Last weekend I, like many Magic Online users, was pretty busy with the Planar Chaos Release Events. I made Top 8 in two different 2x events, one on Saturday and one on Sunday, only to lose in the first round of the Top 8 both times. With intentional draws taken out, that comes to eight total matches of online Magic on the weekend, but I knew that I had some interesting column fodder after the very first match that I played.
My opponent in that round – as is my custom, he will remain nameless to protect the innocent – got off to a bad start at the very beginning, leading off the round by announcing “I’m dead” before playing a single land. I could go on about how this is bad discipline, but I recently spent an entire article doing just that, so let’s move on. He appeared to be color-screwed in the first game, playing Plains but no creatures on each of his first three turns, and then missing his fourth land drop; I won without difficulty via a Weatherseed Totem. The enemy had even more trouble in game 2, when he mulled to five and did not play a second land; I had the Totem again and it was joined by a turn 1 suspended Durkwood Baloth for the win.
Not much interesting about a couple of games worth of manascrew, especially over an opponent with the wrong mindset, you might think. Except there is one strategic consideration for both games: I won the die roll prior to game 1 and chose to play last, while my opponent had the choice in game 2 and chose to play first. When my opponent groused about his poor luck in the second game, I tried to offer him a useful lesson:
mm_young: personally I prefer to draw first in Sealed in this format
mm_young: many mulligan decisions get easier when [you are] on the draw
I hope my point got through his manascrew-induced frustration, but knowing how I sometimes react to manascrew, I doubt it. That’s when I decided to write a column about this principle. I hope he’s reading.
Critical Math
I mean, were you expecting me to write a column that didn’t have math in it? You must not know me very well.
Note: This section refers to the mathematical combination function, (N choose K). If you are unfamiliar with how that math works, I would recommend the Wikipedia page on combination mathematics.
Let’s say you have pulled a starting hand with five spells that cost greater than two and two lands, but you are nonetheless tempted to keep. Maybe you have some hot three-drops, maybe there’s some other reason it feels like a keeper… we’ve all been there, I’m sure you know what sort of situations I am talking about. Bottom line is, you would like to rip a land on or before turn 3, else things could get ugly.
Obviously you don’t get to decide whether you want to play or draw first after you’ve seen these openers, but it is still useful to compare the probabilities of ripping the land in these situations. You have X total lands in your build, or X-2 lands left in your library. You have 40-X spells in your deck, or 35-X spells remaining in your library. The goal is to calculate the odds of having at least one land in your top two cards if you are on the draw, and your top three cards if you are on the play.
The probability that you have only spells on top and the probability that you have at least one land on top add up to 1; in English, this means that one of those two events must happen. Thus, the easiest way to calculate the probability we want is to take…
1 – (probability that you have only spells on top).
If you play first, you get two draw steps before you are in danger of missing a land drop. There are (33 choose 2) total combinations of two cards atop your deck, and there are [(35-X) choose 2] different ways for those top two cards to be spells. So the odds have having at least one land are…
1 – { [(35-X) choose 2] / [33 choose 2] }
… so if you are running the classic 23 spell – 17 land distribution, this returns a probability of 71% that you’ll get there. If you are running 16 lands, the probability is about 68%, and if you are running 18 lands, the probability is just over 74%. In the case of drawing first, the formula is…
1 – { [(35-X) choose 3] / [33 choose 3] }
… which gives the 16 / 17 / 18 land probabilities of getting there to be approximately 82, 85, and 88 percent, respectively.
Of course these numbers are not perfect; describing Magic with probability math rarely is. That formula treats all lands as equal, which doesn’t consider color-screw. Also, you could peel a one- or two-drop that might improve your hand considerably, so the odds of getting either a land or one of those drops would be different. However, these figures are still instructive. Note that you are a long-run favorite to get there no matter whether you played first or drew first, but in the 17-land case you will gain 14 percent if you draw first.
What Would Rules Be Without Exceptions?
The thing I like to say about poker is that you’ll make some money with math, but you make the most money when you are capable of throwing the math out the window. Aces versus kings, the ace-high flush versus the king-high flush… it’s the low-probability events that can acquire the opponent’s entire stack, or cost your entire stack, if you play it right.
