The first real decision in any Magic game, after you chose whether to play or draw, is whether or not you should take a mulligan. Over the years there have been quite a few articles on the internet about taking mulligans, yet I still believe it deserves much more attention. I think that most Magic players have the habit of keeping bad or dangerous hands while they should be mulliganning instead. Every now and then someone writes, “This hand was pretty bad, but it contained lands and spells so I had to keep” or “This is a hand that you cannot mulligan, but you won’t win the game with it either”. These are very bad statements; it indicates that players are way too afraid to take a mulligan. They think that taking a mulligan is a risk, and that they might lose the game on the spot if the next hand (or hands) are even worse. What they do not realize however, is that keeping a really bad hand often gives you a much bigger risk to lose the game. In this article I will try to explain why you should not be afraid to throw away your seven-card hand.
Let’s start with some assumptions to keep things easy. This article will be about mulligan decisions in Limited. I will always assume that a Limited deck contains 40 cards, and that there are eighteen lands in such a deck. There are no mana-sources in the deck, except for lands; so the decks I will be talking about do not contain cards like Kodama’s Reach, Birds of Paradise or any other cards that influence the available mana in the first four turns of the game. A generalization of the required lands to be able to cast all your spells is difficult to make as every draft deck has a different mana-curve. Something we can be sure of though, is that you will lose more than 95 percent of the games in which you do not have a third land in play on turn 6. I will also state that the value of all lands you will draw beyond the first seven is most likely equal to zero, as draft decks usually should not contain any spells with a converted mana cost of eight or more.
The number of lands in a deck is not the only factor that determines whether you should mulligan a hand or not. Other sources of information that can help you in making this decision are the nature of the format that you are playing in, the role of your deck in the match, the contents of your opponent’s deck, the number of cards that you can draw to justify keeping your hand, etcetera.
Let us go over to all the different scenarios that are useful to discuss.
1. Six lands, one spell
Example: Island, Island, Island, Swamp, Swamp, Swamp, Ink-Eyes, Servant of Oni.
In Limited, one spell does usually not win you the game. If the only non-land card in your opening hand is not amazing (for example, it is just a 3/3 creature for three mana, or a removal spell like Dark Banishing), keeping the hand is definitely wrong. So suppose that your only spell is quite powerful, then you are still taking a huge risk by keeping. Most people argue that with six lands in hand; it is likely that you will draw into spells and not into more lands. However, the probability to draw a land (in your first draw step for example) is still 36 percent. The value of any land you will draw at this point is essentially zero, and since you really need to improve your hand as soon as possible, drawing that land card is in fact quite deadly. Let’s say that you will be all right if you do not draw a land in your first three draws steps and if the card you are holding is really good; then the probability that you will be in the game is only 24 percent. This means that you will lose three out of four games by keeping a six-lander, and that you haven’t won the fourth game by any means. There are only four spells in your hand by turn 3, which is nothing special.
If you do decide to take a mulligan, then these are the probabilities to have any number of land cards in your opening hand (one mulligan):
Zero lands: 1.9 percent
One land: 12.3 percent
Two lands: 29.2 percent
Three lands: 32.7 percent
Four lands: 18.4 percent
Five lands: 4.9 percent
Six lands: 0.5 percent
Assuming that most six-card hands that contain either two, three or four lands (and thus four, three or two spells) are as good as or better than your original hand, you have an 80.9 percent probability that the quality of your hand will improve after mulliganning.
2. Five lands, two spells
Example: Forest, Forest, Forest, Island, Island, Kavu Climber, Confiscate.
This kind of hand is quite comparable to the hand that contains six lands. Deciding whether to keep a five land hand or to mulligan it is a lot more difficult though. If we follow the same reasoning, then one would need to draw at least two spells within the next three draw steps to make the hand playable. The odds on netting two or three spells in three draws are 66 percent. You are thus still most likely to lose the game in 34 percent of these situations. The probability that your hand will contain exactly two or three lands after a mulligan (if we assume that a two- or three-lander is better than most five card hands) is 61.9 percent. These probabilities are rather close.
