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Today’s class is going to focus on Math. I know you just inwardly groaned. Don’t worry you won’t be doing the formulas. I’ve already done that. All you have to do is read through the numbers. If you can manage that I’ll post not one but two decklist at the end. Is it a deal? Oh, and there will be homework. (It’ll be fun.)
We all know the simple ways that math affects the game of Magic, but today I’m going to tackle how math should affect our deck building.
First, a simple question. Why is Street Wraith a playable card? Don’t laugh. When it was first spoiled many people stood up and said it was a four-of. What about this card made the experts take notice? At 5 mana for a 3/4 with Swampwalk it doesn’t hold water. So it’s got to be the second ability. Is there some way to make the life loss turn in your favor? (There are a couple.)
The secret lies in why we have 60 cards in our deck instead of 61. Or why you should only put 40 in your draft deck no matter how many bombs you pulled. The reason is math and more precisely the reason is probability. On its simplest level if you have 4 copies of a card in a 60 card deck then you have a 1 in 15 or 6.7% chance of randomly picking that card out of your complete deck. Of course it isn’t that simple. We have multiple cards drawn to start the game and various other factors like Mana requirements to take into consideration. Not to mention the randomness that sometimes causes us to draw over 20 cards before we see even one of our beloved combo pieces.
Even with all that taken into account we are still better off using a Street Wraith to essentially thin our deck to 56 cards. If you commit to always cycling the Wraith our simple probability shown above goes to 1 in 14 or 7.1%. While half of a percent doesn’t seem like much to most people a seasoned Magic veteran knows it could be the difference between making the Top 8 or heading home early.
I know what you’re saying. If the math is so good and the card is so great why don’t we see it on any Decklist that are out there. There are a few reasons for this.
First is that decks that are on the net become viral. Someone daring to change a list does so at their own risk. It trickles down. What the Pros play becomes what we play in the vast majority of tournaments, with only a couple of exceptions.
Secondly, the top level player deals with known factors and unknowns differently than we do. At the start of a game you KNOW your hand and you know what your deck is capable of. If that hand is bad the best players will mulligan. While the rest of us see the same hand as being good enough and we hope for the best. The uncanny sense of when to throw away a losing 7 card hand to exchange it for a 6 card winner is one skill that defines the best players. Street Wraith assaults the Pro’s mulligan skill. Now he has to look at one of the cards as a variable as he makes his mulligan decision. Is the potential of the free thinning draw good enough to keep his current hand. Keep in mind that I will lose my chance to mulligan if I go for it. Now the Pro player is reduced to thinking like us.
Combine these two factors and you see why the Wraith went from a top Uncommon to a Shoebox card.
But I didn’t come here today to talk you into playing Street Wraith. In fact I’ll take any cards that you want to mail me. I came here today to talk about how probability should enter into our deck building.
I’m going to share with you couple of tables that were made to show some percentages you need to be aware of.
When building a deck you need to have an idea about how many card slots you will need to reserve for mana. The answer to that question depends on your mana curve. A concept first popularized by a deck called 'Sligh.' If you have a solid early game presence and don’t plan on going much over 3 or 4 mana in any given turn (like Sligh) then you can have less lands than a deck that plans on winning the late game with a hefty 6 or 7 cc spell (like 5color control). Just as the number a lands you want to see in the game changes so does the number you want to seein your opening hand.
Lands in opening hand
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So if I built my deck with 14 lands I would probably see 1 or 2 lands for my opener. If I went up to 20 lands my percentages slide to most likely seeing 2 or 3 lands to start the game. And finally I could just follow the Rule of Nine and run with 24 lands. At 24 I still am most likely to see 3 or 2 lands but now my chances of 3 are much higher than 2.
