A Mulligan Rant
I have no particular reason to write down this rant now. It is just something which has been stirring in my mind for quite some time and is now bubbling up. There is some correlation with the recent resurgence of MTGO use on my part, though (although that’s already back on a short hiatus until Magic 2013 comes out).
What it is about: There are a lot of articles on the net about the art of mulliganing. Most of those will tell you that you use the mulligan option not often enough. Most – well, almost all – of those articles are utter crap!
That does not mean, of course, that YOU, individual reader, whoever you may be, might not actually mulligan too rarely – maybe you do. Maybe you are one of those players reluctant to send their hand back unless it is completely ridiculous (like no land at all or all land with a draft deck). I don’t know. That’s not my point. My point is that the reasoning typically used in these articles is complete bullshit and, if actually acted upon, would lead you to make extremely poor mulligan decisions – to be precise: mulligan way too often.
See, all those articles tend to concentrate on only one aspect of your mulligan decision: How to evaluate your opening hand. And they really like to go into detail on this! Usually, they just brush over the obvious stuff (too little mana; too few spells; mana color not matching spell colors) and delve into the subtleties: Why an aggressive deck needs to apply pressure fast and thus wants several cheap drops in its opening hand. Why the same deck needs a high threat density and thus cannot use too many lands in its opening hand. Why a control-oriented deck needs a way to stop an early attack in its opening hand. Why this deck needs to develop its mana base as seamlessly as possible, and thus wants more than two lands in its starting seven. Why, in certain matchups, you really want certain key cards in your opening hand. Why some opening hands make for bad curving (like with Tormented Soul as one-drop and Leonin Skyhunter as two-drop). Why the number of dependant drops like auras or equipment shouldn’t outweigh the numbers of independant drops you need to put them on. Why multiples of situational one-ofs in your deck devaluate your opening hand. And so on.
You see, so far, all of this is completely correct! All this has to be taken into consideration when evaluating your starting hand. These are all issues which might cause you to lose the game. But, the conclusion those writers invariably draw is that, if you diagnose one of these problems, you should send your cards back and try again.
…AND THAT IS MORONIC.
Again, and again, and always again, when I’ve read such an article, I waited for an analysis of your chances TO ACTUALLY IMPROVE YOUR HAND BY RANDOMLY REDRAWING IT WITH ONE CARD LESS. And again, and again, and always again, I’ve been disappointed (and each time that happened, I knew the day when I would write this rant here drew nearer).
Now, I admit, it is really, really hard to calculate the chance for a hand meeting such complex criteria as are used in its evaluation. It should at least be obvious, though, that the more seven-card hands you send back because they don’t meet your criteria for a satisfactory starting hand, the less six-card hands will be satisfactory according to the same criteria. It should also be obvious that the chance to get a satisfactory hand gets considerably smaller with each card less. From these obvious observations, you can already conclude that your criteria for a satisfactory starting hand should not even nearly rule out 50% of all possible hands (unless you have a reason to mulligan for something very specific, like a Leyline of the Void which you know your opponent can with 100% certainty not beat if it comes down before turn 1, no matter what else happens in this duel).
But you know what? The percentage of satisfying opening hands (according to the criteria used in these articles) is certainly not much higher than 50%! Actually, at least with limited decks, I am not even sure it reaches 50% at all. If you disagree, just use any program allowing you to draw random opening hands from a given deck in rapid succession and do a count how often you are satisfied with these hands. And then, just for shock value, do the same thing with six-card hands! See, if you play a lot on MTGO, you learn something really important about six-card hands: They SUCK. Big time. (And it’s NOT the shuffler.) Oh, and even in the unlikely case that they don’t, you are still at least down one card.
What really makes me to want to kick the person who writes it, by the way, is something like this: “Yes, this hand is excellent if you manage to draw a land within your next three draw steps, and another land until turn five or so – but what if you don’t?”
Well, I tell you what: I will probably lose. (Although there is the distinct possibility that my opponent’s hand may also suck.) But hey, I’ve got another question for you: What if I take a mulligan, and my new hand is no improvement at all? Oh, right, I will probably lose, too…
Mulligan proponents usually (rightfully) warn you against putting too much faith in your next few draw steps. However, for some reason, they exude at the same time unwavering faith in getting satisfactory six-card hands! Why is that?
I’m going to tell you: The reasons for this are deeply ingrained in human behavior patterns. For one thing, we humans hate to be helpless. Also, we like to appear smart.
It is for the first reason that many better players believe into mulliganing almost religiously. See, one thing which seperates better players from mediocre players is that they always look at their own actions when analyzing a loss. Where most players will just complain about bad luck, they try to perfect their own play, accepting losses as their own responsibility. Certainly, as a general principle, this is a very healthy attitude if you want to improve your playing skills!
