Magic Math – Shadows over Innistrad

Werewolves, Vampires, Zombies, and Humans are nice, but let’s just run some numbers.

How Much Life Loss Can You Expect from Sin Prodder and Sorin?

There are 2 cards in Shadows over Innistrad that reveal the top card of your library for life loss equal to that card’s converted mana cost. The effectiveness of these cards depends on the type of deck you play. Let’s consider 2 macro-archetypes:

An Aggro Deck

16 one-drops
12 two-drops
10 three-drops
22 land

In this deck, the expected converted mana cost of a revealed card is 1.17. That’s not a lot, so even if your opponent would always choose to lose life to Sin Prodder’s ability, the card is likely worse than Chandra, Fire of Kaladesh in a red aggro deck.

A Midrange Deck

12 two-drops
9 three-drops
7 four-drops
3 five-drops
3 six-drops
26 land

The expected converted mana cost of a revealed card from this deck is 1.87. That’s better, but still not a huge amount. Even if your opponent would always choose to lose life to Sin Prodder’s ability, it seems worse than Tireless Tracker in a red/green midrange deck. There are some exceptions—for instance, if you need Sin Prodder to enable delirium or if the format is filled with lumbering creatures so that menace is super valuable—but overall I’m not a fan. To make things worse, Sin Prodder’s trigger is a punisher mechanic that gives the opponent a choice, which is a huge drawback.

Note that this was just a quick analysis as the expected converted mana cost does not tell the entire story. The variance is huge and, moreover, the value of a card can depend on its converted mana cost. But the expected value still provides a useful indication.

Turning to Sorin: that card is always good. The life loss is only incidental, but in a midrange deck, you’re a very small favorite to shoot down an opponent who starts at 4 life with 2 activations.

How Many Instants and Sorceries Do You Need for Thing in the Ice?

An application of the hypergeometric distribution, based on a deck with 60 cards with a certain number of instants/sorceries, gives us the following chart.

Thing in the Ice probabilities

Click to enlarge.

When I have Thing in the Ice in my deck, I would want to be 90% sure I have seen at least 4 instants/sorceries in the top 15 cards. These numbers are a bit arbitrary, but in the context of a Standard deck, they correspond to turn 6 on the play, where I have seen 3 extra cards via card draw spells. This 90% requirement for the top 15 cards corresponds to a deck with at least 23 instants/sorceries, which seems like a good number to aim for.

How Likely Are You to Hit Delirium?

There are a ton of nice delirium cards in Shadows over Innistrad, and they yield interesting deck building challenges. The likelihood of achieving delirium in a reasonable time frame (which is like producing a 4/5 Tarmogoyf) depends on a lot of factors, such as how quickly your creatures die and how easily you can get cards of a certain type into the graveyard.

Any math I do will be riddled with assumptions, but it can still help to get a feel for the new mechanic. I’ll start off by considering a Constructed deck where you have N cards of each non-tribal type and determining how likely it is to see at least four different card types in your top X cards. So if N=4, then this is a deck with 4 lands, 4 creatures, 4 sorceries, 4 instants, 4 planeswalkers, 4 artifacts, and 4 enchantments. All of these cards are assumed to go to the graveyard easily, so I’m talking about 4 Evolving Wilds, 4 Insolent Neonate, 4 Duress, 4 Fiery Impulse, 4 Nissa, Voice of Zendikar, 4 Hedron Archive, and 4 Dead Weight. The rest of the deck consists of lands and creatures that, for simplicity, never go to the graveyard. I won’t claim that this is perfectly realistic, but for this deck, I want to know the probability of drawing at least four different types of graveyard-bound cards in the top X cards.

Delirium formula

Delirium probabilities

So in this elegant setting with a 4-of graveyard-bound card of each type, you can achieve delirium in most games with reasonable consistency.

Of course, for actual Constructed decks, you typically run more than a few creatures and lands, and they may head toward your graveyard reliably if you have plenty of self-mill cards like Gather the Pack or discard enablers like Jace, Vryn’s Prodigy. Moreover, you may not run certain card types, such as artifact or planeswalker, at all. So for the next analysis, let’s suppose that you always have a creature and a land in your graveyard guaranteed. We can then re-run the numbers where you have N cards of each of the three remaining card types (enchantment, instant, and sorcery).

