What Makes for "Acceptable?"

Posted in Top Decks on August 19, 2010

By Mike Flores

This is Opening Hand Week.

I had a couple of different ideas about what I might write about for this week. One of them was a "gauntlet" or SWOT-type article leading into U.S. Nationals (which is this weekend, and my "big event", personally, for the year); or I was thinking about maybe writing about the results from China Nationals.

But Bill Stark sent me a Facebook message about the deck he used to make the Top 8 of Grand Prix–Columbus, the Legacy event that Steve Sadin won a couple of years back. Because, of course, it's Opening Hand Week and Bill had something to say about opening hands.

Besides jerking me back into the mode of Theme Week writing (Top Decks is rarely the officially "on theme" column for Theme Weeks), I thought about something else. Bill always credited my doomed 9th Place deck from U.S. Nationals 1999 (out on tiebreakers) as the inspiration for his Columbus Top 8 deck. Given the week, and the Theme Week, I decided to go with Mr. TheStarkingtonPost.com's point of inspiration:

Bill Stark's Mono-Black Beatdown

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My original:

Brian Schneider's Beatdown

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As you can see, Bill's crediting me is a bit generous. He cut my shadow creatures for things that pump, and the Hatred combo for Sinkholes (which, admittedly let him free up a little land), as well as swapping around where the artifact disruption went (in Duress, out Cursed Scroll) ... but I'll take it.

How does this relate to the theme of Opening Hand Week?

We see two cards that are intimately related to openers:

Leyline of the Void is of particular interest given that we are once again living in a world of Leyline availability. Leylines come into play for free if you have one in your opening hand, and therefore can increase the value of a hand; for example, a questionable seven-card hand that has a relevant Leyline in it suddenly becomes much more acceptable than if it included a different in-match-up relevant spell. Why? For most decks the most limiting resource in a game is mana, and Leylines are efficacious without tapping the actual mana-keg.

Conversely, most Leylines aren't worth their actual costs in mana; that is, you wouldn't necessarily want to pay four mana for one. For example, the historical analogue to Leyline of the Void, Planar Void, only costs rather than .

Subtly, that makes hands without Leylines in them—when you have a sideboarded deck full of Leylines—worse than the same hands if Leylines weren't in your deck. Drawing a random four-mana spell that you may never have the time to play after your opening hand is basically drawing a non-card. For example, at the time that Leyline of the Void was all the rage, Cephalid Illusionist combo decks and Bridge from Below Dredge decks could both kill you (or at least put you in an essentially no-win position) well before you actually had four mana, provided you even drew the Leyline after your opener.

This might prompt you to mulligan what might otherwise seem like a reasonable hand, especially if you had no other anti-graveyard sideboard spells. It might not, if you weren't thinking about it, especially.

In competitive Constructed the main point of interest around opening hands relates to whether or not any opener is worth keeping, that is, acceptable. We can wrap our discussion of Bill's other opening hand-centric sideboard card, Serum Powder, up in that.

    So ... What Makes for "Acceptable?"

An acceptable hand is simply one that you are not willing to mulligan.

The value that a Magic strategy column can bring to this discussion is by highlighting some rules around which we can craft this decision.

Before we get there ... Why would we be apprehensive about mulligans?

Basically, we don't want to be down a card. (Or "another" card.) That's it.

This is the value that Serum Powder could give Bill back at that first Legacy Grand Prix–Columbus. He could utilize any of the mulligan strategies we discuss below without actually spending that sometimes-painful card. That's it.

Sometimes I feel like the basic model for card advantage—while giving tournament players an initial baseline understanding for tight play—has made us stupider. We make decisions based on a truly rude conception of card advantage rather than what might make the most sense. Do you know there was once debate around whether or not Vampiric Tutor was a good card? Come on.

Apprehension about what should be "clear" mulligans comes from this same level one thinking.

    1. The Basic Mulligan Model—Keep Hands With Two or More Lands

Remember that the original (pre-Pro Tour–Paris 1997) mulligan rule was that players could only mulligan all-land or no-land hands. Therefore the basic mulligan algorithm comes from a stance of mana distribution. If you have an acceptable number of lands in hand (generally considered to be "two"), you are supposed to keep.

