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At some point in the life of many spell slingers there comes a realization that building decks that are flashy and fun to play is not always the same as building decks that are good. For some this spawns a desire to advance to an intermediate skill level of deck construction. Whether acquired intuitively through experience or by a deliberate effort to study the game, or often a little of both, this advance is characterized by an understanding of some of the foundational theoretical concepts of Magic: the Gathering. In this series we follow such a player as his eyes are opened to the world of Magic theory and its application to deck construction. In this episode the discussion of deck strategy is developed by introducing the problem of consistency and a number of ways that it can be addressed. Cue theme song.
After a long absence due to a family holiday and summer camp, Dave finally managed to get back to The Magic Shop. He brought a deck with him and set it on the counter, hoping to play a couple of games. Sam welcomed him warmly and after some ribbing for his apparent disappearing act—perhaps Dave was a better magician than Sam had thought—he finally got back to business. “Last time we introduced the concepts of efficiency and deck speed. We discussed offensive, defensive and resource speed and how the combination of these contributes to strategy speed.” Dave nodded as he recalled the previous lesson and Sam continued. Consistency “Once we start talking about the speed of a deck’s strategy, though, we encounter a problem. Each time you build a deck, you pick a bunch of cards that you like or that help your strategy and put them into the deck. As we’ve discussed previously, however, you don’t have access to your entire deck but rather a few random cards at a time. The word ‘random’ is fundamental here. Each time you draw cards from your deck you cannot be sure which card or cards you are going to draw. “The game itself actually sets some limitations that create this situation. One rule of the game defines the minimum number of cards that can be in a Constructed deck as 60. At the same time, another rule of the game defines the maximum number of copies of a particular card that can be in your deck as four (as determined by the card’s English-name equivalent). The sole exception to this rule is that you can have as many Basic land cards as you like. The result is that you cannot simply have a deck that contains 20 Mountains and 40 Lightning Bolts. The 20 Mountains are fine, but you must have 40 more cards and no more than four of these may be Lightning Bolts. Every Constructed deck must work within these limitations. “For example, you build a deck and put in four copies of Wrath of God. Your plan is to ramp up to four mana and play Wrath on turn four, taking out your opponent’s creatures all at once. But when playing your deck you find that sometimes this strategy works and sometimes you don’t draw your Wrath. Your deck is inconsistent. “The ability to enact your deck’s strategy reliably is known as consistency. Consistency implies getting the cards that you need at the appropriate time. But since you draw cards randomly, how can you ensure consistency? The issue of consistency leads to a number of solutions such as deck structure, redundancy, cost distribution, and even mana base composition. But all of these concepts spin out from the core issue that relates to consistency: probability.” Dave groaned and his eyes glazed over almost immediately. “I’ve been away from school too long,” he muttered. Sam smiled. “Before you run for the door, I promise not to get deeply into the math of this. What I’ll do is describe the key concepts and tell you how you can work it out reasonably quickly. If you are interested in the math then you can look into it for yourself or perhaps we can discuss it another day.” Dave nodded his dubious consent and allowed Sam to continue with his explanation. Probability “Imagine for a moment that you have a jar containing 60 marbles. Four of them are black and the rest of them are white. If you reach in and randomly pull out seven marbles, what are the chances that at least one of them is black?” Dave looked perplexed. “Let’s back up a minute and simplify the problem,” continued Sam. “What if only one of the marbles is black? What is my probability now?” Dave considered for a moment. “I’m not sure, but I think it might be 7/60, whatever that works out to be.” “That’s exactly right,” agreed Sam. “Look at it this way: if I draw out all 60 marbles then I have a 60/60 or 100% chance of drawing out the black marble. If I draw out half of the marbles then I have a 30/60 or 50% chance of drawing out the black marble. In our example, if I draw out seven, then I have a 7/60 or approximately 12% chance of drawing out the black marble.” “That’s not very much,” said Dave thoughtfully. “No, it’s not,” agreed Sam. “Now think about that in terms of your deck of Magic cards. If you have a single copy of a particular card in your deck, then in 25 games you’re only likely to get it in your opening hand three times. That’s not very consistent at all. In fact, this is the essence of the consistency problem. “To go back to our original problem, if we have four black marbles, then what are the chances that we’ll draw out at least one in our first seven? If you think about it, it’s really the chance that we’ll draw out exactly one, plus the chance that we’ll draw out exactly two, plus the chance that we’ll draw out exactly three plus the chance that we’ll draw out exactly four. Does that make sense?” “I think so,” responded Dave. “But I can’t work out the numbers.” “That’s ok,” returned Sam, “because there’s a shortcut. If you think about it, what we’re looking for is really the chance that we won’t draw exactly zero black marbles. In probability, everything adds up to 100%, so what we’re after is 100% minus the percentage chance that we’ll draw exactly zero black marbles. If there are four black marbles, then this works out to a 40% chance of drawing the card that we want in our opening hand. That’s a lot better than 12%!”
