When an opponent mulligans, what does it mean? If you are on the draw, especially when the opponent mulligans more than once, you now have different information about the game state. This information must mean something, but what? You should be able to use this information to your advantage and change your game play and your own mulligan decisions accordingly.

What Should a Mulligan Mean?

Let us start with what we know when our opponent does not mulligan. What do we know? We know the opponent has seven cards and will be working from a one-card disadvantage, but with a one-turn tempo advantage. We also can intuit that the opponent has a better hand than “mulligan average.” I will explain what I mean by a mulligan average hand in a moment. The opponent's hand probably, given the construction and requirements of most decks, has at least two or three lands and at least three spells, with at least one spell being castable with the mana in hand. If we also know the deck being played by the opponent, we may know more; for example, if the opponent is playing Zoo with a low land count, a high spell count in hand is likely, and we may know many or all of the cards the opponent could hold in hand if the deck is a “netdeck.”

Our opponent - if rational - believes that the kept hand is better than the “mulligan average” hand. By mulligan average, I mean that the best hand one could expect by mulliganing over the series (mulligan to six, decide if you want to keep and if not then mulligan to five, etc.). Card advantage is so important in most Magic games that we normally do not consider the fact that we could mulligan to four if we needed, and that hand might be better than the five hand, so this factor seldom comes into play in practice. The most important consideration is “is this hand better than an average hand I will get by mulliganing once?” Mulliganing also increases the variance on the downside in the opening hand. That is, a mulliganed hand has a higher chance of being extremely bad (such as a no-land hand). This increase in downside variance is another piece of information to consider.

Okay, our opponent has mulliganed (let's say to six), and we want to put this information to use. What is now different about the mulliganed hand from the “I keep seven” hand? We know the hand has inherent two-card disadvantage. We know the hand probably has at least two lands and at least one spell. We do not know if the opponent can cast any spells with available mana. The opponent still has initial tempo advantage.

If we look over this list, we now know two very important things:

• The opponent has a higher chance of stalling, and…
  
• We have significant card advantage.

Thus, all things being equal, if we do not ourselves stall, we should have the advantage in the game as a whole.

This is worth repeating: If we do not stall, we should have the advantage in the game as a whole. Knowing this, we can apply this information to our own mulligan decision. In particular, we should be less interested in mulliganing than we normally would be if we at least have a hand that will not stall. If we have a “boring but playable” hand, we do not want to increase our own downside variance by mulliganing or taking a lot of risks in play.

The opposite is also true: If we have a hand that is prone to stalling (such as a one-land hand in Limited where the first playable card is a Signet), we should be even more interested in mulliganing than we would otherwise.

To understand more deeply what a mulligan means, we have to understand the conflicting deck strategies. All Magic can be though of as the process of making our own fundamental turn lower than the opponent's. By fundamental turn, I mean the turn at which the deck would win in the absence of opposition. A fundamental turn could be thought of as the average clock a deck puts on an opponent or the “goldfishing” speed. We can try to make our fundamental turn low or make the opponent's fundamental turn high: No other strategy makes any sense.

The idea of fundamental turns and strategies that revolve around each player's fundamental turn is related to “Who's the Beatdown?” by Mike Flores. Another way to think about deck match-ups is to ask “Whose Fundamental Turn Matters?”

Deck strategies can be described as one of the following:

• “Speed Racer”: Low fundamental turn with few to no control elements. In Standard, Snakes on a Plane is one of these, and Heartbeat Combo decks play out much in this manner before sideboarding.
  
• “NASCAR”: Moderate fundamental turn plus control elements that prevent the opponent from increasing the fundamental turn. I don't watch NASCAR, but I do know that one strategy is to get a lead and then slow down a bit and just prevent anyone from getting around you. French Weenie decks running Remand, Bathe In Light, or Ghostway can be thought of as having elements with a NASCAR strategy. If you don't like the NASCAR analogy, “Counter-Sliver” has a bit more baggage but gets the point across for those who have been playing for a while.
  
• “Grand Theft Auto”: Moderate fundamental turn plus control elements that somewhat increase the opponent's fundamental turn. Sea Stompy fits this category. The reason I describe these decks as having a moderate fundamental turn is that the control elements necessarily took the place of elements that could have been part of an even more aggressive approach. Thoughts of Ruin does nothing to speed up Sea Stompy's development but is used to increase the opponent's fundamental turn. In practice, decks with moderate fundamental turns tend to have control elements that are flexible in both protecting the player's fundamental turn and increasing the opponent's.
  
