Mulligan Stew

Posted in Limited Information on January 23, 2007

By Noah Weil


One of the singular pleasures in writing an Internet column is prompt and abundant interaction with the readers. Instant responses help immeasurably in determining what resonates with an audience and what doesn't. Of course the writer likes to think he has a bead on what you guys appreciate. But there are surprises, and it's the online forum and speedy e-mail that lets the author adjust to unexpected public sentiment and query.

For example, since starting the new job people have been constantly asking what it's like to work with Aaron Forsythe. Well here you go: Aaron's a lovely person and likes his latte skim, extra hot. But that's not the topic of discussion today.

Nope, this week is in response to Walk of Ages, vol. 2, where a minor point spun into a sizeable area of disagreement - specifically, my first round opponent's opening hand and how keepable it was. I felt it was a marginal, borderline opener, while others felt it was both obvious and excellent as an initial seven. The controversy surrounding my thoughts towards its viability sparked today's topic, views on mulligan theory. Those commentators made some really strong points about the situation, which I plan on addressing. Before we get to that, I'd like to build some foundation with a definition of the mulligan, as well as give some key questions in the decision process. After a couple of examples, I'll explore the contested situation in more detail.

So let's begin with a definition. Noah W. defines a mulligan as "unfortunate," "an unnecessary evil," "the end result of being ninja-cut," and "the slow boat to concessionville." Powerful description! Why are mulligans so brutal? There are two big reasons:

  • Card advantage is king in Limited. One mulligan has the same effect as an opponent casting a turn zero Unhinge. Oh the pain!
  • Mulligans perpetuate themselves, as well as being worse in multiples. That means you're more likely to have a mulligan-worthy hand with six cards over seven, and starting with five cards is strictly worse than starting with six. So you have a system that not only punishes multiple iterations, but makes multiple iterations more likely.
  • Is there any positive aspect to mulligans? Yep, and it's a doozy:

  • A correct mulligan increases your chances of winning.
  • Kind of brings things back into focus, doesn't it? When you mulligan, you are saying I think I have a better chance of winning with n random cards than these known n+1. When you don't mulligan, you are saying I'm more likely to win with these n cards than a random n-1. It makes sense; the tough part is figuring out which direction actually improves your chances. Unfortunately, end results can be misleading.


    One could say that if you lose a game you should have mulliganed the initial seven. By contrast, if you win a game your mulligan decision was correct. The problem here is that correct mulliganing and winning are related, but hardly dependent. Mulligans are tricky to navigate because you can make a wrong decision on turn zero and win, and you can make the right decision and still lose. As one can imagine, this makes improving this skill far more difficult. What deadly positive reinforcement, when you get to entwine bad decisions and winning. In the long term, there's plenty of edge going to the player who makes correct decisions. All else being equal, given 10,000 games the player who mulligans correctly will win much more often than the player who doesn't. That's just common sense. This is less true for game #5,423, where a mistake-prone player can keep a one-lander, draw picture-perfect for the next five turns and win the match. Hey, it happens. The best you can do is minimize (potential) misinformation and ignore the end result. Determine if you made the right choice regardless of whether you won or lost. I know how tough it is; to not look back at a game and second-guess yourself. And there's nothing wrong with looking back at a game and delving for mistakes. Just don't assume because you lost you did something wrong (and vice versa). Sometimes you do everything right and still lose, and vice versa. Makes Magic exciting!

    But enough rhetoric, let's get to this week's thrust. How does one actually determine correct mulliganing? As you'd expect with a topic this complex, there are many factors to consider. When I look at an opening hand, there are some questions that need answering, to determine viability. For example:

  • Will I be able to play relevant, timely cards?

  • What are the strengths of this particular hand?

  • What are the weaknesses of this particular hand?

  • What's the best-case scenario for the next few draw steps?

  • What's the worst-case scenario for the next few draw steps?

  • How bad are my chances if I get the worst-case scenario?

