Dragons of Tarkir not only introduces several exciting Standard cards, but it also allows us to do interesting math. In this article, I run the numbers to obtain the following conclusions:

  • Play 10 Dragons in a Constructed deck with Orator of Ojutai.
  • Run 22 qualifying creatures at the very least in a Collected Company deck.
  • There are only 0.62 Dragons per Dragons of Tarkir booster on average.

How Many Dragons Do You Need for Orator of Ojutai?

Dragons of Tarkir contains a cycle of uncommons that reward you for having a Dragon:

Let’s focus on Orator of Ojutai for now. Consider a 60-card deck with D Dragons and 4 Orator of Ojutai. For simplicity, we exclude the possibility of mulligans, mana screw, scrying with Temples, and any opposing Thoughtseizes. The number that I’m interested in is the probability of drawing at least one Dragon in the top 9 cards (which corresponds to turn 3 on the play and turn 2 on the draw) conditional on having at least one Orator in the top 9.

The tricky part in determining this probability is conditioning on drawing at least one Orator. I could neglect this for simplicity, but I enjoy leisurely walks in probability spaces, and in the end, I only care whether or not I have a Dragon if I have at least one Orator. So intuitively, we only have 8 other cards to find a Dragon, but since the first Orator could be anywhere in the top 9, it’s not as simple as setting aside one Orator as our first draw and then considering a 59-card deck for the remaining 8 draw steps. Instead, we should look at all possible 9-card sequences of Orators (O), Dragons (D), and other cards (C), such as ODCCCODDC, assign a probability to each, sum up the probabilities for all combinations with at least one O and at least one D, and then divide that by the sum of probabilities for all combinations with at least one O. That’s exactly what I did:

Orator_Dragon_Calculation Orator_Dragon_Chart

With Orator of Ojutai, I want to be able to trigger the bonus in at least 80% of the games where I play it on turn 2-3. If it’s less than that, then I don’t expect the card to be good enough. By my calculations, 10 Dragons gives you 80.5%, so 10 is the number I would recommend. Now, 10 is a lot, so I doubt whether a Dragon control deck will be feasible.

The other Dragon cards have smaller rewards. For Scaleguard Sentinels, Draconic Roar, and Foul-Tongue Invocation, 9 Dragons (i.e., 76.7%) may be okay. And for Silumgar’s Scorn, which is fine even without a Dragon in the early game, 8 Dragons (i.e., 72.2%) seems acceptable.

How Good is Collected Company?

Collected Company is one of my favorite cards in the new set, partly because determining the expected number and total mana worth of creatures is fun.

To obtain the expected number of creatures per Collected Company, we could determine a conditional probability like we did for Orator of Ojutai. However, since Collected Company requires more involved calculations, I’ll abstract away these issues for simplicity and apply the hypergeometric distribution as follows:

CollectedCompany_Calculation

To find the expected total mana worth of creatures per Collected Company, assuming we always take the maximum, we require the mana curve. For any number of creatures in the deck, I assumed an even distribution over 1, 2, and 3 mana, with remainders going to a 3-drop first and a 2-drop second (so it’s 7-8-8 for 23 creatures). Since my head exploded when I tried to do the calculations analytically, I used simulation. My Java code is available here.

CollectedCompany_Chart

Based on these numbers, I’d want 22 hittable creatures at the very least before putting Collected Company in my main deck. This gives a 5% chance of missing completely, a 21% probability of hitting one creature, and a 74% probability of hitting two creatures, for an EV of 1.68 creatures. With a 7-7-8 curve per my assumptions, you can expect to net 3.78 mana worth of creatures per Collected Company. I find these numbers barely acceptable, so 22 is my absolute minimum to maindeck it. The more the better, and going heavy on the 3-drops is sensible.

What’s the Expected Number of Dragons Per Booster?

Dragons of Tarkir is supposed to be the Dragon set, but is it really? By my count, there are 0 common Dragons, 11 uncommon Dragons (out of 80 uncommons total), 10 rare Dragons (out of 53 rares total), and 5 mythic Dragons (out of 15 mythics total). I’m not including cards like the Monuments here—only Dragon creatures. Assuming that there is a 1-in-8 chance that the rare slot contains a mythic, and taking into account that you can’t have packs with duplicate uncommons, I get the following numbers:

Booster_Table

I have yet to draft with the set, but my initial impression is that I would’ve liked the as-fan to be a little higher than 0.62. Right now, I doubt that Pinion Feast is maindeckable in draft, and I am disappointed that there is only one common (Sarkhan’s Rage) with a reference to Dragons in its rules text. I would’ve loved to see one or more cheap Dragons with drawbacks, akin to Slumbering Dragon, at common. Instead, we’ll just have to get lucky and hope to open a good Dragon in the rare slot!