• “Highway Patrol”: High fundamental turn and control elements that greatly increase the opponent's fundamental turn (U/W Control).

For each deck strategy, a mulligan tends to mean something a bit different. There would be sixteen match-ups to consider if we took all combinations. Going over these would be a bore, so it's fortunate that these match-up telescope into a few fundamental ideas, which I will go over, here.

As any opponent mulligans, their fundamental turn probably increases. The fundamental turn of any hand with fewer than seven cards is longer, on average, than the normal fundamental turn. As mulligans accrue and the player is left with five or fewer cards, the chance of stalling (very high fundamental turn) becomes large. Stalling means that the fundamental turn increases drastically. Consider, for an extreme example, a no-land hand that does not draw a land for three turns - the fundamental turn is obviously greatly increased.

Similarly, as an opponent mulligans, the control elements are degraded. For the “Highway Patrol” deck, the high fundamental turn is irrelevant, but the inability to control an opposing low fundamental turn is a huge problem. Thus, when a Highway Patrol deck mulligans, the other player's clock is no longer slowed as readily.

Decks in the middle are a mixed bag. Mulligans can degrade the control element, or the fundamental turn, or both. In play, determining which element has been degraded more (or is absent if the player elected to keep a hand with one element missing) can change our own decisions.

Determining how a mulligan has degraded an opponent's strategy allows us to make more informed mulliganing decisions.

If we understand a match-up and how an opponent's mulligan changes this match-up, we then can modify our own mulligan decisions appropriately.

If we are playing a Speed Racer strategy, the fact that the opponent mulligans means that our decision is easier. We do not have as much worry that the opponent will have a lower fundamental turn, and we also know the opponent may be degraded in slowing our own fundamental turn. Thus, we tend to accept hands with slightly higher fundamental turns but with low downside variance (as before).

At the other extreme, if we have a Highway Patrol deck, we should be more prone to accepting hands where our ability to control the opponent is less than optimal. The opponent will, on average, already have a higher fundamental turn, so our control elements will be effectively stronger.

In the middle, the mixed strategies get more complicated. When a NASCAR deck meets a Speed Racer deck, then only a portion of the NASCAR deck's strategy even matters. The NASCAR deck starts out behind just trying to establish its own fundamental turn and hope it is faster than the Speed Racer (often a hopeless effort). Hence, the NASCAR deck does not want its useless control elements and only wants its fundamental turn elements, in general. When the Speed Racer deck mulligans, the NASCAR knows it has a bit more breathing room but is still probably behind. In all cases, the NASCAR deck has no choice but to mulligan aggressively to hands with the lowest available fundamental turn or at least a lower fundamental turn than the expected fundamental turn of the other deck (including the increase in the fundamental turn caused by mulliganing).

The NASCAR mirror is a bit silly: Both have meaningless control elements and only moderate clocks. The winner is the one who gets the faster clock, and the high number of dead cards means the variance is high - it's almost as though every hand has the potential for effective and hidden mulligans. Knowing this, each NASCAR player cares only about having a low fundamental turn. When an opponent mulligans, the NASCAR player still must look for a fast clock and act almost as though there was no mulligan.

When NASCAR meets a Grand Theft Auto-type strategy, the important elements to the NASCAR deck are its aggressive elements and the control elements of both sides. If the Grand Theft Auto deck is degraded in its control strategy, then NASCAR will likely win so long as the aggressive element is still present. When there is no mulligan, the NASCAR deck probably will need both its elements available for it to win. If the Grand Theft Auto player mulligans, the NASCAR player may tend to accept hands with less control available than they would accept in the absence of mulligans.

When NASCAR plays against a Highway Patrol-style deck, NASCAR will rely heavily on its own control elements. Any clock will be fast enough if that lead can be protected. When the Highway Patrol deck mulligans, the NASCAR deck will be able to accept almost any hand with some clock but fewer control elements to protect that clock than NASCAR would otherwise require. The Highway Patrol deck's degraded control element will mean the NASCAR deck is attacked a bit less, so less NASCAR control will be needed.