This table is also useful for using multiple color decks. I may be running a Red/Green deck where I decide to have 22 lands but what mix of lands should I use? For simplicity I say you look at 14 Forest and 8 Mountains. Now the chart shows at 22 Land you’re most likely to see 2 lands to start with and you have strong chances for 3. Sliding down and comparing 14 to 8 we can see that the lands I’ll see will probably be one of each with a 2 land hand and 2 Forest with 1 Mountain with a three lander. If that works for your deck then that’s a good build. If you need to draw early Mountains for burn and don’t need Green until you drop you fatties then you should reconsider your mix.
Please note that multicolored lands can add to both types total. For example if I had 4 Stomping Grounds in the above scenario I would have 22 lands still but now I could have 16 Forest and 10 Mountain sources.
Comes into play tapped lands or the new Borderposts (which in most cases are the same) can use this chart as well. CIPT’s are fine when you have no spells that need that mana on that specific turn. You can’t exactly drop a Birds of Paradise one turn 1 when you just played Vivid Grove. So let’s say you have a deck with no 1 drops. Running 8 CIPT’s is okay since your probably are only going to see one at most in your opening hand any way.
While the first table dealt with opening hands the next table deals with timing of turns. Using a couple of assumptions like 1 draw per turn and 1 land per turn the table below shows you on what turn you can probably see the chosen card. The number in parenthesis shows by which turn at 85% certainty. I honestly use the second number most. 17 out of 20 games is a pretty reliable number to go by.
Turn to plan to see card
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4 Total #1 : Turn 3 (16) #2 : Turn 17 (31) |
7 Total #1 : Turn 1 (7) #2 : Turn 7 (17) #3 : Turn 15 (26) |
10 Total #1 : Turn 1 (3) #2 : Turn 3 (11) #3 : Turn 9 (17) #4 : Turn 15 (23) |
13 Total #1 : Turn 1 (1) #2 : Turn 2 (7) #3 : Turn 5 (12) #4 : Turn 10 (17) #5 : Turn 14 (22) |
16 Total #1 : Turn 1 (1) #2 : Turn 2 (4) #3 : Turn 3 (9) #4 : Turn 7 (13) #5 : Turn 11 (17) |
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5 Total #1 : Turn 1 (12) #2 : Turn 12 (25) |
8 Total #1 : Turn 1 (5) #2 : Turn 5 (15) #3 : Turn 13 (22) |
11 Total #1 : Turn 1 (2) #2 : Turn 2 (9) #3 : Turn 7 (15) #4 : Turn 13 (21) #5 : Turn 18 (26) |
14 Total #1 : Turn 1 (1) #2 : Turn 2 (6) #3 : Turn 4 (11) #4 : Turn 9 (16) #5 : Turn 13 (20) |
17 Total #1 : Turn 1 (1) #2 : Turn 2 (4) #3 : Turn 3 (8) #4 : Turn 6 (12) #5 : Turn 10 (16) |
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6 Total #1 : Turn 1 (9) #2 : Turn 9 (21) #3 : Turn 19 (30) |
9 Total #1 : Turn 1 (4) #2 : Turn 4 (12) #3 : Turn 11 (20) #4 : Turn 17 (26) |
12 Total #1 : Turn 1 (1) #2 : Turn 2 (8) #3 : Turn 6 (14) #4 : Turn 11 (19) #5 : Turn 16 (24) |
15 Total #1 : Turn 1 (1) #2 : Turn 2 (5) #3 : Turn 4 (10) #4 : Turn 8 (14) #5 : Turn 12 (18) |
18 Total #1 : Turn 1 (1) #2 : Turn 2 (3) #3 : Turn 3 (7) #4 : Turn 5 (11) #5 : Turn 9 (14) |
As an example if I have 4 of a certain card in my deck I have good chances of seeing it by turn 3 but if I require 85% certainty I can only hope for turn 16. My second copy has good chances of hitting by 17 but at 85% I won’t see it until turn 31. YIKES! Of course card draw and cards like Street Wraith will greatly change these factors. To keep it simple let’s say that Serum Visions puts you a turn closer since it draws only one card and Tidings puts you 4 turns closer since it draws 4.