  • With this hand, how do I win?
  • Strategic_Planning

    Readers of this column know these kinds of questions are similar to how I play regular Magic. The essence of "How do I win? How do I lose?" forms the base of all kinds of decision trees, mulligans most definitely included.

    Does it seem strange to start thinking about the endgame on turn zero? Why not? When should you start planning out your strategies? Your opening hand defines a lot. If it's not a hand that plays to how your deck should work, send it back and look for one that does. Of course that requires an understanding of the strategies inherent to the format, which means a lot of practice. Luckily that's fun too. For Limited especially, decks can often play multiple roles, ranging from very aggressive to very controlling. Even if you've drafted what you consider an aggro deck, certain openers can lead you into the control route. If the hand is viable, there's no reason to resist a new stratagem. Just acknowledge the new plan with a hand, and act accordingly. And yes, what your opponent does also affects your plans. In fact, what kind of deck they're playing often alters mulligan decisions for games two and three. For Game 1 though, you're on your own.

    Knowing some of the criteria, let's apply these questions to a test hand. What do you do with these seven cards, on the play?

    Aven Riftwatcher
    Midnight Charm
    Celestial Crusader

    Q: Will I be able to play relevant, timely cards?
    A: There's a guaranteed two-drop in the hand, and considering how young the game is, the "drain one" ability of the Midnight Charm could be very relevant. With a single land over the next three draw steps, 6/7 of the hand can be played. These cards are definitely timely i.e. you have early spells for the early game.

    Q: What are the strengths and weaknesses of this particular hand?
    A: The strengths definitely revolve around the three-drops. Those two are fairly strong, and play well together besides. In addition, there's a source of card advantage and a removal spell here. The major weakness is missing a land or two and the fact that that Blightspeaker and Celestial Crusader compete at the four-mana level. Just as unfortunately, the removal spell is quite narrow, especially considering the tap and first strike abilities to be weak in conjunction with these particular creatures.

    Q: What's the best-case scenario for the next few draw steps?
    A: Land immediately, and hopefully some harder removal or more defensively oriented creatures. Despite the turn-three 2/3 flier, this hand is more controlling than aggressive (although it could play either role). As such, drawing lands and control cards fits this hand's style.

    Q: What's the worst-case scenario for the next few draw steps?
    A: Not lands generally, big expensive spells in particular. Cards that tie up the mana, like Melancholy or Rathi Trapper, are also unappealing.

    Q: With this hand how do I win?
    A: With two sources of card advantage, and some effective life gain options besides, this hand often plays the control route. Getting the opponent to trade resources while you search out Rebels is ideal, especially since you have a creature that can protect your searcher. The Aven Riftwatcher is actually a bit of a tease here, as it's card disadvantage and playing it prevents Stonecloaker availability. However, it's a good race card against non-removal decks and can be a big push with Celestial Crusader. The ideal way to play this hand will depend a lot on what your opponent does, but there are options no matter which direction you go.

    Final analysis: It's not a perfect hand, but openers rarely are. It has options, and it only needs one more land in the next two draw steps to really take off. In addition, it has life-gain cards to gain back some time in case you draw a few blanks. It's a keeper.

    How about this one on the play?

    Jodah's Avenger
    Mana Tithe
    Knight of the Holy Nimbus
    Aeon Chronicler

    Q: Will I be able to play relevant, timely cards?
    A: Yes, some. The Knight of the Holy Nimbus clearly loves the dual plains, and Mana Tithe is great in the very beginning. A turn-two Knight followed by countering whatever you want is a highly effective opening.

    Q: What are the strengths of this particular hand?
    A: Those inexpensive white cards promise a lot of early damage. There are very few cheap, common answers to a 2/2 regenerating flanker. The Force Spike even plays well with KotHN's costly regeneration-suppression ability.

    Q: What are the weaknesses of this particular hand?
    A: On the surface, the weaknesses are a five drop in another color and a six drop in another color. More specifically, the hand has a lot of internal conflict. You have an early drop, and nothing else for turns upon turns. You have a mass pump spell with one creature it can enhance. The opening turns are aggressive, but the second half of the hand revolves around card advantage and control.

