Keeping with a Plan

Posted in Limited Information on March 16, 2010

By Steve Sadin

What happens when someone asks you a question about a play decision? Do you know how to explain your answer in a way that your less experienced friend or acquaintance will understand? Are you explaining your answer in a way that they will actually learn the correct lesson from it?

When you are formulating your answer to your friend's question, you must ask yourself: Are you actually answering the right question?

Oftentimes when someone asks you a question about a play decision, you can give them a quick yes/no answer. But if you take the time to go beneath the surface a bit, you can help your friend in a really significant way and improve your own understanding of Magic in the process.

Mulling About

You are playing in a Zendikar / Worldwake Sealed premier event on Magic Online, and you have constructed the following deck:

Bonus Exercise Sealed Deck

You sit down for your first game of Round 1 and you draw an opening hand of:

Searing Blaze, Urge to Feed, Surrakar Marauder, Ruthless Cullblade, Hedron Rover, Mountain, Mountain

Do you keep on the draw? How about on the play?

Before I get into my own answers, I should mention that I was very impressed with the quality of the answers that I got in the forums last week. Most of the posters were correctly able to identify that this hand is not keepable on the play or the draw.

Often times a hand has a critical flaw, a single key reason why you can't keep the hand. Other times a hand is unkeepable for a number of reasons, any one of which would be enough to force you to throw the hand away.

Forum user Axelvanrossomme calculated the odds of drawing a Swamp by turn two on the play or on the draw. On the play you have a 28% chance of drawing a Swamp by turn two, and on the draw you have about a 47% chance of drawing a Swamp by turn two. Even if you up the Swamp count a bit, the odds don't look great. With 10 Swamps, you have about a 30% chance of getting a Swamp in your first draw, and about a 52% chance of drawing a Swamp by your second draw step. With 11 Swamps, you have about a 33% chance of getting a Swamp in your first draw, and about a 54% chance of getting a Swamp by your second draw step. Even if you go up to 12 Swamps, you still only have about a 36% chance of getting a Swamp in your first draw, and a 60% chance of getting that crucial Swamp by your second draw step.

Often times deciding whether or not to keep a hand really does come down to simple math. If you have that math memorized, or you can calculate it quickly, you will be able to make much more informed mulligan decisions.

Calculating the Odds of Drawing a Given Card

It's actually pretty simple to calculate the odds of drawing at least one copy of a card in a certain number of draw steps. To calculate the odds of drawing a card in a single draw step, you simply divide the number of copies of the card by the total number of cards in your deck. So if you have three removal spells out of a total of 25 cards remaining in your deck, you have a 12% chance of drawing one.

To calculate the odds of drawing a card in several draw steps, you must divide the number of all the other cards in your deck by the total number of the card that you are looking to draw remaining in your deck. So your odds of not drawing a removal spell in your first draw are 22/25, or 88%. You then multiply that by the odds of you not drawing a removal spell in your next draw step, which would be 21/24, or 87.5% (since we are looking to find the odds of drawing at least one removal spells, you only need to continue calculating the odds for situations where you have drawn a non-removal spell). To find the odds of drawing at least one removal spell during those two draws, we look at the inverse of the fraction that we get by multiplying the two odds of it not being a removal spell. So in this case, we have 22/25 × 21/24, meaning that we have a 77% chance of not drawing a removal spell in those two draw steps, or a 23% chance of drawing at least one removal spell.

Simply going by the math, we can see that this is not a desirable hand to keep. The thing is, while this hand is fine with a Swamp, it still isn't great. If, however, simply drawing a Swamp in the first couple of draw steps would guarantee me a sizable advantage, then I would strongly consider keeping this hand. But since drawing a Swamp would simply make this hand average, there's no way I can justify keeping it.

What's the Plan, Man?

Forum user Abyzz brought up a very good Martin Juza quote when explaining why he would mulligan this hand: "If you are keeping, always have a plan."

While Abyzz's short post seemed to emphasize the importance of having relevant things that you can definitely do in the short term, as well as a reasonable way to transition into the rest of the game, I would like to extend this analysis a bit further.

You should not interpret Juza's quote purely as an argument against speculative hands. It is very rare that you will draw a completely made hand, especially in Limited. You will almost always need to draw into something, be it a specific land, a two-drop, a second creature, a way to deal with a 3-toughness creature, etc. The fact that you are missing something does not make a hand bad.