“I guess you’ll need a few other options in your deck or you will lose quite a few games,” concluded Dave. Deck Structure “With this in mind,” continued Sam, “we can start to look at some ways in which we can actually improve the consistency of our decks. Let’s start by setting some baselines.” Sam pointed to the deck that Dave had brought with him. “How many cards are in that deck?” “60,” replied Dave immediately. “Why?” countered Sam. Dave paused and looked a little perplexed. “I don’t know. I thought all decks contained 60 cards.” “They usually do, but you should understand why. It is worth noting that a common mistake for beginning players to make is to create decks that are arbitrarily large; 80-, 100-, and 250-card decks or more are not uncommon. This is fine if you’re just playing around, and there are even casual formats designed to contain this many cards. However, for most Constructed play, the standard deck size is 60 cards. The reason for this, as you may have guessed, is probability. “As we discussed earlier, you must have at least 60 cards in your deck and no more than four copies of a particular card except for Basic lands. You may have more than 60 cards in your deck, and you may have fewer than four copies of a particular card. But the question is, how many should you have? “Going back to our discussion of probability, we can quickly determine a couple of things. First, let’s assume that we have four copies of each card in our deck, but we want to include a lot of different cards so we build a deck that is larger than 60 cards. If we build a deck that has 60 cards in it, then the probability of drawing a particular card in our opening hand is, as discussed, 40%. If we go to an 80-card deck, that probability drops to 31%. At 100 cards the probability is about 26% and at 200 cards it has dropped to 13%.” “So, the more cards in my deck,” said Dave, “the less chance I have of drawing a particular card.” “That’s right,” agreed Sam. “But what about dealing with a Mill deck?” asked Dave. “Your deck should be able to deal with this type of strategy, but having a bigger deck is not the answer. This type of strategy is not overly common and in any event takes a long time to implement. Your deck should be capable of dealing with this strategy from within the 60 cards you have at your disposal. Building a bigger deck is not the answer.” “But I’ve seen tournament-winning decks that had more than 60 cards,” persisted Dave. “Certainly this has occurred from time to time. There are extremely rare situations in which it may make sense to have 61 or even 62 cards in a deck. However, even the pros debate this. You will know when you might be in such a situation because you will be doing math to figure it out. But know that it almost never happens and as a rule you should stick with a 60-card deck. “I hear ya,” replied Dave. “Now let’s assume that you’ve decided that 60 cards is the right number for your deck. As we’ve said, if you have four copies of a particular card then there is a 40% chance of drawing at least one of them in your opening hand. In fact, if you have 3 copies then the probability of drawing at least one in your opening hand drops to approximately 32%, with only two copies it drops to about 22% and, as discussed earlier, with only a single copy the probability of drawing it in your opening hand drops to about 12%. Clearly, the more copies in your deck, the better the chance that you will draw the card that you want.” “But I often see decks that contain less than a full set of four copies of a particular card. Why might this be?” asked Dave. “This situation does occur more often in decks with more than 60 cards,” conceded Sam. “The baseline, even for the pros, is a play set of four copies of each card. However, other considerations do come into play. For example, if a card hurts you when drawn too early or in multiples then you may want to include fewer than the full four copies. If a card is Legendary, then you usually only want to draw one copy. Likewise, if a card has a particularly high casting cost, you may only want to see it later in the game—if you draw it early it will just sit in your hand. In previous lessons we have also mentioned other mechanisms that can improve your chances of drawing the cards that you want, such as using ‘tutors’ like Idyllic Tutor, ‘filters’ like Ponder, or even just straight card draw like Ancestral Vision. In these cases you may want fewer copies of a particular card, but for most cards you will want more copies. The reasons not to include four copies of a particular card are a topic for another conversation, but for now it is important to understand that four is the baseline and that there are reasons to include fewer.” “Ok, so basically, I should build all decks with exactly 60 cards and should include four copies of each card,” summarized Dave. “As a baseline, that’s correct,” concluded Sam. Redundancy
