# Magic Math – Kaladesh: Smuggler’s Copter, Glint-Nest Crane, and Inventor’s Apprentice

Kaladesh offers several intriguing deck building challenges that just beg for someone to run the numbers.

## How Do I Balance Crew Members and Vehicles?

Vehicles are powerful, but you don’t want to be stuck with multiple airships and no one to pilot them. What is a good mix?

To analyze that, we need a proper metric, preferably one that captures consistency for interactive games of Magic. I formulated the following:

We are happy if our deck is such that there is at least a 90% probability that the number of creatures we draw in our top 12 cards strictly exceeds the number of Vehicles in our top 12 cards.

The top 12 cards represent turn 5 on the draw and turn 6 on the play, i.e., the midgame, where you really need to start your engines. The requirement of drawing at least one more creature than Vehicles represents the notion that your opponent always has a removal spell for one of your creatures, which seems reasonable for real games of Magic. Finally, this goal is based on the tacit assumption that every creature is capable of crewing every Vehicle.

As an illustration, the configuration of 0 Vehicles, 6 creatures, and 6 lands (or other cards) counts as a success. I didn’t condition on drawing at least 1 Vehicle. The configuration of 2 Vehicles, 4 creatures, and 6 lands is successful as well. But 3 Vehicles, 3 creatures, and 6 lands counts as a failure: Since your opponent is assumed to have a removal spell for one of your creatures, there will be a Vehicle in your garage without a driver. The configuration of 4 Vehicles, 2 creatures, and 6 lands is a massive failure as well, but for simplicity I don’t attach a value to how bad a failure is. This is not a big problem because many-Vehicle configurations are unlikely to occur if your deck contains enough creatures.

For any 60-card deck with a certain number of creatures, Vehicles, and other cards, we can use the multivariate hypergeometric distribution to determine the probability of drawing any configuration of Vehicles, creatures, and other cards in your top 12 cards. For each configuration, it is easy to assess whether it is a success, i.e., if you have at least one more creature than Vehicles. Finally, for any number of Vehicles in your deck, you can determine the amount of creatures required to be happy under our stated 90% target.

### Results

 Number of vehicles in 60-card deck Minimum number of creatures needed 1 9 2 13 3 16 4 18 5 20 6 21 7 23 8 25 9 26 10 28

So if the only Vehicles in your deck are 4 Smuggler’s Copters, then I recommend 18 creatures to go along with them. Creaturelands or Gideon, Ally of Zendikar also count as creatures for this purpose, and creatures that put creature tokens onto the battlefield or offer card selection (such as Pia Nalaar or Veteran Motorist) can count as slightly more than one creature.

Playing a deck with more than 10 Vehicles doesn’t seem realistic. In fact, looking at this table, the Red-White Dwarves deck with 10 Vehicles that I posted last week may need to cut one Vehicle. That deck had 26 pilots (22 creatures and 4 Needle Spires), so 10 Vehicles is pushing it. Although you could do creative accounting for Pia Nalaar and Veteran Motorist, 9 Vehicles may be a more realistic amount.

And perhaps I should even go down to 8, because the numbers in the table above are all based on the target I specified. If in the new Standard metagame you regularly lose more than one pilot by turn 5-6, or if you want 95% consistency rather than 90%, then you need to tighten your requirements on the number of pilots. What’s more, not every creature in that Red-White Dwarves deck could pilot Skysovereign, Consul Flagship by itself—when the assumption of one creature per Vehicle no longer holds, you effectively need more crew members or fewer Vehicles in the deck.

But as long as you keep these issues in mind, the above table should offer a helpful guideline for building decks.

For Limited, the same metric recommends at least 10 pilots for a 2-Vehicle deck, 12 pilots for a 3-Vehicle deck, and 14 pilots for a 4-Vehicle deck. This is assuming that every creature can pilot every Vehicle, which is not realistic. Especially in Limited where you don’t have full control over your creature base and where many common and uncommon Vehicles have crew costs of more than 1, you simply won’t always find good drivers. Take Renegade Freighter. Aether Theorist is too small to pilot it, and Peema Outrider is too big to profitably take the wheel.

For that reason, I think 2 Vehicles is a realistic amount for the average creature base. You could even add a single pump spell, fight spell, or equipment to your deck at that point, as 3 cards that are useless without creatures on the battlefield is an acceptable number to me.