It's perfectly fine for your hand to be incomplete. You just need to make sure that you have a reasonable chance of drawing out of your problem in a timely manner. Further, if you draw out of your problem, you need to make sure that you are actually gaining advantage. If you need to first get lucky in order to get a chance to play your game, then you should probably mulligan.

A speculative hand needs to have upside. If you're hoping to get some lucky draws just to get back to even, you will probably be way better off seeing what six cards can offer you.

How Much Do Your Spells Actually Cost?

The biggest issue with this deck, which was correctly identified in the forums, is that this deck should not have a 9 / 9 split of Mountains and Swamps. But how many Swamps should this deck play? Nine Swamps is clearly not enough, as there are significantly more black spells in this deck, the deck absolutely needs black on turn two, and it has a number of spells.

However, this deck also has a lot of spells, most notably 3 Searing Blazes. When you have that many two-drops with requirements, you also need a lot of Mountains, right?

The important thing to keep in mind when thinking about this type of question is that there is a big difference between a two-drop like Searing Blaze, and a two-drop like Kor Aeronauts. While Kor Aeronauts gets significantly weaker when you can't reliably cast it on turn two, Searing Blaze doesn't necessarily lose that much value.

In this deck, it's fine to think of Searing Blaze as a three-, a four-, or even a five-drop. In fact, since it is particularly important to play it with landfall in this deck, and there are a lot of relevant black two-drops in this deck, it will be very rare that it is even appropriate to cast a Searing Blaze on turn two.

That being said, you still don't want to choke on your Searing Blazes.

I think that it's ultimately right to run 10 Swamps and 8 Mountains in this deck. While you absolutely need to get black mana early, if you can't cast your Searing Blazes to remove key blockers, this deck could find itself in a good amount of trouble going into the late game.

If, however, one of the Searing Blazes were replaced by a Burst Lightning or a second Magma Rift, then I would strongly consider switching to 7 Mountains, especially if I had a black spell to replace Akoum Battlesinger.

Is There a Different Way to Look at the Hand?

When I was just getting into competitive Magic, if I saw a two-land hand with a spell that I could cast, I would keep it in a heartbeat. But if I saw a one-land hand, I would mulligan it pretty much immediately.

While it took me quite a while to learn how to evaluate hands in an effective manner, there was one lesson that really helped me along the way. One of the most important lessons that I learned early in my Magic career was that, instead of looking at what I have in my opening hand and using that as my sole gauge of quality, I should think about what I need.

This tiny change in perspective had a dramatic effect on my ability to properly evaluate hands.

Appearance and function are two very different things. Many hands that look like they are two-land hands are functionally one-land hands.

Imagine that rather than a hand of:

Searing Blaze, Urge to Feed, Surrakar Marauder, Ruthless Cullblade, Hedron Rover, Mountain, Mountain

—which Steve circa 2000 would have kept—Steve circa 2000 was instead looking at a hand of:

Lightning Bolt, Urge to Feed, Surrakar Marauder, Ruthless Cullblade, a four three-cost Hedron Rover, Hideous End, Mountain

Steve 2000 would have mulliganed without giving it a second thought.

Yet this hand is actually noticeably better (in pretty much every way) than the original, real version of this hand that has two Mountains in it.

While rules of thumb are important, you can't let them blind you to the reality of the situation that you are dealing with. The number of lands that you have in your opening hand is not actually a very good gauge of whether or not you should keep your hand. If you instead try to understand what you need, what likelihood you have of getting what you need, and what the consequences will be if you don't, then you should do pretty well for yourself.

By employing this type of thought process, even if you make a mistake, you will be able to go back over your reasoning and understand where and why that mistake occurred.

Bonus Exercise

You won Game 1 of your Sealed match with a six-card hand against what appeared to be an aggressive red-white deck that couldn't quite get anything going. The only spells that you saw out of your opponent's deck before winning on the back of an unmolested Vampire Nighthawk were one each of Goblin Shortcutter, Kor Aeronaut, Highland Berserker, Apex Hawks, Veterans Reflexes, and Join the Ranks.

You sideboarded into the following version:

Sealed Deck

Your opponent chose to play first, and on your opponent's third turn your hand consists of:

Surrakar Marauder, Stonework Puma, Searing Blaze, Hedron Rover, Swamp, Mountain

Your board consists of:

Surrakar Marauder (untapped); Swamp, Mountain (tapped)

Your opponent's board consists of:

Goblin Shortcutter (tapped and attacking); Plains, Plains, Mountain (untapped)

Do you block? Why?

Post your answers in the forums!

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