There are two schools of thought on how aggressively to mulligan: you can throw back any hand that isn't amazing, or you can keep almost any hand that has the potential to get there. In Two-Headed Giant, you can mulligan very aggressively as you have a free mulligan. This means that you have the luxury to ship almost every starting seven that isn't to your liking. If the hand isn't great, you can send it back. However, in normal Magic you are put under pressure right from the word "go."
How I have mulliganned has varied throughout my career. To begin with, I don't think I ever mulliganned—the fear of losing a single card was too much and I lost many games to screw/flood/bad hands. Then I noticed that many better players were not afraid to mulligan some of their worse hands, and that the trade off of a single card against having a good game plan right off the bat as worth it, so I began to mulligan almost every hand that didn't have enough land or the right curve. It was when I started to temper my urge to mulligan that my Limited game picked up.
Two of the game's best players and my respected mentors, Olivier Ruel and Jelger Weigersma, both gave me the same advice—most hands will get there by themselves. I think it was this advice that was one of the main factors in pushing my game to the level that it is today. What they meant was that most hands, in a good deck, have the potential to develop well enough to win the game, even if they looked a little sketchy to begin with. This seems to echo the never mulligan rule most beginner players advocate—so where does the fine line between when to keep and when to mulligan begin? What do you look for in an opening hand? What are the factors that you take into account when you decide whether or not to take a mulligan?
The single most important factor is mana. How many land do you have? Is it enough, too few or too much? Do you have all your colours? Will you need the colours you do not have early enough for their absence to matter right now? How likely are you to draw the crucial land before it becomes too late? You want to have on average three to four land when you are on the play and two to four when you are on the draw. Preferably, you want both of your colours represented and if you are splashing, and have a splash card in hand, then the hand is stronger if you also have your third colour.
If you play the usual seventeen- or eighteen-land decks and you have two land in your opening grip, you will play your third land on time on the play 75% of the time, and 87.5% of the time on the draw. This is far more likely than most people assume, meaning you have a greater luxury to keep these semi land light hands. However, the trap you have to avoid is when you need to not only hit your third land drop, but then find your fourth either immediately or the turn after. On the draw you will make your fourth land drop on time 50%, but only 25% of the time on the play! It tends not to matter so much in Limited when exactly you hit your later land drops, or at least, it is not a significant enough of a factor to think about whilst choosing to mulligan.
The variation in these percentages has inspired many players to opt to draw first. This is almost only ever correct to do in Sealed, as the format is much slower. You are less likely to be put under immediate pressure and the tempo you lose you will often be able to regain through the additional card. However in Draft, decks are far more tuned; the average curve will be a lot smoother and a lot more aggressive, so the tempo shift almost never works out (unless you have a really removal-heavy red-black deck featuring lots of cards like Assassinate).
So other than land, what is it that you look for in a good hand? To start with, you have to expect to play most of the cards soon—it's no use keeping a two land hand with five six drops. It is also referable to curve out. This not only maximises the use of your mana each turn, but it will mean that you apply new pressure every turn. This is why it is so important that your deck has a good mana curve; enough early creatures so you have good odds to draw them to begin with but not enough so you draw too many in the late game and enough late game cards so that you have something to do with at the end but not enough so that you draw too many too early on.
I like hands having enough land, some early game to survive and a single great late game spell that you can plan towards. I am always content with a bunch of early filler so long as I know my hand is going somewhere. Four Islands, Blind Phantasm, Primal Plasma and a Jodah's Avenger is an example of a mediocre hand that easily has enough potential to win the game. Its plan is simple: drop the vanilla guys to stall until the Avenger goes the distance, and if it doesn't, hope to draw enough gas to fill in the blanks.
One last thing that is important to an opening hand is having a solution to the first real problem they present. This means that if your opening hand only has a single removal spell, the rest of your cards should be able to carry themselves in dealing with the average threats that your opponent will throw at you, so that when he commits to his ace, you have your removal still waiting in the wings.
