The Math of Banning Sol Ring in Commander



Commander, as a casual format, has no real obligation to be balanced. And no matter how large the banned list becomes, it's likely that there will always be something degenerate (like Hermit Druid combo). However, I think it's important to note something here: if you build Hermit Druid, you know you're violating the spirit of the format. You know you're playing a cutthroat deck streamlined to win, quickly, in the same way every time. On the other hand, Sol Ring seems innocuous, particularly to newer players. But, no matter your intentions, it's not a fair card.

Since bannings in Commander are carried out by the inscrutable Rules Committee, this article is aimed at you, the players. My goal is to convince you that Sol Ring is an unfair card, or, at the very least, open your mind so you can observe it yourself. If you've never worried about Sol Ring, you will hopefully find this article informative; if you insist that it's fair you may find some facts here that surprise you.

As you go back to your games with Sol Ring (unless of course you don't allow it anymore in your area), I hope you'll be more mindful of the situations it creates. Get sick of it. The more players realize that Sol Ring enables unbalanced gameplay, the more it behooves the Rules Committee to do something about it.

Let's start at the top. How can we be so sure that Sol Ring is unbalanced? A general rule of thumb is that a fair land and an artifact for 2 should be about the power level; Sol Ring costs 1, so it should do less than a land. But it's rare to see a land that can tap for two mana, even with a drawback, and Sol Ring has none! It provides a tempo advantage far beyond what's acceptable by modern standards. It's on par with the Moxen (which are banned) in terms of power level - and typically acknowledged to just be stronger in this format than they would be.

In the words of Mark Rosewater (the head designer of Magic since 2003) it's "beyond broken." In fact, it's considered by many (including pros, cube enthusiasts, and so on) to be the best card ever printed - and even those who dispute that must acknowledge that it's in the top handful.

Beyond that, it appears in every deck, which flies in the face of the individuality that makes up the core of the format.


Unfair in any printing

However, whenever it's suggested that Sol Ring be banned in Commander, the suggestion is met with a plethora of counterarguments. There's ample evidence of this discussion on the MTGCommander forums as well as the MTGSalvation ones; over the course of dozens of posts the arguments on each side devolve into sound bytes and anecdotal evidence. Look at this fifteen page thread. Three pages in, they're not even talking about Sol Ring anymore! That's how this discussion goes.

First, I'll provide an analytical look at the arguments not to ban Sol Ring. I want to see if they hold water (spoiler: they don't). I'm not going to be waving my hands and bringing up situations which are barely possible; I will actually be making factual statements and computing probabilities. I won't go through all the math as I go for the sake of brevity, but in the spoiler you'll find an indication of the sorts of calculations I'm doing, with necessary mathematical background here.

The focus of my article is going to be the strength of untapping with a Sol Ring on the second turn. Even in singleton, that happens more often that you might imagine; in a four-player game where each player has Sol Ring in their deck, someone will cast it on his or her first turn just over a quarter of the time. Using Partial Paris mulligan rules, if players are willing to mulligan to five looking for that turn one Sol Ring, that number is closer to sixty percent.

In an N-card deck, suppose you are concerned with K specific cards (for example, K is 1 if you're talking about Sol Ring, or it could be 35 if you're worried about your odds of drawing land). Now suppose there are P players who are each going to draw D cards. Note that I do not consider the cases where Sol Ring is drawn but there are no lands in the hand; this makes the math notably more complicated and affects the results by much less than 1%.

The odds that one player will draw none of those K cards is
(N-K choose D)/(N choose D)
So the odds that no player will draw any of their K cards is
( (N-K choose D)/(N choose D) )^P
Then the odds that at least one player will draw at least one of those cards is
1 - ( (N-K choose D)/(N choose D) )^P

For example, the odds that at least one player will have a turn one Sol Ring in their opening seven or first turn draw is
1 - ( (99-1 choose 7+1)/(99 choose 7+1) )^4 = 28%

We can compound that calculation to investigate mulligans. The odds that a player will not see Sol Ring in their opening 7, their following 6, their following 5, or the card drawn their first turn is
( (99-1 choose 7)/(99 choose 7) )( (99-1 choose 6)/(99 choose 6) )( (99-1 choose 5+1)/(99 choose 5+1) )
So the odds that at least one of the four players will find one if they're all willing to mulligan to five looking is
1 - [ ( (99-1 choose 7)/(99 choose 7) )( (99-1 choose 6)/(99 choose 6) )( (99-1 choose 5+1)/(99 choose 5+1) ) ]^4 = 55%
And under partial Paris mulligan rules, where we don't replace cards before drawing new ones, that's instead
1 - [ ( (99-1 choose 7)/(99 choose 7) )( (99-7-1 choose 6)/(99-7 choose 6) )( (99-7-6-1 choose 5+1)/(99-7-6 choose 5+1) ) ]^4 = 58%

While the focus of my article is the strength of untapping with a Sol Ring on turn two, let's not forget that the card is often beneficial immediately. Lightning Greaves and Sensei's Divining Top are widespread, and both love to be played off of a first-turn Sol Ring. Two-cost artifact accelerants (like Signets) are common sights in Commander as well - most multicolored decks play several - and allow Sol Ring to provide an even more absurd boost to your second turn. Keep in mind that untapping on turn two with it is only a snapshot of the power of this card.