    Q: What's the best-case scenario for the next few draw steps?
    A: Land, land, land? It's not pretty. You need lands to win, but placing your entire defense on the back of a Force Spike and a 2/2 seems…fragile. For every non-land you draw, you're preventing yourself from getting to the good stuff, yet at the same time you need spells to stay alive. Ideally you'll draw a couple of lands, than some four and three drops that either shore up defense or are extra-aggressive. Without knowing the rest of the deck it's hard to say what's available, but a very specific run of cards is needed.

    Q: What's the worst-case scenario for the next few draw steps?
    A: Anything non-land will be worthless for a few turns, yet a steady stream of lands may not provide enough interaction to stay alive until Aeon Chronicler and Jodah's Avenger come to town. Anything creature-relevant like more Fortifies will be hideously bad.

    Q: How bad are my chances if I get the worst case scenario?
    A: Pretty bad. Either the opponent has more aggressive creatures than you or more removal than you. Either way, he's well set up to take advantage of your gaping holes. The worst-case scenario is fatal, and considering how precise your needs are, it seems all-too likely.

    Q: With this hand, how do I win?
    A: This hand leading to a win will have far more to do with your opponent than the hand itself, which is a poor place to be. If they keep a really slow draw or mulligan to nothing, or have a bunch of creatures that Nimbus Knight can block somehow, you can have the opportunity to get back in the game. The question with this hand isn't how it can win, but what the opponent does so you don't lose. That's not a good place to be!


    Final analysis: Send it back. On the surface it looks reasonable, but it really doesn't go anywhere. The Fortify adds almost nothing to the game plan, making it close to a mulligan anyway. Needing so many things to go right for you, and so many things to go wrong for an opponent, means there's a fundamental problem here. Can this hand win? Sure, but not often enough for my liking. Spin the wheel and try it with six.

    The analysis above is fairly convoluted, and in a tournament setting you won't have the luxury to run down the questions and make probability tables and whatever else you'd want to do. Eventually things become instinctive, but even then there are borderline cases. There is a simpler set of guidelines you can use with mulligans, if you only want a couple of questions to answer instead of a bunch. I hesitate to talk about shortcuts like this. There are as many exceptions here. Still, in the interest of completeness, here's the short version of the questions above:

  • Does this hand give me something to do on or before turn three?
  • Does this hand give me something to do afterwards?
  • Answering "yes" to these usually (usually!) means the hand's a keeper. Applying these criteria to the two hands above does correlate with my view on mulligans. The first hand had some early drops and removal and something to do with three lands and more. The second hand covered the first condition but failed on the second, meaning it ran out of gas too quickly. These questions are about having something to do in the critical early turns, and staying influential after the beginning is established. The ultimate goal in regards to a starting hand is to put yourself in one position: To be happy drawing either a land or a non-land. Hand #1 wanted a land, but after that it was happy. Hand #2 wanted both lands and spells, and therefore it was too dangerous to keep.

    …Which brings us back to the controversy that prompted this week's topic. Here's the hand in question, along with the owner (Rob's) thoughts and my own from last week:

    Jaya Ballard, Task Mage
    Herd Gnarr
    Jolrael, Empress of Beasts
    Yavimaya Dryad
    Fungal Reaches

    Rob: "Opening hand is fine, so I keep. Both Jaya and Dryad can be cast off reach on turn 3."

    I put this hand at way more borderline than Rob. It's all right, but on the draw it's extremely slow. If the Dryad comes down on the third turn to block something you can catch up, but that's a question mark. Your first play is either a 2/1 or a 2/2 you don't want to block with. I might keep this one, but it's right on the edge. I don't necessarily disagree with Rob hanging on to it, but he's more complacent than this is worth.