I sincerely hope that these tables can help you with the subtle underpinnings of deck design. Here are two decks that I have designed that maximize the percentages.
The first list is a simple reanimator deck. If you are unfamiliar with the concept I would understand. There hasn’t been a strong pure reanimation deck in quite awhile. Graveyard hate is just too easy to come by and completely wrecks the whole idea. What a reanimator mage does is dumps some big, heavy, game changing, high casting-cost creature in his graveyard via some discard spell or ability. Then as soon as possible plays some spell like Zombify to bring that creature from the graveyard to play at a much reduced cost. Imagine only paying 4 for an Akroma, Angel of Wrath.
In my deck I tried to put in 4 general type of cards. The obvious reanimation spells, some nice targets for reanimation, some utility discard outlets, and I like to accelerate the mana a tad so I can reanimate on turn 3. To keep the math easy I started looking for 10 of each type with 20 land. Using either table above You can see that I can be 85% sure of getting each of the 4 pieces by turn 3. I am also over 40% likely to see each in my opening hand which makes mulligan decisions pretty easy.
For reasons to be revealed later I’m just going to say “targets” instead of actually telling you what I like to reanimate.
The Profs Reanimator
10 Targets – See end of Article
4 Llanowar Mentor - Counts as discard and acceleration (12 of each now)
4 Vigor Mortis – If you have G in your reanimation deck you gotta go with this one.
4 Dread Return - Some potential targets play well with the flashback.
2 Makeshift Mannequin – I like the Instant speed but I do dislike the targeting thing.
10 Forest – 14 sources means 85% chance of first turn Green Source. With 16 Green one drops we have to have this level of confidence.
6 Swamp – 10 sources assures us of turn 3 or better. That’s when we are playing our Reanimation spells.
If I explained the numbers well you should see that this deck routinely puts a target in play on turn 3. No guarantees but strong potential is there. It does basically nothing to halt the opponent’s progress other than what your Chosen target may do.
Let that sink in and then see the abuse that I created using the Cascade Mechanic.
Everyone out there is talking about how Cascade can be maximized so that you can predict what second spell (or third in a cascade chain) will be. I can tell you that my second or third thought after reading and then rereading Bituminous Blast was the deck below. I honestly wished for a two or even one drop with Cascade.
The idea is basically the same as Reanimation without the Graveyard issues. My goal is to play my targets from my hand which does two things. First it allows us a greater scope of targets (i.e. Darksteel Colossus). Second it lets us drop the whole discard utility cards which allows us to increase the number of other factors.
So how does Cascade help to Animate cards? If you build the deck with the right curve you have potentially 36 cards that can be copies of Hypergenesis. And that Hypergenesis can be played without Suspend costs. All we have to do is make sure all of our cards have Casting costs of 5 or more. Not a problem with our targets and with a little help from Evoke it’s not a problem for our utility cards.
Hyperanimation by X
12 Targets
4 Ardent Plea - 3rd turn Cascade into Hyper
4 Violent Outburst - Same
4 Bloodbraid Elf – I didn’t use Demonic Dread since it requires a creature to target. I stopped my Cascade choices at 12. That is 85% sure to see in my opening hand. Basically no Cascade means you need to Mulligan.
4 Cloudthresher – Fairies go splat on this windshield and isn’t a bad Hyper target.
4 Shriekmaw – If you opponent foolishly plays a creature with your Hyper then you drop the Maw second and say surprise.
4 Pillar of the Paruns – The only spells we’re going to consistently cast are Gold cascaders.
Now for the Homework. I want you to make a top 10 list of your favorite Reanimation or Hyperanimation targets.
Hope you like the lesson and please post. I love to hear from my readers. Even if you hate my work I would rather hear something than nothing. Hopefully I’m the first to get this idea for Cascade out there. Let me know if you’ve seen it somewhere else.
Class dismissed.
