SCG Daily – The Mulligan

We’ve had some excellent pieces on how to know when to mulligan, why bad players often don’t mulligan enough, etc. Those were all quality articles. But what I want to figure out, or at least raise for inquiry, is how to balance the impact of losing an extra card against the possibility that another random hand of six cards will actually help you “win more.”

“Tron is infy better than Magnivore because you don’t mulligan at least twice a match with it.”
Mike Donovan

“That’s not actually a valid argument. Magic is not a contest over who mulligans less, it’s a contest of who wins more. If Magnivore mulligans more and still bashes more face overall, then who cares?”
Richard Feldman

Richard’s statement here is actually one of the more poignant things I have heard in awhile, so I decided I’d devote a daily to it.

Ignore the specifics mentioned within the above quotes. Richard goes on to say that he doesn’t feel that Magnivore mulligans any more than any other deck, and Mike clarifies his position a little bit, but that’s not the point. What I am really interested in is what’s between the lines. Why does mulliganing matter?

I actually don’t believe there’s been an article that’s satisfied my tastes on this matter. Now, we have had some really good pieces on how to know when to mulligan, why bad players often don’t mulligan enough, etc. Those were all quality articles. But what I want to figure out, or at least raise for inquiry, is how to balance the impact of losing an extra card against the possibility that another random hand of six cards will actually help you “win more.”

Obviously, there are plenty of reasons not to mulligan. Even though I am going to play down the impact of pure card quantity per se, being down a card from the get-go is the pits. Entire decks are built around sacrificing a particular resource to eventually achieve a net advantage of one or two cards, and often those will be enough to carry a game. Furthermore, there is always the possibility that a mulligan will yield an inferior hand, and then you’ve shipped a grip back for nothing.

All of this is not difficult to understand. But I want to know what the reasons are to mulligan. I’m not talking about obviously bad hands like the ol’ one-lander; I’m referring to the times where it is correct to ship back an on-the-surface reasonable hand because it’s not going to be good enough to win you a match.

I want to get one thing out of the way really quick, though. You know that scene in Goodfellas where Joe Pesci shoots the guy at the bar out of nowhere? He actually didn’t do that because the guy called him “funny.” He did it because the moron said something like, “Yeah, ship that hand back; you can’t even cast that Faith’s Fetters you’re holding without your White splash, so it’s like a six card hand anyway.” If this example doesn’t serve you well, you know what I am talking about. Justifying a mulligan because one of the cards isn’t immediately useful.

For one, even if you have like two lands and a Blazing Archon, that doesn’t automatically make it a six-card hand. It’s not as if Blazing Archon takes a look at the buddies next to it, sees only two geographic formations, and jumps to the bottom of your deck when you’re not paying attention. It’s still there, it can still be cast much later on, it still means you’re necessarily not going to draw it later, and it can still be discarded to Shrieking Grotesque and the like. Now, I understand the point that it’s not going to immediately affect the game-state, and would generally agree that many two-land Blazing Archon hands need to hit the bin, but that argument in and of itself isn’t valid.

Also, the other flaw with the “it’s like six cards anyway” argument is that it doesn’t at all account for why you expect your next six cards to be any better. Just because something is effectively a mulligan doesn’t mean that you ought to actually mulligan that hand just because you might as well. If a hand is like a six-carder, but those six are savage, then who cares?

So, to use Richard’s terminology, it seems like you keep a hand when you believe it will “bash more face” over another randomly distributed hand containing one fewer card.

I don’t think it’s too big of a stretch to extend this to mean that you want the cards in your opening hand to do the best job of gaining strategic advantage against a given matchup. I’ll talk more about that tomorrow, but what I basically mean is that with every deck you have a plan of how things are going to go. You want your opening hand to conform as well as possible to that plan. If you’re playing Zoo against Heartbeat, you want to maximize your damage output ASAP, and thus on the gradient of good hands the best are those that put a 2/2 and a 3/3 out quick, and then continue to apply pressure with enough burn to finish the job either before Heartbeat can go off, or after they cast Heartbeat but in response to an Early Harvest. If, conversely, you’re playing Heartbeat against Zoo, you want hands that enable you to win as quickly as possible – or at least Savage Twister away their board at a healthy enough life total – at the expense of later-game versatility and resiliency. Thus if you have a pair of Heartbeats and an Early Harvest but not a whole lot to do with the mana, you still might keep the hand because of its explosive potential.

Thus you have to do certain things. I remember playtesting a game against Heartbeat with Niv where I had a reasonable enough hand – something like three land, Disrupting Shoal, Compulsive Research, Electrolyze, Hinder – but I shipped it back because I felt that a random six-card hand would probably be of a higher quality than that one. It’s not like my hand had three finishers, no land, nothing to do with the mana, useless cards for the matchup, etc. It’s just that this hand doesn’t accomplish very much, and is probably on the low end of the “good hands against Heartbeat” gradient.

My thesis is something like this: a hand doesn’t have to be “bad” for you to mulligan it. It just has to be “worse” than what you could expect from a new grip of six.

I guess part of arriving at this conclusion is that you have to understand a certain principle about card advantage. Ready for this, because I am sure someone will get irritated:

There is nothing inherently good about card advantage.

You with me yet?

It is not as if someone is out there handing out trophies.
“Ooh, I’m up four cards against this guy!”
“Congratulations, here’s some free stuff.”

The idea behind card advantage is, obviously, sound. It basically says that, all things being equal, if you have more cards it is more likely that you’re going to be able to beat your opponent. None of you have some sort of fetish for putting bad spells in your deck, so one of your cards will (more or less neutralize) one of your opponent’s, or will otherwise have a similar effect on the game state. To put it another way, say you Savage Twister away three of your opponent’s 2/2 creatures in a Limited match. Savage Twister is not good because it killed three creatures. Matches are not decided upon the killing of creatures, but upon the ending of games. Obviously, though, Twistering three guys makes it easier for the game to end in your favor, because even assuming a worst-case scenario (you’re both in topdeck mode, you have no follow up to the Twister, and the only difference in the board position is that now you’ve got two more lands in play than your opponent) you still have a higher threat density remaining in your deck than he does. Thus you’re more likely to peel, and therefore are more likely to win.

The point there is that Twister, in that situation, is good not because it nets you cards, but it generates a mathematical advantage. In that case, cards are part of the advantage equation. But in many cases they are not.

If I am playing Niv-Mizzet Control against Gruul, for example, netting cards doesn’t necessarily do anything for me. Obviously I win a lot of games through repeated two-for-ones with Threads and Pyroclasm and Electrolyze, etc, but the two-for-ones are only really important because they ensure that, at some point, my opponent is going to draw land and I am going to draw gas. But assume that most of the cards in my deck are instead straight up one-for-ones. At that point I am the one with Dragons, and he is the one with multiple 2/1s and 1/1s. I don’t need any extra cards at that point to retain advantage. Therefore, the situation is the same as it is with the real Niv-Mizzet deck: it is in my opponent’s best interest to kill me as quickly as possible, lest he be overtaken by superior cards.

All of that is to say that now my opponent’s method of advantage is to end the game before I can cast all of my spells. This is why I fear a five-card hand from Gruul that contains both Kird Ape and Scab-Clan Mauler much more than I do a seven-card hand sans either of those cards. The extra cards don’t accomplish his goal of ending the game faster than the aforementioned five-card hand, so they literally do not matter.

I hope this made sense. I felt that the concept on the message board thread was really interesting, and so I wanted to explore it. I await your feedback, fearless readers.