In Magic, this is simply a way of saying that the one moment when you absolutely need the math in the previous section to work out for you, is usually the one moment when it will not. Knowing that you were a 70-80% favorite is little comfort when you lose a game 3 that you needed to make Top 8, or make money, or make the next Pro Level. Sometimes you need more than math; those are the cases I’d like to consider now.
The big reason I like to draw first is that most of my Sealed decks end up being three colors or more. If you open a poor pool, you might have to go three colors just to have enough playables; some pools are only strong if you squeeze in your bombs from multiple colors. A good example is from one of the PEs last weekend: I opened all the good Slivers in Green and White with Tromp the Domains, and the possibility for a heavy splash with two Evolution Charms, Prismatic Lens, and Chromatic Star. I agonized over which color to splash, since Red offered me Dead / Gone and Cautery Sliver while Black offered Strangling Soot and Kor Dirge. Eventually I opted to splash both Red and Black, and two of the three matches I won might have gone a different way had I not played Kor Dirge and Dead / Gone in the same game.
When you go three colors or more like this, drawing first becomes very important. Don’t even think about it in terms of the math in the previous section; you simply want to find your lands or mana-fixing cards, so getting an extra draw step to get one card deeper can be key. Ideally, you would not keep any hands that have unplayable splash cards in them, but sometimes other concerns intervene – for example, on a couple of occasions with the four-color deck I kept a hand with a two- or three-drop, a Calciderm, and an unplayable splash card. In these cases I was very thankful to be drawing first, even if it meant the ‘Derm would be getting in there a little late.
There will often be set-specific considerations that determine whether you want to play or draw first. In Onslaught Block, for example, drawing first was sometimes the worse option, as the possibility of being the first to attack with your morph became especially important when the morph could be a Haunted Cadaver or Skirk Commando. The card disadvantage of playing first was not as big in Mirrodin Block with its Thoughtcasts and card-advantage artifacts, and the mana risks of playing first were not so large with the Affinity mechanic and the presence of mana Myr.
One thing that you have to keep in mind is the mana-hungriness of the format. It might seem that you don’t need so much mana in TTP draft, because the suspend mechanic allows you to set up your big plays early in the game. However, many of the format’s bombs demand a lot of mana, such that Tim Aten ran eighteen lands in his aggressive deck W/R deck … in draft. This is just another reason that I prefer to draw first in Sealed Deck.
You also have to show flexibility by format. In Two-Headed Giant Sealed, for instance, the first mulligan is “free,” i.e., you mulligan to seven cards, and the player in the B seat gets a draw step even if his team plays first. As a result, not only do I recommend playing first, but you should mulligan much more liberally than you might in a one-on-one match. The “free” mulligan serves as mana fixing anyway, and half of the team doesn’t even lose card advantage if they play first, so almost every one of the above-mentioned reasons for drawing first do not apply.
This is similar to a rule taught in fixed-limit poker: if you would call a bet, it is usually preferable to raise instead. You have the same probability of hitting one of your outs if you raise as if you had only called, plus there is a probability that the opponent will fold to your raise or be scared into folding later on. Similarly, the “free” mulligan gives the same card advantage as if you didn’t send it back, plus there is a probability of mulling into a better hand. The whole point of the 23/17 land / spell split is that if you get two free seven-card hands, the odds that one of them will be playable is clearly in your favor.
I wish that I had more useful things to say about 2HG strategy, but my team was a failure on many levels. First, I chose the name “Johnny Utah” before I realized that my teammate was all of three years old when Keanu Reeves delivered his famously goofy performance in “Point Break.” Then we made the classic mistake of thinking that a card pool with some bombs in it was a good card pool. Finally, we did not play to the best of our ability en route to a 1-2-1 record. So, that’s all you get from me about Two-Headed Giant. You’re not missing much.
This article written while playing Magic Online PEs. I have to say, I feel like a completely different Magic player now than before I had MTGO. Yes, there is some financial cost to getting that much practice in, but I have to be honest, that money was probably going to be spent on Magic anyway.
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