"Two lands" is not a terrible baseline rule, but even when more strategic questions are not in play (you are going first in a Game 1 situation and you don't know what your opponent is playing), it is far from perfect. For example, what if your opening hand has two (or more) lands ... but you can't actually play any of your spells? For example, you are a Jund deck and you have two Mountains, but the rest of your spells are Putrid Leech, Sprouting Thrinax, Maelstrom Pulse, Blightning, and Grave Titan?

Not only can you not play any of your cards, you are nowhere near being able to play any of your spells! If you lucksack into a black source you can play a Blightning (maybe on turn three, maybe not) ... but after that?

Not a great opening hand.

Just based around mana-development considerations, I wrote a pretty well-received set of blog posts last year around some slightly more developed concepts.

The opening hand was this:

Kitchen Finks
Civic Wayfinder
Civic Wayfinder
Fire-lit Thicket
Broodmate Dragon
Gift of the Gargantuan

My Two-Headed Dragon teammates (and fellow columnists here) Paul Jordan and Steve Sadin both said that the second part in particular was one of the best things I've ever written; so if you want to check out the original, you can here and there:

Part I: You Make the Play - Keep or No?

Part II: You Make the Play - Statistics for Dummies

We can imagine a similar hand with a more modern deck list. Here is one that I plucked from a Magic Online 4-0 performance and have been playing around with a bit this week:

hccga's Titan Force

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Analagous Opener:

Bloodbraid Elf
Borderland Ranger
Borderland Ranger
Inferno Titan
Raging Ravine

Bloodbraid Elf makes for a slightly less attractive opener in this hand than Kitchen Finks did in the original study (four mana versus three), but the other cards are pretty parallel (Civic Wayfinder and Borderland Ranger in particular); on balance, hccga's deck plays 24 lands and my Jund deck from last year played only 23.

In either case it seems pretty clear that if you get to three lands you are going to get to enough lands to play your six-drop (Borderland Ranger, Borderland Ranger, and Cultivate are all worth an additional land or two).

So the question is ... Do you keep?

It's important to point out that right now, you can't play any of your cards.

If we reduce the question to purely one of mana distribution (forget for a moment that this hand is completely non-competitive against Runeflare Trap combo, a second turn Fauna Shaman, or almost any White-Blue Control opening hand), we can reduce the question down to "how likely am I to have three untapped lands on turn three?" versus what is the likelihood I have to lose if I don't have three untapped lands on turn three?

Different math is used if you are on the play or on the draw, and the math would be much different if you had two Raging Ravines rather than one and a Forest.

Given hccga's deck list, I reduced this question to the following possibilities:

  1. We can draw any land on turn one or turn two.
  2. We can draw any untapped land on turn three.
  3. We can draw Explore on turn one or turn two (which potentially changes the math).

The presence of Explore as a possibility is what makes this opening hand different if we have two Raging Ravines ... we can't play Explore on turn two if our second land comes into play tapped.

In order to fulfill the first condition we have:

  1. 22/53 likelihood of drawing any land on turn one
  2. 22/52 likelihood of drawing any land on turn two (provided we haven't already drawn a land on turn one ... which would fulfill our condition).

On top of that we have seventeen possible lands we can draw on turn three (Rootbound Crag comes into play untapped on turn three because one of our lands is a Forest).

The Explore gives us an additional wrinkle between point two and the preceding paragraph. Basically, if you draw Explore on either turn one or turn two you get an additional 22/51 before a [now] 17/50 chance of drawing untapped land on turn three.

Again taking only mana distribution into consideration, most players will keep that hand as—all those points put together means you will hit your third land—your third untapped land, no less, more than 8 times in 10. Heck, some of the time you'll even have a Bloodbraid Elf in play on turn three!

So what about hands that aren't just about mana development?

    2. Strategic Mulligan Model—Keep Hands With "Blah"

These hands are all about pattern recognition. For example, many Necropotence players would only keep hands that had either Necropotence or Demonic Consultation (i.e. virtual Necropotence) in the opening hand. Necropotence was a special case: it would undo any aggressive mulligans at no mana cost.

More modern systems might be to keep only hands with Bitterblossom in the Faeries mirror; or hands with Bitterblossom or Thoughtseize in the mirror on the draw; or hands with Bitterblossom, Thoughtseize, or Broken Ambitions in the mirror on the play. Bitterblossom was so important to the Faeries mirror in Standard that if one player had it and the other didn't, the one that didn't have it would usually be completely overwhelmed. Therefore having Bitterblossom in your opening hand was considered of paramount import; but the ability to remove a Bitterblossom (via Thoughtseize or Broken Ambitions) would at least even the playing field.