"It just makes mana, it's the things you do with that mana which are the problem."

Let's get this one out of the way right off the bat. The degeneracy of fast mana is well documented through the history of Magic. Having access to too much mana too early upsets the game balance; it's why Black Lotus and the Moxen are banned in every format but Vintage.

"It's easily answered."

Legacy staple, Commander dud

This is another common argument against banning Sol Ring - actually a generic argument against banning anything: Don't take out the powerful cards, just play more answers to them. In this case, the argument is bogus.

If our Sol Ring player is on the play, only a one-cost removal spell will suffice to keep them from untapping with it. The options are Crumble, Crush, Mental Misstep, Nature's Claim, Overload, Oxidize, and Shattering Spree. I guess Force of Will belongs on the list too.

If you take your first turn before Sol Ring drops, you can additionally answer it with Annul, Artifact Blast, Shattered Dreams (if you can guess who has it), Duress, Steel Sabotage, or any two-cost Shatter/Disenchant/Naturalize variant.

What most of these cards have in common is that they're not very good in Commander. They're each a narrow one-for-one piece of removal in a format where card advantage is paramount.

Even so, let's assume people play these cards. Let's say each deck has three cards which can answer Sol Ring before it becomes a problem (judging from the deck database this is a very generous estimate even in decks of the appropriate colors). In that case, there is still less than a ten percent chance that anyone can answer the Sol Ring before it untaps.

Note that I haven't taken into consideration that people might mulligan in search of their Sol Ring removal; if that is something that actually happens, I think we can all agree that the format has been warped.

"It helps players catch up when they fall behind."

As opposed to most other arguments I address here, this one is true. A topdecked Sol Ring will often allow a mana-screwed player to recover. However, that problem can be managed much more practically with proper deck construction and careful mulligans (and yes, sometimes mana screw does determine a game, just like in every other format). And of course, Sol Ring has no predisposition to help players who are behind; it's just as likely to be drawn by the player who is already ahead, giving them a further boost of advantage compared to the mana screwed player. Allowing Sol Ring in case players get mana screwed is analogous to allowing people to own space lasers just in case their microwave ovens break down. It's a poor solution which brings serious and unnecessary consequences.

"It's only a problem in 1v1, and it's already banned there."

In a duel, Sol Ring is so back-breaking that dropping it on turn one is often game over. As a result, it's banned there. In a multiplayer game, it's still plenty strong to be a problem.


Sol Ring has so many friends!
Planeswalkers are fantastic in this format. There aren't that many low-cost answers to them, so usually they're just attacked. A turn-one Sol Ring allows you to drop any of the http://gatherer.wizards.com/Pages/Search/Default.aspx?action=advanced&output=spoiler&method=visual&type= [Planeswalker">&cmc=+=[4]"]ten four-cost planeswalkers on turn two. At this point in the game there probably isn't a single creature on the table to threaten them, which means they provide a considerable threat to the rest of the table.

Any deck which depends on attacking with the commander loves a turn-one Sol Ring. Turn-one equipment (especially boots) into turn-two Kemba-equip-swing quickly becomes a problem for the entire table.

Mana denial is pretty scary when it's two turns early. Killing everyone's first two lands with Armageddon/Ravages of War/Ruination (but leaving your Sol Ring untouched) is pretty brutal. Perhaps worse would be a threat on turn two (such as a planeswalker or commander) then a turn-three land sweep done any of several ways. That's still early enough to slip under most countermagic, particularly on the play.

I realize that my argument here is not so rigorous, but the point I'd like you to take away is this: If you drop Sol Ring on turn one, there are many ways for you to drastically alter the balance of a game very quickly, even against multiple opponents.

"It doesn't belong in every deck... my deck doesn't want it."

In an argument against the ubiquity of Sol Ring, three-plus color decks sometimes claim that their mana restrictions are so stringent that Sol Ring does not belong. In order to see if that's really true, I went over to the deck database and looked through the lists of three and five color generals which did not include Sol Ring.

Since I'm concerned with the benefit of untapping with Sol Ring on the second turn, it was easy to come up with a metric. I counted the number of cards that can be cast off of two lands and a Sol Ring but not two lands alone. That means three and four cost spells with no more than two colored mana in the costs. I also limited my count to the spells that you would actually want to cast on your second turn; Harmonize is good but Day of Judgment is not.

In order to put your Sol Ring to use right away 50% of the time, you need nine such cards. For a two-thirds chance you need fourteen. Seventeen cards gives you a 75% chance of getting an immediate benefit from Sol Ring.

