Mulligan Factors

Posted in Limited Information on August 26, 2015

By Marshall Sutcliffe

Marshall came back to Magic after discovering Limited and never looked back. He hosts the Limited Resources podcast and does Grand Prix and Pro Tour video commentary.

Making mulligan decisions is one of the hardest skills to learn in Magic. The reason is pretty simple: It's not really possible for you to know if you are correct or not. At least not without a TTSC (Time-Traveling Super Computer). Our game is so utterly complex that when it comes to making tough decisions like whether you should take a mulligan or not, the true answer isn't really provable at this time.

While we wait on our TTSC to be built, how do we get by?

Sadly, we have to rely on our feeble human brains and our flawed memory and intuition for the most part. I only say this is sad because we can't compare our intuition against the "correct" answer by plugging it into a computer afterwards.

It's useful, then, to at least look at some of the factors that go into making the decision. Even if it doesn't give us a perfectly clear answer, at least considering some of the more important factors will get a closer to that answer than not. Well, usually anyway.

Adam

My friend Adam, whom I've mentioned here before, is learning to draft. He started at the very end of Khans of Tarkir/Fate Reforged and really dove in for both Magic Origins and Fate Reforged/Dragons of Tarkir. He's made huge strides in his drafting ability, mainly because of his willingness to take advice and his dedication to tracking his drafts. He sends me every draft he does, including a screenshot of his final build, and a file that lets me look at his whole draft, pick-by-pick.

But lately his questions have gone further than picks and deck building; he's asking about mulligans.

As his draft mentor, I wanted to come up with some hard answers for him. I want to give him something concrete to reference in the future. My efforts toward this were in vain, and I've given up on that pursuit. But as I said earlier, even though I can't provide him with a full picture of how mulligans work from a mathematic perspective, I can still give him some of the major factors that go into mulligan decisions.

Let's use some examples from Adam's latest draft to guide us.

First, here is the deck that he drafted, which we are using for all three of our examples:

As we can see, Adam has put together a nice one here. The deck looks solid, and I'd be happy to take it to battle. It's not bad at all, for a guy who started drafting less than a year ago!

Mulligan Decision One

Let's look at his first mulligan decision.

Adam is on the play here, versus an unknown deck.

What do you think when you see this hand? Does a red flag go up because it only has two lands? What about the fact that those lands are the same color? Zero two-drops in our opener isn't great either.

The real question that comes to mind for me is this: What cards do I actually want to draw in the first few turns to make this hand work?

As an exercise, I've made a list of the remaining cards in the deck, and divided them into two groups. The first group, on the left, is the group of cards that we would be happy to draw in the first two turns of the game. The second group, which is on the right side, are cards we'd rather not see in those first two draw steps.

I've included all lands, as well as any spells castable with the two Mountains we start out with on the list. Your list may vary; that's ok. Part of the skill of taking a mulligan is understanding which cards in your deck are actually good for you at this stage of the game and which aren't.

If you add up all of those cards, you get 20 total. With two draw steps, you have about an 85% chance of drawing one of these cards. This is a very high percentage, but it's not the end of the story.

Simply drawing one of these cards doesn't mean that the hand is a keeper. Why? Because of two main reasons:

  1. There are cards here that don't put you in a highly advantaged situation, but that do let you continue to build a board. Basically they let you play a game of Magic but don't put you miles ahead of your opponent.
  2. The decision whether to mulligan or not doesn't come down to simply figuring some odds on if you'll find decent cards on top of your library in time. It comes down to that chance weighed against the average quality of a six-card hand in this deck.

And this is where things get too complicated for human brains. It's not really possible to know how "good" a six-card hand is on average. Just figuring out what "good" means in this scenario is a complicated exercise. It's certainly not something you'll be doing at the table in real-time.

The tricky part is that you'll find opening hands that fit some baseline criteria for being a keeper, but that also may be worse than an average six-card hand. It's tough.

Let's look at another example hand, similar to the first.

Mulligan Decision Two

This is another Game 1 scenario, and again Adam finds himself on the play with this opener:

The first thing that will jump out to you is just how similar this hand is to the first example. Three-drops, two lands, Instincts, and Elemental. The second thing you'll notice is that this one has both a Mountain and a Forest. How does this change the outlook?

As you can see, we add a full four more cards that we can draw in the first couple of turns that make us at least minimally happy. With a few lands off the top of the deck, this hand is pretty bonkers. And the fact that all four of our green two-drops are live here (where they weren't in the first example) changes the decision dramatically.

It's interesting to note that just the one Forest in this example makes this hand much, much better than the first example.

The same caveats as the first example apply, though. You still want to consider if this two-land hand is better or worse than an average six-card hand. What do you think?

Our last mulligan decision is decidedly different than the first two.

Mulligan Decision Three

Here we have a bit of a curveball on our hands.

Here we have the opposite problem to what we had before. We've got five lands and just two spells, and we are on the draw.

I tried to make a list of the cards we'd like to see of the top of the deck, but the reality is that we just want to see spells. Sure, some will be better than others depending on where we are in our mana curve, but overall just any spell is good. With the mana we have in our opening hand, we can cast all but one of our main deck spells (the exception being Skysnare Spider).

With seventeen lands in it, the deck is a little over 42% lands. Given that we have five lands in our hand, the remaining cards in our deck were about 36% lands. Assuming the game goes ten turns from now, and assuming that we keep, we should expect on average to see about six spells and four lands out of those ten draw steps.

Even if you consider this enough incentive to keep it, you have to also factor in that the order in which these cards comes off the top of the deck is very important, and completely out of your control.

For example, if you draw three lands in a row with this hand, you could be in big trouble if your opponent has a quick start to the game. Three spells in a row could see you flood the board with awesome creatures and dominate the middle part of the game.

Putting It All Together

As you can see, the prospect of actually figuring out the "correct" mulligan is daunting. The good news is that simply by looking a bit deeper at these different factors, you can help train your brain on what to look for and what to consider. Even if you don't come away with a perfect proof of your claim, you'll have more information to work with—and that's almost always better than not having it.

For the record, in a real game of Magic, I would mulligan the first and third examples, and keep the second one. After looking closer at what cards I want to draw and how many turns I have to do it in, I would probably keep the first hand but still mulligan the last one.

Making these decisions on the fly is difficult, but recording your decision and going back to look at it more closely is a great way to help see the bigger picture when it comes to mulligans.

Until next week!

@Marshall_LR

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