“For example, if you are playing a Control deck based on counter magic, Counterspell is a good place to start. But you can only have a maximum of four copies of Counterspell. Fortunately, there are other cards with the words “counter target spell” on them. You can include cards like Cancel, Rune Snag, and Mana Leak. With four copies of each, suddenly you now have 16 counter spells in your deck. What are the chances that you’ll draw counter spells now? In fact, with 16 counter spells in your deck, there is a 90% chance that you’ll have at least one in your opening hand! Up that number to 20 cards and you have a 95% chance of having at least one in your opening hand.” “Wow!” exclaimed Dave. “Those are pretty good odds.” “They certainly are,” agreed Sam. “Adding different cards to your deck that fulfill the same general purpose is known as redundancy. Building this kind of redundancy into a deck allows you to enact your strategy with a high degree of consistency. If you consider our earlier example of drawing marbles from a jar, you can see that we have simply changed the definition of what represents a black marble. In some of our previous illustrations we associated the copies of a particular card with the concept of the black marble. However, now we can generalize and say that any spell that can counter another spell represents the category of things that we are looking for, i.e. black marbles. “Take a look at this deck:”
“This deck has a few interesting things going on. The strategy of this deck is to disrupt the opponent’s game and then, once this has been achieved, to attack with a threat that is difficult to answer. The most obvious aspect, though, is the redundancy built into this deck in terms of counter spells. With a total of 21 cards with the words ‘counter target spell’ written on them, there is a 98% chance that you will have at least one by turn two. Those odds mean that this deck can enact its strategy with an extremely high degree of consistency. It will then hope to draw into a Nevinyrral’s Disk to clear the board, gain card advantage (since it didn’t have any artifacts, creatures or enchantments in play itself) and then enable its win conditions. “Another interesting side note is the fact that there is only one true creature, plus four ‘man-lands’ in the Stalking Stones. The Rainbow Efreet is difficult to answer because it can be phased out in response to removal. The Stalking Stones are difficult to answer because they are lands and playing a land can’t be countered. The Stones will be activated once the opponent has few cards remaining with which to answer them and even then they can be protected with counter magic. The point here is that the main strategy is highly redundant and drawing the win conditions can wait until control has been established.” “I notice that even some of the counters have fewer than four copies,” pointed out Dave. “Yes,” agreed Sam. “In this case, there would have been a number of cards available that could fill the general role of a counter spell. The best and most powerful ones have been included with a full four copies. Each of the others have a variety of drawbacks, and the deck’s designer chose to include fewer of each, potentially in order to avoid a high concentration of a particular drawback. However, overall, there are still a highly redundant 21 counter spells.” Cost Distribution (a.k.a. Mana Curve) “We can continue extending our concept of black marbles into other interesting areas. For example, I hate doing nothing on my first turn except playing a land. I like to get off to a fast start by actually playing some kind of spell. In order to be able to do this I need to have a card in my opening hand that costs exactly one mana. The key is to determine how many of these I’ll need in my deck in order to have one available to me on my opening turn. If I have ten spells in my deck with a casting cost of one (i.e. ten black marbles), then I’ll have about a 74% chance of drawing one in my opening hand. If I increase that to 12 then it becomes about 81%.” “Why don’t you just fill your deck only with spells that cost one mana?” asked Dave. “Then you could play them on any turn.”