However, they often tend to take this approach way too far. For one thing, chiding yourself for every little mistake or subtly wrong play decision may mean that you hold yourself to unrealistic standards. Everyone makes mistakes – there is no such a thing as a perfect player or a perfectly played Magic duel. Just because your play has been not-perfect or even average by your own standards, it does not mean that you deserved to lose against another player who played worse, but got lucky.
And then there is the inability to simply accept bad luck. If you look too hard for things you could have done to prevent a loss, you might lose sight of a simple important truth: Sometimes, you just can’t win. No matter what you do. There is a large element of chance in Magic, and sometimes fate just stacks the cards against you. This is something you need to realize when you really want to improve your game, because otherwise your analyses of games you play will just be incorrect. There are games you win because you are lucky, and games you lose because you are unlucky.
As I said, it is an improvement to get the mindset “my wins may be luck or skill, but my losses are my fault” over our default mindset of “my wins are because of skill, but my losses are due to bad luck”, but to really be able to judge your playing skills and your playing decisions correctly, you need to acknowledge both skill and luck and identify the parts those two factors play in the game.
The thing is that many good players, when they look at an opening hand they KNOW has problems which may cause them to lose the game, are averse to accepting that fact and putting their hope in their next draw steps and the possibility that their opponent might also be holding a sketchy hand. They have succesfully trained themselves to take responsibility for the outcomes of their games, and they are actively looking for factors they can influence with their decisions. Thus, they mulligan, because this is usually the only active option which is open to them. It just feels better to do something than to admit that one is helpless.
Then, there is the desire to look smart, or at least not stupid. Many, many years ago, there was an article in the Duelist (a PRINT MEDIUM about Magic – would you believe it?) which contained excellent and eye-opening advice. I’m not sure if these were the exact words used, but the message was: “Don’t be afraid to look stupid!”
It gave an example which I will try to recreate as faithfully as possible without remembering the exact situation: You are playing a white weenie deck in a standard tournament (remember, that was a time when WotC debated if Serra Angel and Savannah Lions were “too good”, and White had no access to creatures even close to the power level of, for example, Hero of Bladehold, which is able to close a game in short order on its own). Your opponent plays UW control, probably with 4 each of Swords to Plowshares and Wrath of God, an assortment of (actually good, including the original) counterspells, some rather clumsy card drawing (something like Jayemdae Tome or Treasure Trove), and 3 or 4 Kjeldoran Outpost as winning conditions. He has 14 life, 5 lands in play (3 Island, 1 Plains,1 Kjeldoran Outpost) and 4 cards in hand. He is tapped out with the exception of an Island (expect no free spells from that deck, although it probably doesn’t matter, and also no relevant 1-mana spell) and just ended his turn after wiping your board with Wrath of God. You have only 6 Plains in play (you got a little flooded), and after drawing your card this turn, look at your options: Your hand contains 2 Savannah Lions and 2 White Knights. Your decks consists of more Plains and more small creatures, 4 copies of Crusade, 4 Swords to Plowshares, 3 Disenchant and 3 Armageddon. What do you do?
One thing you should realize is that, if you play out all your creatures, another Wrath will leave you totally resourceless. (Okay, you might be able to topdeck an Armageddon on your next turn, but even in that unlikely best case scenario, and even if your opponent, who might have dropped a sixth land in the meantime, does not counter your Armageddon, you are still left with no pressure on the board at all, and an opponent with a full grip who will probably recover faster than you.)
Another thing to consider is that your Savannah Lions will very likely be ambushed one by one by soldier tokens from your opponent’s Outpost over the next few turns, without costing him a card, and he can activate his Outpost even with counterspell mana up. If you do not draw (and resolve) more creatures very soon – preferrably ones which can not easily be traded against Outpost tokens – your offense will be slowed down to a crawl over the next few turns, with just two White Knight attacking into an ever renewed soldier token. If your opponent also has a Swords to Plowshares, he will soon completely stop your attacks if you do not draw into more pressure.
I hope you realize that there is a strong disincentive against just playing out all your creatures and hoping for the best: If your opponent just wraths away your board and leaves you empty-handed, you will look pretty stupid – didn’t you see that coming, noob? Why didn’t you play around it?
Well, of course you see it coming! But then again, you should realize that there is just nothing you can do about it. If your opponent has the second Wrath, or finds it soon, you will lose that game, no matter what you do. Not immediately exerting as much pressure as possible again will only increase his chances of drawing it soon enough. This means that your only hope of winning this game is putting your faith in your opponent not having that Wrath and trying to reduce him to zero lifepoints before he finds it or another way to stabilize. It means, that you, OF COURSE, play out all your creatures and accept that there is no subtle, advantageous playing option for you in the face of the possibility of getting blown out by that Wrath; that you accept the outcome of this game is largely out of your hands and you might look stupid to a casual observer who will notice that you “just walked right into that second Wrath”. It is the correct play to do so.