Choosing to keep or to mulligan now comes down to other criteria. The most important one is the quality of the two spells in your hand. While in this 9th Edition booster draft you have two spells that are both powerful, they are also quite slow. In order to make up for this lack of speed, you will really need to draw either a creature that you can play on turn 2 or 3 or a useful removal spell. In order to make this decision, it is important to know what cards are in your deck, and in which quantities. If the Kavu Climber and Confiscate really are the top of your mana-curve, then keeping can be justified. However, if there are more expensive cards in your deck, or lots of situational cards (like combat tricks, or discard effects) then a mulligan is the way to go. This opening hand: Forest, Forest, Forest, Island, Island, Trained Armodon, Confiscate is a lot better already, and is a hand I would keep ten times as often as I would keep the original Kavu Climber hand.
3. “Lands and spells”
Example: Forest, Forest, Forest, Swamp, Waking Nightmare, Moss Kami, Serpent Skin.
Most of you will encounter a lot of resistance when it comes to mulliganning this hand. There is quite an acceptable amount of lands in the hand, and the spells are not too bad. The problem is that this hand as a whole is horrible. You will most likely lose if your opponents play good creatures on turns three, four and five (which isn’t anything special). You will also lose if a removal spell kills Moss Kami on turn 6. Of course, there is the possibility that you will draw Gnarled Mass and Thief of Hope early on, but you are in deep trouble if that does not happen. Remember that there is still this 80.9 percent probability that you can keep the next six card hand. If your deck does not support many expensive and/or situational cards, I would definitely advise taking that mulligan.
4. One land, six spells
Example: Mountain, Akki Underling, Spiraling Embers, Honden of Infinite Rage, Yamabushi’s Flame, Gibbering Kami, Sokenzan Spellblade.
A lot of players would be tempted to keep this hand going second. Their reasoning is that the hand is really good, and that you will probably win the game if you draw the lands you need. However, to be able to get in the game, you would need to draw three lands early on. Sure, Akki Underling will save some damage in case you miss your third land drop, but no matter how you want to approach this situation, you will need three more lands on the top on your deck (say in the top five cards) to be able to put up a fight. By not mulliganning you take a huge risk, the probability of missing your second land drop on turn 2 is already 25 percent. Maybe if the spells in this hand are clearly the best spells in your deck, keeping can be the correct decision, but definitely mulligan otherwise.
5. Three lands of one color, four spells of the other color
Example: Plains, Plains, Plains, Hypnotic Specter, Gravedigger, Highway Robber, Dark Banishing.
I would mulligan such hands, here is why: if we assume that there are nine Swamps in this deck, then the probability of having at least one Swamp on turn three is 60 percent. This means that in 40 percent of these scenarios you will be in real trouble. You won’t lose 40 percent though, as you can always draw White spells that you will be able to play, but you are basically still stuck with four Black spells that you are not able to play. I would advise to mulligan most of the hands in this category, the only exceptions I can come up with are hands with cards that each have a really high power level and only require one colored mana, such as: Mountain, Mountain, Mountain, Nezumi Cutthroat, Nezumi Graverobber, Thief of Hope, Scuttling Death.
As a guideline when it comes to mulligan decisions, I would advise this: when you are in doubt whether or not to keep a seven-card hand, always mulligan. Of course if you are a player that takes too many mulligans in general then this statement is wrong, but as most players take too few trips to Paris, I think it is right. Furthermore, I do not believe that the difference between playing first and drawing first is very important for a mulligan decision. Most hands that you would shuffle back going first should still be mulliganned when you are drawing first. This is true because the extra draw step you get is as much of an improvement as the loss of tempo is a disadvantage in most cases. You will get punished for not making your second land drop a lot more when your opponent is able to play his 3/3 creature already on the following turn. Also, the number of mulligans your opponent takes is insignificant to your decision to mulligan or not. Keeping a slow hand when your opponent took two mulligans is still a bad decision; it results in giving the opponent a window to come back in the game. The best way to punish someone for his mulligans is to put pressure on them as early as possible.
There is no average of the number of mulligans you should be taking per tournament or per season even. You do not know what would have happened if you did mulligan that questionable draw, or if you would have kept that six-lander (a decision to mulligan does not become incorrect when the top four cards on your library were spells). That is why these decisions can be quite difficult to make; I hope the guidelines I gave you will help you think about the matter some more. Even though it’s just one decision you have to take, taking the wrong one can have big consequences.
Rogier