    My opponent called the hand perfectly keepable. I expressed the idea that this hand, drawing first, was borderline. While I might/probably would keep it, it's not ideal and there are many things that could go wrong. As we all soon discovered, the bad things did happen and my opponent lost that game with this opener. Was my disquiet accurately placed, or were these concerns just piercing, obvious post-game insights? Let's see what the people had to say:

    1. Genjuro6: "The opponent's hand game 1 was clearly a keeper. Not even borderline. I know it is a kneejerk reaction after losing to say "Oh, I should have mulled," but I think the odds are miniscule that a mull to 6 is a better hand than that. Sure, you run the risk of being tempoed out, but a Limited deck too fast for that hand is probably white, and therefore you should be safe running the Jaya out turn 3, as was the case here. If your opponent suspends Ivory Giants turns 1 and 2 against a nonwhite deck, you lose, the opening hand didn't matter. It generally seems that Noah is quick to go to the "should have mulled" in hindsight, but when it comes down to actually making the decision, nobody would actually mull the hand."

    Genjuro6 is correct that even the best of hands can be blown out if an opponent has the right answers. He's also completely correct that in this situation I would keep this hand.

    1. Snowfire: "I agree that the opponent's hand is a giant, obvious keeper. Yes, it's a bit slow, but expecting perfection every hand is silly. Most Limited games offer enough breathing room that a double-bomb hand like that will carry the day if not crazily rushed, like you were able to do - don't forget that he didn't know your deck for the first game. Things may have been different if he had a 5-mana bomb and a 7-mana bomb as opposed to 3 and 5, but that hand is quite keepable."

    Snowfire brings up the excellent point of keeping a hand with double bombs being worth some risk. Here's the point of contention I had, and why I was so against the keep: Rob didn't play the hand like it had two bombs. He led with Jaya on his third turn; a creature that he had no plans to attack or block with. Therefore his third turn was blank, which is a rough start when you're drawing first already. I like the hand a lot more when you play Yavimaya Dryad first, giving you more mana to play with as well as a creature you can thoroughly toss aside. As I said last week, Rob split his focus between control and aggression, and that was his undoing. The forum goers were correct and the hand is totally reasonable. It just required the right progression of cards to maximize, hence my erroneous disquiet. Thanks to everyone who set me straight!

    Finally, Pierrebai brought up an interesting point:

    1. "I did find interesting that you thought your 1st opponent's hand was a mulligan and yet kept a hand that had no play until the 3rd turn unless you drew a plain in the 2nd match."

    A fair question. Why did I like my own hand in Game 2 of the second match? Here it is again:

    Fledgling Mawcor
    Zealot il-Vec
    Ivory Giant

    This hand wasn't perfect, but I'm still a fan. With ten Plains in the deck, on the draw, there was time to find something. No matter what, it had the option of a morph on turn three and Trickbind for any opposing suspend cards, if needed. It also had the powerful Zealot-Mawcor combination, a pair of cards worth absorbing a bit of extra risk to use. And finally, it had the potential of a first-turn suspended Ivory Giant. There was some danger, but it had guaranteed plays and the potential for some real excellence. In Limited, that's often the best you can hope for. Winning the game aside, I still like the keep here and would do it again.

    That's all the time we've got this time. Mulligans are an exceedingly complicated topic, and this week really just skimmed the surface. To wrap it up for now, I'll give a few scenarios, all hands being on Game 1 of the match. Your mana base is in parentheses. Would you mulligan? Feel free to give your thoughts in the forums. The results will be discussed next week. Until then, thanks for reading.

    Click on a card to see a larger version.

    On the play (9x Island, 8x Swamp)

    Looter il-Kor
    Nightshade Assassin
    Think Twice
    Tendrils of Corruption
    Liege of the Pit

    On the draw (9x Mountain, 8x Forest)

    Tromp the Domains
    Savage Thallid
    Sulfurous Blast
    Ironclaw Buzzardiers
    Empty the Warrens

    On the play (10x Plains, 7x Forest)

    Ivory Giant
    Ivory Giant
    Thrill of the Hunt
    Thrill of the Hunt
    Sporesower Thallid

    On the draw (10x Swamp, 8x Mountain)

    Strangling Soot
    Midnight Charm
    Needlepeak Spider
    Hammerheim Deadeye

    On the play (7x Island, 7x Plains, 3x Mountain)


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