Just like that, it is often the correct play to NOT mulligan that admittedly sketchy hand and hope for the best. If you lose that game because your next draw steps do not solve the issues you identified with your opening hand, you might look stupid to other players – or even yourself – because you could CLEARLY see that this hand had issues (“Noob!”) and didn’t act upon that knowledge. If, on the other hand, you DO mulligan that hand because of its subtle imperfections and lose the game then, other players (and maybe yourself) will be much more willing to accept that you lost this game because of bad luck – after all, you DID all you could do, you DID mulligan an unsatisfying hand!
There obviously is a point when mulliganing more often does not improve your chances of winning anymore, but instead reduces them. I want to tell you that, if you mulligan your hands for other than the most obvious reasons (too little mana, too few spells, stark color mismatch between mana and spells), you will reach that point very soon – certainly much sooner than the typical article about mulliganing implies! If you feel the desire to mulligan that much, you should instead opt for the following:
1. Build decks which give you a higher percentage of opening hands which are satisfying according to your criteria.
Of course, while there might be room for improvement with your deck-building skills, you will invariably hit a ceiling here. (Also note that a deck which delivers more satisfying opening hands is not necessarily a deck with a higher win percentage!) I just cannot resist to link to an example which illustrates this concept extremely well: Ted Knutson was probably the most clueless person to ever try his hands at strategic advice on the Wizards site, and this was possibly his worst article.
Take a close look at the deck he uses as an example. It is completely horrible – not because of its power level (which, of course, can only be judged relating to the options the deck builder had at his disposal, and compared to the power level of the decks he intends to throw it against), but because of its inherent inconsistencies. For example, that is 24 lands plus 4 Llanowar Elf in a deck which consists mainly of spells costing 1-3 mana. It contains Grizzly Bears together with a Verdant Force (which, if we assume an environment of equally powerful decks, will almost never get cast even with 28 mana cards). It uses Elves as mana acceleration, although it has only a few cards it can actually accelerate into (the Elves will often not accelerate you to 5 mana, rarely to 6 mana, and practically never to 8 mana, since you will miss land drops in the meantime – this means that your only good acceleration targets are 4 Trained Armodon and 3 Order of the Sacred Bell, unless you want to play an early Blanchwood Armor on your Elf). And yes, the Elves ARE acceleration and not taking the slot of lands, because, apart form that single, in any event misplaced Verdant Force, the deck could very well do with 24-26 mana cards – and it SHOULD, because it is an obvious early game deck, even though it might have a few trumps in the lategame with Blanchwood Armor or Shivan Dragon. By the way, those 8 Mountains are just enough to seriously impede the deck’s ability to put out 2nd-turn Elvish Warriors or even 3rd-turn Trained Armodons and noticeably weaken the Blanchwood Armors, but not enough to guarantee the option of casting those dragons with 6 mana (in other words, Shivan Dragon does not belong in that deck). Llanowar Behemoth is, of course, just not worth the inclusion in a constructed deck even on this low casual level, unless you have serious token production going on – in an G/r deck with weenies, enhancers and burn it is a typical win-more card. All in all, a reasonable build of this deck would end its mana curve at 4, would splash Red only for single-colored burn spells, would play Llanowar Elves only as a substitute for lands to avoid flooding, and would make better use of their acceleration (by replacing those 5+-mana creatures with more for 3 or 4 mana).
Now, of course, this article wasn’t about deckbuilding, but about mulliganing, but that is just it: When evaluating his examples for opening hands, Knutson applies standards which might or might not be reasonable for hands from a well-built deck, but are nearly impossible to meet with opening hands from this deck! If you build a crappy deck, you have to keep crappy hands. It’s that simple. If you aren’t afraid of nightmares, just imagine what a typical spread of 6-card hands from this deck would look like… (Hint: It will look a lot like those 7-card hands, just with one card less!) How lucky do you have to be to get a satisfactory 6-card hand with THIS deck?
Well, but once you draw your starting hand, it is obviously too late to correct your deck’s build. All that is left then is the second option:
2. Adjust your criteria for satisfactory opening hands so that your deck can actually produce such hands (much) more often than not.
