Solve the Equation – The Math of Burn in Commander
June 28, 2022 by
Benjamin Nicol 
(Dragon's Approach | Art by Andrew Mar)
Burn After Reading
Feel like your deck just is not coming together? Welcome to Solve the Equation, where we take a look at the numbers and see what's making your deck and in-game decision-making fall flat.
I love playing burn decks! There is something about slinging Lightning Bolts at an opponent's face that's cathartic for me. Unfortunately, while burn is a viable aggro strategy in many other formats, it has long been an underachiever in Commander. The math gets a lot hairier here. Burn decks perform best when there is as little thinking to do as possible. Every spell is going straight at your opponent’s face. However, with 120 life points to whittle down, 3 damage feels pretty lackluster, and a singleton format means we can't even rely on the burn spells we need.
Well, what if I told you there's one burn spell you can rely on having in your hand? Come on! It's 2022, the age of power creep. The last few years have given burn a bunch of new toys which I think might just make it playable.
Damage Output
Dragon's Approach shares some similarities with Lightning Bolt. The biggest similarity is, of course, 3 damage, but this spell hits each opponent. Our opponents each have 40 life, which means it would take approximately 13.3 Dragon's Approachs to kill our opponents. Admittedly, this is much worse than the 6.6 Lightning Bolts it would take to kill an opponent in a 1-on-1 format such as Modern, but when you start to count how many Bolts it would take to kill off each opponent in Commander, 13.3 sounds like a perfectly fine starting point.
Now, what if there was a way to make our Approaches as efficient at killing our opponents as Lightning Bolt is in Modern? For this we can turn to one of the game’s most broken mechanics: Companion. Legendary creatures with this mechanic can be played as your commander without any deckbuilding requirement. Obosh, the Preypiercer is the perfect burn commander and can leverage Dragon's Approach better than any other deck.
Obosh, the Preypiercer doubles the damage that our odd-costed cards deal. 6 damage to each opponent for 3-mana is a very appealing rate. That's 18 total damage for 3 mana off of one card. That's a combined 15% of our opponent’s life totals, which is the same damage output of a single Lightning Bolt in a 60-card format.
18 Damage / 120 Life (3 Opponents) = 15%
vs
3 Damage / 20 Life (1 Opponent) = 15%
How Many Do We Need?
Time to break out the hypergeometric calculator to figure out how many Approaches we want in our deck. It's always important when deckbuilding that we remember our goal. Are we going to beat the table exclusively with Dragon's Approach? Probably not, so we want to make sure we can at least get a free Dragon out of the deal! If we cast the spell approximately five times, let's see what we get.
Without Obosh, the Preypiercer:
- 15 damage to each opponent (45 total / ~38% of your opponents’ life) + Dragon of our choice
With Obosh, the Preypiercer:
- 30 damage to each opponent (90 total / ~75% of your opponents’ life) + Dragon of our choice
So we don’t actually need to cast this spell a ton of times to have a big effect, but we do need to reliably have the cards in our hand. Let’s imagine a hypothetical game that's expected to go about 10 turns. If we can draw, on average, approximately 2 cards a turn over those 10 turns, then by turn 10 we'll be 27 cards deep into our deck.
Let’s take a look at the odds at different Dragon’s Approach counts:
10 Approaches
- Chance to draw 5 or more of the wanted card = 9.58%
- Chance to draw exactly 5 of the wanted card = 7.25%
- Chance to draw 5 or less of the wanted card = 97.7%
20 Approaches
- Chance to draw 5 or more of the wanted card = 69.7%
- Chance to draw exactly 5 of the wanted card = 21.8%
- Chance to draw 5 or less of the wanted card = 52.1%
30 Approaches
- Chance to draw 5 or more of the wanted card = 96.8%
- Chance to draw exactly 5 of the wanted card = 5.99%
- Chance to draw 5 or less of the wanted card = 9.16%
40 Approaches
- Chance to draw 5 or more of the wanted card = 99.9%
- Chance to draw exactly 5 of the wanted card = 0.421%
- Chance to draw 5 or less of the wanted card = 0.533%
10 is definitely not enough, as the overwhelming odds suggest we won't draw enough cards. 20 is moving in the right direction, but a 22% chance of failing to draw 5 Approaches is higher than I would like. 40, on the other hand, nearly guarantees we draw the Approaches, but at that point we'll have more Approaches than lands and will barely be able to fit anything else into our deck. It looks like the sweet spot would be somewhere between 30 and 40 Approaches.