But some decks can support 3 Vehicles. If you drafted at least 12 small, cheap creatures that are happy to hop into a Sky Skiff or Renegade Freighter, then you could play up to 3 copies of those cheap common Vehicles. But you should mind your crew costs—I wouldn’t recommend putting a combined crew cost of more than 6 in your deck, as your board of Bomat Bazaar Barge, Aradara Express, and Demolition Stomper deck is going to have trouble finding enough crew members.

I doubt we’ll see successful 4-Vehicle decks very often. I guess if you were lucky enough to open a Sealed deck with 2 Smuggler’s Copter and 2 Fleetwheel Cruiser, then you can play them all and cruise to victory, but this will be rare.

## How Many Artifacts Do You Need for Glint-Nest Crane?

Let’s take a look at some numbers.

These numbers should be interpreted as a priori expected probabilities for the entire game. The interpretation is that you set aside 1 Glint-Nest Crane from your deck, draw any number of cards (representing your opening hand and any number of draw steps, hopefully including at least 2 lands), and finally put the ability of Glint-Nest Crane on the stack. For the more mathematically inclined, they are the hypergeometric probabilities of seeing at least one success in four draws from a 59-card deck with a given number of artifacts.

So now that we have these probabilities, how many artifacts would I recommend?

For a good recommendation, we can let the past guide us. When Shahar Shenhar won the 2013 World Championships, he ran a list with Augur of Bolas and 24 instants and sorceries for a 79.9% chance of hitting 1 in his top 3. Intuitively, that feels like a good number to me.

Glint-Nest Crane has flying as small bonus, and I’m willing to accept a slightly smaller hitting probability as a result. Therefore, I would suggest a minimum of 17 artifacts, which yields a probability of 75.4% to hit an artifact with Glint-Nest Crane.

In a 17-artifact deck, Glint-Nest Crane comes with a free artifact at least 3/4th of the time, which is pretty sweet, and I think the body is also relevant in the context of the current Standard: Glint-Nest Crane blocks Sylvan Advocate and Selfless Spirit, survives Kozilek’s Return, and pressures planeswalkers. I think we’ll see this little Bird often in the coming Standard. And the more artifacts you add to your deck, the better it gets.

## How Many Artifacts Do You Need for Toolcraft Exemplar or Inventor’s Apprentice?

What is the question? I defined the following performance indicator.

We are happy if our deck is such that there is at least an 85% probability of having at least one artifact after drawing 10 cards and facing an artifact removal spell in half of the games.

This metric is similar to the one I postulated for my Vehicle analysis, with a few differences:

• I’m okay with 85% consistency rather than 90% because the fail state is still a creature that can attack and block. It may be a lowly 1/1, but that’s still better than a Vehicle without a driver.
• I focus on the top 10 cards—that’s turn 3 on the draw and turn 4 on the play—rather than the top 12 because these are 1-drops that need to attack early. It’s best to follow them up with Scrapheap Scrounger, Smuggler’s Copter, Key to the City, Bomat Courier, or a Clue from Thraben Inspector immediately on turn 2 rather than waiting for an artifact until turn 5-6.
• I assume your opponents have a single artifact removal spell in half of the games rather than all of the games because you give your opponents fewer turns to play one and because noncreature artifacts like Clue tokens or Key to the City are hard to destroy. But it seems safe to assume that Smuggler’s Copter or Scrapheap Scrounger are often going to die to Harnessed Lightning or Grasp of Darkness. (Scrapheap Scrounger may eventually return, but that might take a few turns.) Fortunately, Declaration in Stone is never going to be a good removal spell for artifact creatures against us.

By taking the average of the hypergeometric probability of seeing at least one success in ten draws (from a 60-card deck with a given number of artifacts) and the hypergeometric probability of seeing at least two successes, we get the following.

According to my 85% target, you should play at least 14 artifacts (or artifact-generating cards) in a deck with Toolcraft Exemplar or Inventor’s Apprentice. The more the better, especially if you run multiple artifact-matters cards. But 14 is a good amount to aim for.

I’ll have more quantitative analysis of Kaladesh for you later, so tune back in 1 or 2 weeks from now. There are still plenty of interesting questions involving Combustible Gearhulk, Dubious Challenge, and more, but for now, I hope to have given you relevant insights for Vehicles, Birds, and Artificers.