I have played a lot of ramp the past few weeks. I think that in the current Standard ramp vs. ramp (whatever color or colors you are playing in addition to green, if any) have their own mirror rules. You really want two accelerators in your opening hand. Shipping hands that don't have two are less painful because especially cards like Cultivate will un-mulligan you. But in the mirror, if the opponent has two accelerators and you only have one, you will often be facing an unbeatable threat on turn four, uncontested. Good luck beating a Primeval Titan when it immediately grabs a pair of Tectonic Edges for your lands.

    3. Additional Mulligan Models and Opening Hand Considerations

The two most well-known general rules for evaluating opening hands include shipping the ones that don't have two lands and shipping the ones that don't fall into whatever strategic model your match-up requires, but there are loads that come with experience, or only have to do with particular decks. Additionally, there are decks that can theoretically operate without a particular element (similar to what we talked about in the previous point), but don't operate as well.

For example, the Kuroda-style red deck that Josh Ravitz used to make Top 8 of the 2005 U.S. Nationals Championship was "fine" without Sensei's Divining Top in its opening hand, but had an overwhelming advantage in most match-ups when it did have one. In the current Standard Fauna Shaman decks can play like National Qualifiers-era Naya Vengevine decks, but go completely Vengevineinsane when they do have a Shaman in hand. Their expectation, in some match-ups, probably doubles on the spot!

Here are some more:

    Limited—Mulligan Hands with Six or Seven Lands

You might—depending on which two spells you've got—also mulligan many five-land hands. But you should almost always mulligan a six-lander. I mean ... what are you going to do? If your one spell is a two-drop (most Limited decks really want a two-drop), what are your chances of beating an opponent who not only also has a two-drop, but I don't know ... something else as well? Similarly, what if it's your awesome spell ... say, a five-drop (or even bigger)? Um, you're probably going to get all beat to hell by his two-drops before you ever get a chance to hit your five, six, or seven.

Bonus Aside: Last night, after writing the first draft of this article, I made the finals of an eight-man draft on Magic Online. Up a game, going into Game 2 of the finals, I intentionally kept a hand with six Forests and Islands, and one Garruk's Companion (his creatures were soft to a quick three power threat) to see how this note might work in real life; he promptly played Doom Blade.
End Aside.

    Some Combo Decks—Keep Any Hand With Lands and Spells

Decks that have a huge number of Ponders and Preordains, or older-school stuff like Brainstorm and Sleight of Hand. Going even further into the sick two-drops from Treasure Hunt to Impulse to even Spreading Seas. These decks can basically improve even tight one-land hands with great consistency, despite often playing fewer lands than the opponent.

    Some Control Decks—Mulligan Hands with Finisher X

Some decks have only one Rainbow Efreet (or insert whatever kind of expensive six-drop, or stage three finisher, or whatever). While having one in your opening hand isn't necessarily an auto-mulligan ... it often will be. Not only is a hand of six cards plus a card you don't want to see before you've established overwhelming card advantage is basically the same as a regular six-card hand, against some decks that can disrupt you early (i.e. before you've established a countermagic wall, overwhelming card advantage, etc.), you run the risk of exposing your finisher to discard. Again, not an automatic mulligan ... but certainly something to consider.

There are lots of variations to a great many of these rules and models. For example, you might want to have particular stuff in your opening hand that is superb early but poor late (like Mana Leak); or just cards that will interact with the opponent's beatdown (like some kind of Lightning Bolt when you are the control); Leylines figure in here. Sideboard cards will often improve the value of an opening hand more than "regular" spells, and so on.

If there is one thing I want you to take away from this article—besides actually working out the likelihood of your getting what you want out of your opening hand, considering the math whenever possible—it is to not overvalue the loss of that one card when you are forced to mulligan. I know that most players think they are acting in service to card economy, but long run, their apprehension is almost always misguided. For example, don't you get more cards by being able to actually play a three-mana Cultivate (which will itself actually get you back one card) than not mulligan but also not be able to play your spells at all?

"It seems so simple when you put it that way!"

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