Your intuition lies.

It’s not your fault – and it’s not your intuition’s fault, either. Your brain evolved in the context of catching that deer for dinner, not getting eating by that lion, and figuring out whether the human from that other tribe is going to stab you or offer to trade with you.

It notably did not evolve in the context of understanding the relative accessibility of Magic cards based on their mana costs.

Mike Flores has said, paraphrased, that “Six mana is way more than five…maybe two mana more.” I like this quote, because it captures a truth about Magic card costs and accessibility within the game in a neat, pithy statement. It doesn’t explain why this comment might be true, or why Mike’s experience has retrained his intuition so that it now tells him that this is true.

Today, I’m going to take a look at the stats behind the statement, at how card accessibility within the game shifts with mana cost, and at exactly why seven mana is twice as bad as six mana.

The numbers behind it all

The basis of that pithy statement that “Six mana is way more than five” is in how quickly we get access to our lands. In general – setting aside accelerators such as [card]Llanowar Elves[/card] for the moment – we have to draw and play our lands to be able to cast our spells. You need to have six lands to cast that [card]Primeval Titan[/card], and seven if you’re going to hard cast [card elesh norn, grand cenobite]Elesh Norn[/card]. That’s an easy idea to understand.

So how do those lands come to us, and what does that really mean for our spells?

Hitting our land drops

The simplest way our intuition lies to us is when it tells us that “Six mana isn’t so bad…it’s just one more land than five mana.” Your brain then tells you that you will draw your sixth land just as easily as you drew your fifth land, and that you’ll draw your fifth land just as easily as you drew your fourth. Based on this intuitive understanding of your access to mana, you may jam some more high-cost cards into your deck.

But it doesn’t work that way.

Let’s take a look at a typical sixty-card deck with twenty-four land.

Here’s your chance of having enough lands to play your first land and cast a spell that costs one mana on turn one (on the play):

For this and all the other examples today, I’m not considering things like “having the right color mana” or “having an otherwise playable hand.” The important thing today is comparing between mana costs, so these other considerations can be safely ignored. So we’re just literally saying, “Will I have access to enough lands to cast this spell by this turn?”

The odds of being able to cast your one-mana spell start extremely high and very quickly approach 100%. That’s not surprising – it would be a weird deck that couldn’t manage a one-mana spell after a few turns.

So that’s for one mana. What do the prospects look like for other mana costs?

In this table, the mana cost of the spell we want to cast is in the column on the far left (from one to seven), and the turn of the game runs across the top. You can cross reference the turn and the mana cost to find out the odds that you’ll actually have enough lands to cast that spell by the time you reach that turn.

For example, if you’d like to know your chances of being able to cast a four-mana spell on turn six, you can go to the “turn 6” column and the “4 mana” row, where you’ll discover that the answer is 80.3%. So you have an 80.3% chance of actually having the four lands you’ll need to cast your four-mana spell by turn six.

How much more does that cost?

So that’s a nice, dense set of numbers. But what does it mean in terms of actually casting your spells?

Well, let’s take a look at this another way. On what turn are you 50% or better to cast that spell? 75% or better?

Here’s the same table, color-coded for turn / CMC combinations where you’re going to be able to cast the spell less than 25% of the time (red), 25-50% of the time (orange), 50-75% of the time (yellow), or more than 75% of the time (green).

Right away, it’s obvious that the ability to cast spells does not experience the same “progression” at each mana cost.

The two-mana spell likelihood curve is very, very flat. You’re over 90% likely to have the two lands you need to cast that spell on the first turn where you’re able to cast it. In contrast, you’re less than 50% to be able to cast a five-mana spell on the first turn you are theoretically going to be able to cast it.

We can make the comparison really obvious. Here’s the turn on which each CMC of spell hits the 50% mark on being castable:

So what does that mean?

Well, it means that in our twenty-four land deck, we’re better than 50% to be able to cast any spell up to the four-mana mark as soon as possible.

Then things start to slide.

We only pass the 50% mark for our five-mana spells on turn six. So by this (very relaxed) criterion, that five-mana spell effectively costs six mana much of the time.

That’s already pretty bad, but we were being pretty lax, requiring only that we beat the 50% mark. More realistically, if we’re going to say that we can cast a spell by a given turn, we want to have all the lands we need 75% of the time or better.

In that case, we cross the 75% mark on this schedule:

So that makes our mana issues entirely clear. Costs from one through three remain pretty much on schedule. After that, things start to drift. We can be pretty sure we’ll have the lands to cast our four-mana spells by turn six, and our five-mana spells by turn eight. After that it gets really bad, and you can see why decks that want to regularly cast six-mana creatures either play for the long game or run a plethora of ramp elements.

In other words, six mana isn’t one more than five mana, it’s more on the order of three more.

Hopefully this is all pretty clear…but it’s also still pretty theoretical. Let’s try applying it to some practical examples.

How the pace of mana plays out in practice

So let’s consider three familiar archetypes from the current Standard environment in terms of three familiar decks and the cards they want to cast.