Delirium probabilities PART 2

So in this setting where you need to find at least two of the three remaining card types, it will be substantially more difficult to reliably achieve delirium if you only have 4 sorcery, 4 instant, and 4 enchantment.

There can be endless variations and calculations, and in the end a lot depends on how easy it is to get card types into your graveyard (not just your hand) in real games of Magic. But as a starting point, this exploratory analysis points me in the direction of building a deck with at least 6 instants, 6 sorceries, and as many different card types as possible.

The New Pro Tour Top 8 Playoffs

Starting with the upcoming Pro Tour Shadows over Innistrad in Madrid, there will be a change to the best-of-five playoff matches in the Top 8 of Pro Tours: the second game will be another pre-sideboard game. So you only get to sideboard from game 3 onward.

This change is fine with me. In a normal match of Magic, you play 33.3% pre-board games and 66.7% post-board games, assuming the match goes to game 3. Since 40% pre-board games and 60% post-board games matches those numbers more closely than 20% and 80%, respectively, the addition of a second pre-board game seems okay.

This change is good news for decks that excel in pre-board games and are weak to sideboard hate. If you wonder how much this matters, then you may be happy to learn that with a probability P to win a pre-board game and a probability Q to win a post-board game, your probability to win the match is:

P2Q + P2(1-Q)Q + P2(1-Q) 2Q + 2(1-P)PQ2 + 4(1-P)P(1-Q)Q2 +(1-P) 2Q3.

Not the most elegant formula, but at least it allows me to plug in the reasonable numbers of P=0.7 and Q=0.4 for an Affinity-style deck to obtain a match win percentage of 53.8%. That’s not overly dominant, so decks that are particularly strong pre-board don’t have a huge edge. I probably won’t take this Top 8 change into account when selecting my deck for the upcoming Pro Tours.

What is the Probability of Hitting with Duskwatch Recruiter?

This card hasn’t received a lot of excitement, but it’s a strong 2-drop that is good early and good late. It allows for the very reasonable sequence of Duskwatch Recruiter on turn 2, an activation and transformation on turn 3, and a 5-drop creature on turn 4. But regarding that activated ability, how often can you expect to hit at least 1 creature?

Duskwatch Recruiter probabilities

So, for most Standard decks, you’ll have about a 3/4 probability of getting a free card. Taking into account that you get a choice if you hit more than one, I’d argue that the activated ability is better than that on Azure Mage. Combine that with an impressive 3/3 on the back side, and you have a card with serious Constructed potential.

Triskaidekaphobia is Awesome!

This has got to be one of my favorite cards in the set. From the Greek tris (three), kai (and), deka (ten), and phobia (fear), the name captures the fear of the number 13. Beautifully, in the picture of the card, there are 13 tools on the ceiling, 13 log in the stove, 13 bloody spots on the wall, 13 stones in the arch, and 13 broken pieces on the ground.

The number 13 has long been considered unlucky in western culture. For instance, Friday the 13th is a day where many superstitious people expect bad luck. This more specific fear of that particular day also has a name: paraskevidekatriaphobia. Just rolls off the tongue, doesn’t it?

Well, it could get even worse, as fears regarding the number 13 aren’t the only numerical fears that have led to a name with Greek origins. Irrational fear of the number 666 (the so-called number of the beast) is known as… hexakosioihexekontahexaphobia.

Try saying that thirteen times in a row.

As for the playability of Triskaidekaphobia, I don’t see Standard prospects because it’s a little too awkward against an opposing painland to work. But it could act as a reasonable win condition in Limited. I haven’t gotten to see the card in action at my prerelease, so I’m curious to learn about other people’s experiences. If you have any fun Triskaidekaphobia stories to share, then please do so in the comment section of this article!

2 thoughts on “Magic Math – <i> Shadows over Innistrad </i>”

  1. Pingback: Card Knock Life #42 – Damned and Restricted | CARD KNOCK LIFE

  2. Pingback: » Shadows over Innistrad Constructed Set Review – Red

Comments are closed.

Scroll to Top