset regarding luck and variance. If you are playing a Standard match with Mardu and next turn you are dead you can still topdeck some points of burn to finish him off. If he’s at 4 you can still draw your remaining copies of [c]Stoke The Flames[/c], if he’s at 3 you have more chances by drawing also [c]Lightning Strike[/c], if he’s a 2 even [c]Crackling Doom[/c] would do the job! The point is if you bring your opponent within range because you played better, then you are in a better position to get “lucky” by topdecking the right card.

Look at this video


There’s no doubt that Craig Jones was extremely lucky. His chances were probably not more than 10% but his part in being lucky was the decision to [c]Char[/c] Olivier’s face instead of the creature or make some other plays. He saw that there was no other way to win expect with a topdecked [c]Lightning Helix[/c] and he worked for it.

The Concept of Deserving the Win

This is one misconception that I heard a lot from players. It’s not chess where the better player always win; in Magic there’s variance that can fill or widen the gap between the two player’s skills. A Magic game is always won due to the sum of variance and skill. A player can play badly but still win given the cards drawn by each player.

The Perfect Mindset

Once we have washed away all the dark thoughts, what we can do is think about what we could have done differently to win the game. Usually we have a certain degree of responsibility in our losses, so doing the best to understand what went wrong despite variance is an important exercise. One thing to avoid, though, is being obsessed with the fact that we are always at fault. Sometime we just can’t win. Sometimes we aren’t able to get a good enough perspective on our own play to tell which decisions we made might be questionable. Sometimes we make the right decisions the entire game and still lose. Usually I talk to people that I know are good and can give me a helpful outside perspective on my plays.

Wrap Up

Understanding variance is fundamental to achieve a good level of plays because it let us focus on being a better player. Also it’s better for our minds and for the overall enjoyment of the game. I hope you can toss out all the bad feeling that drawing outside the mean value might provide you and keep playing your best games of Magic.