Delver

Shahar Senhar took down GP Salt Lake City with a fairly typical Delver list (good job Shahar, by the way):

Delver (as played by Shahar Senhar)

[deck]4 Delver of Secrets
4 Geist of Saint Traft
2 Invisible Stalker
4 Snapcaster Mage
1 Batterskull
1 Dismember
4 Gitaxian Probe
2 Gut Shot
4 Mana Leak
4 Ponder
1 Runechanter's Pike
2 Sword of War and Peace
2 Thought Scour
4 Vapor Snag
4 Glacial Fortress
9 Island
3 Moorland Haunt
1 Plains
4 Seachrome Coast
Sideboard
1 Batterskull
2 Celestial Purge
2 Corrosive Gale
2 Dissipate
1 Divine Offering
1 Jace, Memory Adept
1 Negate
2 Phantasmal Image
1 Revoke Existence
2 Timely Reinforcements[/deck]

Like many Delver lists, Shahar’s ran 21 lands. This means that the table I included above doesn’t apply. Instead, Shahar’s odds looked like this:

As we’d expect, the one-mana spells are castable pretty much all the time, right out of the gates. Fifteen of the spells in the main deck cost one mana, with another six being “free” (costing just Phyrexian mana).

The two-mana spells should be castable 85% of the time on turn two, which quickly climbs to 90% or more on subsequent turns. Another eleven cards in the main deck cost two mana.

So you can already see that over half the cards in this Delver build will be castable almost all the time, which explains the agility of the deck.

At the three-mana mark, there are only two types of spells in the main deck – the two Swords and the four Geists. They will be castable over two thirds of the time starting on turn three, rising steadily to hit the 80% mark on turn five and the 90% mark on turn seven.

Finally, Shahar’s deck ran one [card]Batterskull[/card] in the main deck. He’ll be casting that sucker just 31.9% of the time on turn five, and will barely cross the 50% mark by turn seven. Even by turn ten, the deck is not quite at 75% to be able to cast that [card]Batterskull[/card].

It’s a compelling argument against overloading the deck with Batterskulls.

Note that this numbers don’t account for one of Delver’s very handy tools, Ponder. As I’ve talked about before, Ponder strongly increases your access to cards…which in Delver certainly includes lands. This will help mitigate some of the deck’s clunkiness in casting bigger cards (although not all of it).

Esper Walkers

What about a nice, slow control deck instead?

Here’s Beaux Bruggman’s Esper Walkers deck from the Sacramento Standard Open:

Esper Walkers (as played by Beaux Bruggman)

[deck]2 Tragic Slip
1 Doom Blade
1 Go for the Throat
4 Mana Leak
2 Snapcaster Mage
3 Think Twice
2 Forbidden Alchemy
3 Liliana of the Veil
3 Lingering Souls
1 Oblivion Ring
2 Day of Judgment
1 Sever the Bloodline
2 Sorin, Lord of Innistrad
1 Batterskull
2 Curse of Death's Hold
2 Gideon Jura
2 Consecrated Sphinx
2 Island
4 Plains
4 Swamp
2 Darkslick Shores
2 Drowned Catacomb
3 Evolving Wilds
2 Glacial Fortress
3 Isolated Chapel
4 Seachrome Coast
Sideboard
1 Batterskull
2 Nihil Spellbomb
2 Ratchet Bomb
1 Volition Reins
2 Celestial Purge
3 Geist of Saint Traft
1 Karn Liberated
3 Despise[/deck]

Beaux’s deck features twenty-six lands – five more than the Delver list we just looked at. If you think about it that way, it’s a pretty big sacrifice. Shahar’s deck gets to run five more spells than Beaux’s. Hopefully, our land-heavy control deck has something to offer its pilot in return.

Here’s the odds breakdown for a deck with twenty-six land:

First, take a look at the four-mana mark. That’s where [card]Day of Judgment[/card] lives. This deck can expect to cast a Day on turn four a little over 70% of the time. Given how critical a sweeper can be for a control deck, this seems like a good thing.

For a more direct comparison with the Delver list, consider the castability profile of the five five-mana spells in this deck. On turn five, the deck is a little over 50% to be able to cast one of these big-ticket spells. That rises to 67% by turn six, and 76% by turn seven. Given that these spells are the deck’s finishers, those odd don’t look bad at all.

Notably, all the deck’s “gotta survive!” cards cost one, two, or three mana, and this deck is almost assured to be able to cast the one- or two-mana spells right away, with only a bit of lag on the threes.

Beaux chose a pair of [card consecrated sphinx]Sphinxes[/card] as his biggest finishers. At six mana, these beasts are only 42% likely to be castable on the sixth turn, and don’t pass the 75% mark until the tenth turn.

What if we wanted to end the game with [card]Karn Liberated[/card]? At seven mana, Karn is only 29% likely to be castable on turn seven. He doesn’t pass the 75% mark until turn twelve. There’s a reason those Cruel Control decks from Lorwyn-Alara Standard sometimes ran up to half land.

Note that there is a little bit of a mislead in these numbers, too. Much like Delver with [card]Ponder[/card], this deck has tools to plow through itself faster. [card]Think Twice[/card] and [card]Forbidden Alchemy[/card] both increase your ability to get access to your land, potentially shaving a turn or so off of the clocks described above. Of course, being one turn faster means Karn on turn eleven instead of turn twelve, so the planeswalker golem is still a slow option.

Beware of the nonlinear

The thing that trips up our intuitive brain in cases like this is that the odds that we’ll have the resources we need drop off dramatically as we place bigger demands on those resources. For most decks, even those running very land light, like Delver, cards in the one-three mana range will almost always be castable “right away.” Once we pass that magical breakpoint, things slow down.

This is one aspect of [card]Birthing Pod[/card]’s power. In addition to tutoring, Pod says that yes, indeed, your seven-mana creature is arriving one turn after your six-mana creature. For the rest of us, that’s not going to be the case.

So don’t let your intuition fool you – retrain it. Four mana doesn’t just cost four mana, and five mana costs way more than four.

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