This is exactly where practically all mulligan articles fail. Do not just list all the possible issues your starting hand can have; identify when you can actually expect to improve on your situation with a mulligan! I really cannot give you hard and fast rules for this, because Magic is simply too complicated (mulliganing is actually more an art than a science), but the best way to get a feel for the correct balance between keeping and redrawing is building the deck in question online and drawing A LOT of 7-card hands, as well as a lot of 6-card hands – maybe even 5-card hands and 4-card hands – so that you see what you can realistically expect. Also, while the “forbidden” peek at the top card of your library isn’t too useful (because you should be able to calculate your chances to get a single helpful card, and a small amount of data can only mislead you here), actually playing out games with the deck and watching how sketchy hands unfold over the next few turns will give you an impression how well your deck develops questionable opening hands – some decks “mulligan well”, and some decks “keep well” (also, some decks do both or neither). If you do this often (and I mean OFTEN – it is a skill which requires years of practice!), you will get a general sense of the rewards of mulliganing which you can apply even to decks you didn’t play yet. Ask yourself: How lucky do I have to get with my next draws to make this draw acceptable if I keep it, and how lucky do I have to get with my mulligan to improve my hand as much?
Before I present you with a few basic statistics to conclude this entry, just one more thing: Of course, I assume that you actually draw your hands randomly, and do not use a shuffling technique which improves the distribution of cards according to your needs. I must admit, whenever I read in how many situations some pros claim it is correct to mulligan and compare this to the hands I get via true randomization, I ask myself if, maybe, these pros have found a way to draw opening hands which justifies their high standards for keeping them…
With a 60-card deck containing exactly 24 lands, your chance to have at least 2 lands and at least 2 non-lands in your opening hand of 7 cards is 84%. With 30 lands, it is 90%; with 18 lands, it is 69%. In an opening hand of 6 cards, these probabilities are 75%, 81% and 58%. 5 starting cards give you 59%, 65% and 45%; 4 cards 36%, 39% and 27%.
This means that with a typical mana distribution of 40%, you will already mulligan nearly every sixth of your initial hands just because they don’t meet the fundamental requirements of providing you with at least two lands and at least two non-lands! Also note how much each mulligan reduces your chances to meet that basic criterium even further – every fourth 6-card hand in a typical deck fails to do so.
Now for examples of slightly stricter requirements: Here are the probabilities for an aggressive deck (deck A), running on 21 lands, where you, quite reasonably, wish to have at least 2 lands and at least 3 non-lands in your opening hand, and for a controllish deck (deck B) running 28 lands, where you want to see at least 3 lands, but still at least 2 non-lands:
A: 74% with 7 cards; 59% with 6 cards; 35% with 5 cards; 0% with 4 cards.
B: 69% with 7 cards; 53% with 6 cards; 30% with 5 cards; 0% with 4 cards.
These are realistic mana distributions and seemingly reasonable requirements – but they already require you to mulligan more than every fourth hand with the aggressive deck, and for the controllish deck, they seem already too strict – would you really mulligan a two-lander in the hope of getting a three-lander or four-lander with only 6 cards (your chance for that is just a tad over fifty percent)? Don’t you think you’re better off hoping that an otherwise fine two-lander will deliver the needed additional land during your next draw steps than hoping for the miracle of a perfect 6-card hand and risking a totally unplayable one? (Actually, if you really need your land drops in a deck, it is usually a wiser course to use a lot of card draw for 2 or less mana than to rely on seeing 3 lands in your opening seven cards.)
(I’m not giving numbers for 40-card decks here, but believe me that with comparable land percentages the probabilities for desired opening hand distributions do not increase significantly there.)
Now don’t forget the additional issue of colored mana, and you might understand that you just do not have that much room to manoeuver for applying additional criteria. As a general rule of thumb, I suggest that mulligans because your initial hand doesn’t meet the “at least 2, not more than 5 lands” requirement should make up at least three quarters of your mulligans to six, and that you should save mulligans which are not due to mana screw, color screw or mana flood only for really extreme cases. Also, when playing a monocolored deck which can operate well on two mana, one-landers should not be automatic mulligans, especially not when you’re already below seven cards – some of them might actually give you a better chance at winning than a hand with one card less (remember that taking a mulligan and hoping to draw that second land are BOTH options which test your luck!)
One last thing: You probably know stories of decks mulliganing to 5 or even 4 cards and still winning against 7-card hands, or you have been there yourself (I certainly have). Yes, it happens sometimes. Does this mean that less cards aren’t that bad? Nope. Less cards ARE bad. These stories may illustrate that you can sometimes get away with reducing your starting hand significantly. But they may also illustrate that your opponents’ hands aren’t always perfect either; or that getting lucky with the top of your deck can offset an initial disadvantage – both of which also applies when you keep a less exciting 7-card hand.
In the end, the only thing which is certain when you take a mulligan is that you end up with one card less. It has obviously become a trend to downplay that disadvantage, but you should not fall for this.