“Couldn’t I just play two Savannah Lions or equivalent on turn two?” asked Dave. “You could,” replied Sam, “but you would run out of cards more quickly that way. There is a balance between being able to do something at all, and being able to do something relevant. Historically, this has led to the concept of the mana curve, also known as cost distribution because it involves viewing your deck in terms of slots organized by casting cost. “As we discussed in previous lessons, the game puts a natural limit on the development of mana resources by allowing you to play one land per turn. The idea of the mana curve is that you have relevant spells to play on each turn and therefore use all of your mana to maximum advantage on every turn. This is done using a tiered system based on mana cost. Consider the following deck:”
“While later versions of this deck tended to rationalize into 4-ofs for most creatures, this is the ‘original’ and illustrates the concept of the mana curve very well. This deck has a total of 25 creatures. The casting costs break down as follows:
“With this breakdown, there is a 65% chance of drawing a creature that can be played on turn one. This would be the bottom of the spectrum and I’d expect many similar decks to play even more than this. Adding up the creatures in the one-mana and two-mana slots, you have a 92% chance of playing a creature on turn two. Note that additional spells, like burn spells, aren’t counted in this part of the curve.” “Why is that?” asked Dave. “The reason is that you only want to count spells that you actually plan to play on the turn in question. For example, if I have four one-mana creatures and four Shock spells, I’m probably not that interested in playing Shock on turn one. I’d probably rather save it for a later turn when I can gain a tempo advantage by removing one of my opponent’s creatures. “But the important point is that I can improve my overall consistency by managing the cost distribution of cards in my deck. This will improve my opening hands and early turn plays such that I can achieve my strategy a high percentage of the time.” Versatility “One thing that I noticed,” Dave interjected, “is that when we talked about redundancy and now when we talk about cost distribution, the thing that hasn’t really been covered is utility spells. Some things can obviously be made highly redundant, such as creatures, counter spells and burn spells. But what about other spells like those that remove enchantments?” “That’s a good question and it leads us to our final point for today: versatility. When selecting cards for a deck, sometimes a card with a narrow purpose could still be good. For example, if you play against people that tend to play a lot of creatures, then a card that does nothing but kill a creature might be a valid choice. Even then, it may be useful to select a card that has more targets. Take Terror for example. It can destroy a creature for two mana. Mortify, on the other hand, can destroy a creature or an enchantment for one more mana. It’s a tradeoff of cost against versatility. A card like Oblivion Ring can remove any non-land permanent from the game for three mana, but the tradeoff here is that if Oblivion Ring itself is destroyed, that permanent comes back into play.” “I think I get it,” returned Dave. “Having a versatile card is like having multiple cards in your deck that do different things.” “That’s right,” agreed Sam, "and it frees up those extra slots to allow you to build redundancy into your deck." Conclusion “Well, we’ve covered a lot for one day. Let’s just play a few games with what little time we have left. After all, that’s what it’s all about,” concluded Sam. “Sounds great!” agreed Dave. “Next time, we’ll talk about how to use our cards wisely in order to gain tempo.” Until then, Brad Lohnes, masquerading in the MDV forums as Amadeus, is a casual player from the early days of Magic. After a ten-year hiatus from the game he stumbled upon it once again. This has sparked a passion to fathom the depths of this complicated pass-time while continuing to enjoy it at its most basic level. Originally from Canada and having lived in New York City for several years, Brad now lives in New Zealand with his wife, dog and cat. He is a software engineer and enjoys traveling, hiking, and writing.
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“Let’s
take a look at the Wrath of God example,” continued Sam. “In this case, I have
four copies of Wrath of God in my 60-card deck. However, I’m not so much
interested in whether it’s in my opening hand as I am about whether I can play
it on turn four. Now, in some games you will play first and in others you will
play second. If you play second, you will draw a card on your first turn, but if
you play first then you won’t. For the sake of calculating probabilities it is
best to consider the worst-case scenario. From this perspective, the worst-case
scenario in MTG is when you play first, because you’ll only have access to seven
cards on your first turn. You’ll get an extra card on your second turn, third
turn, etc. So this means that on your fourth turn you’ll have drawn a total of
ten cards. Given these parameters, we can calculate that there is about a 53%
chance of drawing a Wrath of God in time to play it on turn four. That means
that this plan works only slightly more than half of the time.”
“Now,
if you’ll recall, we said that even if you have a 60-card deck and you include
four copies of a particular card, you still only have a 40% chance of drawing it
in your opening hand. So, then how do you improve your chances of getting the
cards that you want when they are randomly selected by nature? The answer is
simply to have lots of cards that you want! More specifically, you want to
include similar cards that fit in with your strategy.
Classic
Draw-Go. 
“That’s
true,” responded Sam. “But one thing you’ll find is that generally cards with a
higher casting cost also have a higher power level. This is certainly not always
the case, but basically you want to be able to do something relevant in the
later turns. For example, for one mana you might be able to play a Savannah
Lions on turn one. Now imagine that your opponent does the same. On turn two you
play another Savannah Lions, but your opponent plays a Watchwolf. He has used
his two mana to play a creature that is relevant on turn two. A Watchwolf is a
more powerful card than a Savannah Lions after turn one.”
Orcish
Librarian.