When Grand Theft Auto plays Speed Racer, the control elements are the key. In general, the Grand Theft Auto deck has to look for hands with control elements and not worry much about its own clock (a la “Who's the Beatdown”). As the Speed Racer deck mulligans, the Grand Theft Auto deck can become the beatdown if the fundamental turn of the Speed Racer deck becomes high enough. Estimating this is tough and is one of the reasons that decks with Grand Theft Auto-like strategies can be difficult to play optimally. If the Speed Racer's deck has mulliganed enough that the fundamental turn switches to Grand Theft Auto's favor, the Grand Theft Auto deck then become primarily concerned with its own fundamental turn and can accept hands with very few control elements. If, however, the Grand Theft Auto deck does not gain fundamental turn advantage, then the Grand Theft Auto's aggressive elements are irrelevant, and the control elements remain the key cards in deciding mulligans. Nonetheless, the fact that the Speed Racer deck has mulliganed means that, all things being equal, the Speed Racer deck's fundamental turn is higher, and the Grand Theft Auto deck can accept fewer control elements (even though they are the key to the match-up).

When Grand Theft Auto plays NASCAR, almost anything can happen. If Grand Theft Auto gets an aggressive start, then Grand Theft Auto will likely win. Grand Theft Auto becomes the beatdown simply because its control elements are contained by the NASCAR deck. If Grand Theft Auto does not have a fast clock, then it must have control elements and a lot of them. While neither the NASCAR nor the Speed Racer decks strategies, as described here, do anything to deal with the clock established by the Grand Theft Auto deck, the NASCAR deck will be able to protect its own clock, so even more control will be necessary from the Grand Theft Auto in the absence of a clock. All this points toward the need for a reasonably aggressive hand on the part of the Grand Theft Auto player. If the Grand Theft Auto player establishes a low fundamental turn, Grand Theft Auto may win. If not, anything may happen. Thus, when the NASCAR opponent mulligans, the Grand Theft Auto player still must start with as low a fundamental turn as possible, and mulligan decisions should revolve around having a lower fundamental turn than the opponent.

The Grand Theft Auto mirror is especially important because this mirror is often what a Limited game is. Each deck has a clock (not a very good one, usually) and a bit of removal. The most important element is naturally having a low fundamental turn. When an opponent mulligans in the mirror, the Grand Theft Auto player can expect a degraded clock and can accept a much worse (but non-stalling) hand. Of course, in Limited, with terrible manabases, an opponent's mulligan should induce one to keep very boring but non-stalling hands. In Constructed, the mirror match between Grand Theft Auto strategies defies a simple rule. The game will revolve around one player establishing a faster clock and the other player trying to slow the clock down. The other clock will not be the determining clock, but this could change rapidly. Mulligans will degrade the ability to set a clock or may degrade the ability to slow a clock, but it's difficult to know what will happen. Good luck with this one. My thought is that if the opponent has degraded resources through mulligans that I would try to establish a clock and see if the opponent's control elements are the ones that are degraded. I would care a bit more about having a low fundamental turn when making mulligan decisions, but the situation is unclear.

Finally, when a Grand Theft Auto deck plays a Highway Patrol deck, the Grand Theft Auto's aggressive elements are the only cards that much matter. Slowing down the clock of the Highway Patrol deck is meaningless. Thus, a Grand Theft Auto deck player should take the opportunity afforded by a Highway Patrol deck's mulligans to select a hand with the best possible clock. The control elements of the Highway Patrol deck may be degraded, so having a reasonable clock may be sufficient.

Every piece of information our opponent gives us must be used if we are to maximize our play. When our opponent mulligans, we automatically have the ability to change our play, and with some thought, we can change our tactics and mulligan decisions to great effect. I was undefeated at a recent PTQ going against the State Champion here in New Mexico. The format was Block Constructed. My opponent, Brandon Remley, mulliganed to four on the play. I was very happy that I had worked through this exercise when I opened a six-land hand. I had already thought through the situation and realized that, in the absence of my own deck stalling, I should win. Thus, I happily kept a six-land hand and won, even though Brandon put a lot of pressure on me with a turn 2 Azorius Guildmage and then a top-decked Twisted Justice. Had Brandon not mulliganed, I would have been forced to throw that hand back because I could have expected a faster clock from him. With the added information the mulligans provided, I was able to accept a bad hand that was still nearly guaranteed to be good enough.

Thanks for reading,

Jeff Stewart