There are other influencing factors as to whether to keep your opening hand, other than the specific composition of it. The rest of the deck is very important when making a mulligan decision. If your deck has an abundance of two-drops, then keeping a hand without one is less of a problem as you are likely to draw into one. If your deck has lots of late game, then a hand of five land and two defensive creatures is a must-keep, whereas in a very aggressive deck it would be an auto-ship. The stronger the deck, the more average an opening hand you can keep—if you have enough mana, then the deck will provide the rest in good time.
Visualise how the hand is going to play out before you keep, before you even make a land. Some hands will leave you many dead draws. For example, if you are lacking one of your main colours then ten or so cards you can draw will be dead until you find that crucial land, or if you have only one Mountain, then your Blood Knight is effectively turned off. If you keep a weak hand on the strength of a good removal spell, in a deck with very little removal, you must be aware that you will have to cling to it, and if you have to waste it, you will have to end the game quickly because your deck will have few outs to any opposing bombs.
Now for a few examples, all with the following deck:
Do you keep these, and what are the reasons for your decision? Are there any circumstances that would alter your decision? Think about it before you click on the link. Unless stated otherwise, think of the difference between having these hands on the play and on the draw.
This hand clearly divides those players who are content to let a hand develop by itself and those who throw back debatable hands in the search for something better. I think the decision to mulligan this or not is very tight on the play. I think either decision might almost be correct. This deck has a lot of removal it can draw to stay alive until the Trike hits and the hand contains enough mana to cast any spell in the deck, so none of your draws are dead. I would keep this on the play and mulligan on the draw, where I felt I could get a better hand, especially with the extra draw. If this was Game 2, and I knew my opponent to have a slow deck, I would also keep this going second.
This hand is going to need to draw into some spells to make stuff happen as it currently offers no early threat to your opponent, meaning you will always be on the back foot. Luckily, it has the Essence Warden to keep you alive until you do draw into some business spells. It also has the potential to steamroll your opponent if you rip a nice curve. The Ghostfire will almost certainly be used on the first creature with power two or greater just to ensure you do not fall too far behind. In a deck lacking removal this might be a big problem, but luckily this deck has plenty to chose from. A keep in all situations, but not the happiest.
This hand is going to need to get there. Right now, all it can do is suspend Phthisis and play a next to useless Rathi Traper, which will lock up fifty percent of your mana each turn as it now stands. There are many powerful spells in this grip, but you are going to need to draw a lot of land for it to be worth it, making this an easy mulligan on the play. More consideration is needed about whether to keep it on the draw or not. The Battlemage is going to be thrown out as a vanilla guy as soon as possible, and even if we draw the land needed (involving a Forest, not just two land) to play the Harmonize, we will need to hit solid cards off it—both more land and some crucially needed spells. I would send this back on the draw.
Interestingly, what would happen if you mulliganned into this as your six-carder, minus the War-Pride? It would become an auto-keep on the draw, and a slightly harder keep on the play; a keep that would, I acknowledge, need to get there.
This hand is a mulligan on the play because of the lack of synergy in the hand. The Assassinate is never well suited if you are going first as it is far more likely that your creatures will be the ones tapped. The Omenreader is in direct conflict strategy-wise with the removal and has little to accelerate to. The Grave Scrabbler is the worst card in the deck, with only one madness outlet, and is just a very bad vanilla dork.
However on the draw, the Assassinate gains enough to justify keeping this hand. Sure, if you draw one of your two splashed cards, you still couldn't use them, and at the moment most additional land draws are dead. But for now, you have enough to survive well enough to draw into your bombs and card advantage.
This is an easy keep no matter the situation. Though only the Harmonize is a card worth getting excited about, this hand has everything. It has enough mana, albeit none of the splash colour just yet, but it is both unlikely to flood or screw. The most important aspect is that it has a solid curve, something that is quite difficult for this deck given how few two drops it has. It has enough aggression on the play to force some good trades and then drop the elbow with the Harmonize, and on the draw it can trade its guys away in the early game so that the Harmonize will launch into the lead mid-game. And all this time, the Dark Withering looms as the answer to almost any serious problem to opponent can present.
As a side note, when you mulligan to six, you will keep almost any hand that contains enough land, and on five, you will keep anything with a land in it. Let's hope you don't have to mulligan to four too often,