Magic the Gathering

Theory

Magic The Classroom : Hyper Math

By Dan Eckstein ⋅ April 30, 2009 ⋅ Post a comment ⋅

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.

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.

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 Greenseeker
4 Thought­sieze
4 Birds of Par­adise
4 Elves of Deep Shadow
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.
4 Llanowar Wastes
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 Hyper­ge­n­e­sis

4 City of Brass
4 Reflect­ing Pool
4 Exotic Orchard
4 Gem­stone Mine
4 Tendo Ice Bridge
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.

Dan is a High School Teacher who does everything he can to squeeze Magic into his schedule. Between being a Father, Husband, and Coach it’s pretty hard. Articles by Dan focus on tips and lessons for beginners that he has learned while teaching his students how to play their best. As a player Dan has a propensity to go Crazy For Combos so occasionally these articles happen as well.

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