(Keep in mind that this ignores the possibility of casting multiple small spells between your first and second turns. I'm also ignoring the benefit of Sol Ring to casting your commander. If your commander's casting cost includes at least two colorless mana - such as Uril, the Miststalker, Riku of Two Reflections, or any shard or wedge Dragon - and your mana base is pretty stable, Sol Ring single-handedly lets you cast your commander two turns early.)

Looking at a few dozen decklists without Sol Ring, the average number of cards that Sol Ring lets you cast on turn two is 17. Furthermore, the standard deviation is 4, meaning that almost no deck has fewer than thirteen options if it untaps after casting Sol Ring turn one.

That is, most decks can abuse Sol Ring right away pretty consistently. Even the ones that claim they can't.

"It's not a good topdeck late in the game."

As a late game topdeck, Sol Ring is almost always better than a land. It generates one mana immediately, like a land, but then counts as two lands from then on out. Furthermore, including Sol Ring in your deck doesn't decrease your odds of drawing business spells. It replaces a land in your deck list, not a spell.

"As soon as you ban Sol Ring you'll start complaining about the next best card."

In any format there is a "most powerful card," or at least a small group of cards which are the most powerful. It's also true that if you ban the most powerful card, the next best card steps up to that role. This is sometimes used to suggest a slippery slope; if we keep banning the most powerful card we'll end up only allowed to play bad cards - or even no cards!

This use of the slippery slope argument is fallacious. This is not a call to always ban the most powerful card. It's a call to ban Sol Ring specifically because it is a problem. If there were a card that was just a tiny bit worse than Sol Ring, I would include it in the same breath and argue that they be banned together, but that's not the case.

Mana Crypt tries very hard to be like Sol Ring, but I think the discussion of banning Mana Crypt is separate (and much more complicated). The life loss attached to Mana Crypt is a real liability to decks interested in the long game. Though comparable to Sol Ring in terms of tempo boost, the decision of whether or not to include it in your deck - and even play choices if you do include it - are non trivial. As a result Mana Crypt is less ubiquitous than Sol Ring and provides much more good tension.

Sensei's Divining Top is another powerful, low cost, ubiquitous artifact legal in the format. I would understand if it were banned for time concerns (on the 1v1 list, it is), but in terms of raw power it's not obvious to me that it's problematic. Between the cost to use it, the interaction with shuffle effects, and the choices available when activating the abilities in response to one another, Sensei's Divining Top is a fairly complicated card. Like Mana Crypt, the conversation about banning it on power level would be complicated and punctuated by discussion of the good tension it provides.

"This isn't an official format so you can just ban it by your house rules."

Commander is not a sanctioned format. In principle, each playgroup could have their own banned list, tailored to encourage what they find fun and discourage what they hate. However, it's in the interest of the format to keep to the "official" banned list as much as possible. It's convenient for all of us that the Rules Committee carries enough influence that a single official banned list even exists!

It allows you to play outside your playgroup. If your group has a particular banned list which doesn't match with the guys next door, you have to reconcile that before you can even play with one another. Any new player to the area will have to learn your banned list before they can join the format (and, unless you're particularly organized, there won't even be a way to find out the banned list before showing up to the event). Having house rules banning cards inhibits the social aspect of the game and alienates new players.

Having a standard banned list saves playgroups the trouble of coming up with their own banned list. Players who are new to the format, only play casually, or spend most of their time in a different format probably don't have the depth of familiarity necessary to make a strong banned list for Commander. Adopting the official banned list saves them the time and frustration of discovering for themselves why each card there is banned, one by one.

Many would contend that the official banned list is not perfect (and really, what banned list is?). Even so, just by virtue of being widely accepted it makes the game run more smoothly. That's why I'm arguing for this single change to the list rather than trying to rework the entire thing.

"Wizards just put it in the preconstructed decks so it can't be that bad."

The inclusion of Sol Ring in the preconstructed Commander decks does make it seem unlikely that the card will ever be banned. That said, this isn't the first time a problematic card has been put into a precon; Jitte came in one, and Stoneforge Mystic was banned in Standard despite being in the event decks. Sometimes necessary action has awkward consequences.

Not being privy to the development of these decks, I can't offer any insight beyond what Wizards announced: every Commander deck plays Sol Ring so these ones had better include it as well. I don't read that as an endorsement of Sol Ring in the format so much as a resignation that Wizards doesn't have the power to ban it (so they've got to play along to sell product).

Banning a card is contrary to the spirit of the format.

Commander makes a point to have a small banned list; it aims to be a format where players can basically play any card they want. I see the point of such a move and I agree with the sentiment. However, the fact remains that some cards are just problematic. That's why the banned list exists.

I'd be happy to hear your thoughts on the topic (though I realize that discussion can become heated - please be courteous). However, I'd like to say again: I'm not waving my hands and guessing numbers. It's a fact that Sol Ring is not a balanced card. As awareness of this fact spreads, so too does the chance that the Rules Committee will see fit to do something about it.

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