The Dragons are Approaching
All that said, this is not simply a burn deck. One thing many burn players love even more than a Lightning Bolt is a Dragon that can dish out even more damage. The exciting text on Dragon's Approach is not the damage output; we want Dragons! The biggest pitfall a burn deck runs into is running out of gas, but once we cast enough Approaches, they can solve this issue. Plenty of the format’s best Dragons can draw us cards, gain advantage, or just do more burning in general, and we can get them for free just by pursuing our burn strategy.
Card Advantage Dragons
The Approach spells don't add any card advantage on their own, so oftentimes the first Dragon we want to grab should be one that refills our hand.
Knollspine Dragon - We're dealing loads of damage to our opponents, so this Dragon draws a veritable butt-ton of cards.
Dragon Mage - Not only will Dragon Mage refill the hand, but it can also screw up our opponents’ plans. It's important to be careful with this one, because if opponents are low on cards, it could help them refuel, too.
Damage-Dealing Dragons
Our burn spells won't be enough to finish our opponents off, so we may want to grab a Dragon that can deal out enough damage to take us the rest of the way. We want to focus on odd-mana Dragons, since they'll deal double the damage with our commander’s ability.
Balefire Dragon - This card will clear one opponent’s entire board. One of the the biggest factors that can throw a wrench in our plans is an opponent who has a ton of creatures attacking us. This will quickly and continually take care of that issue.
Drakuseth, Maw of Flames - Just read the card. So. Much. Damage! And double it!
Terror of the Peaks - The next Dragon we bring out is really going to hurt. Plus, if an opponent tries to take it out, it'll cost them even more life.
Utility Dragons
Some Dragons will help keep our strategy going, including by bringing out even more Dragons!
Bladewing the Risen - If one of our Dragons was taken out earlier, we can bring it right back.
Ancient Copper Dragon - Our spells are expensive, so the more help we have on mana, the better. Not many Dragons can create more mana than this one.
It's All Coming Together
Time to flesh out the rest of the deck with some key support pieces!
Cost-Reducers
The biggest knock against Dragon's Approach is that it costs three mana. There are a number of cards that can reduce the cost of the spell and will quickly allow us to cast multiple spells a turn. What makes these spells stand out over a traditional ramp spell is that they apply the discount to each spell we cast in a turn.
When Dragons Aren't Enough
When Dragons and burn spells aren't enough, sometimes we need a little extra push to take us the rest of the way. On the surface, Mizzix's Mastery seems contradictory to this strategy, as it exiles the cards from the graveyard. However, sometimes you just need to push through a little bit more damage, and this spell can deal a boatload to just close things out.
Oh, and who could forget Thrumming Stone? This artifact is getting a reprint in Double Masters 2022, which will hopefully make it more accessible. This card can potentially cast through an entire library of Approaches and win the game on the spot!
Check out the full deck here:
Obosh Burn
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What are your favorite burn cards in Commander? Is Obosh the best burn commander out there? I certainly think so, but the EDHREC data shows it at 7th for that dedicated archetype. Some of the more popular include Torbran, Thane of Red Fell, Toralf, God of Fury, and Firesong and Sunspeaker
Which one is your favorite? Is there a better Dragon's Approach deck? Let me know in the comments below.
Benjamin Nicol
Ben is a Michigan native who fell in love with Magic just a few years ago in 2019. He loves making big splashy plays in Commander as well as crunching the number to optimize his decks. Outside of Magic, he works in marketing and loves a great cup of coffee to start each morning… maybe with a splash of hot chocolate for his sweet tooth.
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