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Boiling it Down #2: A Mathematical Analysis of Hearthstone Mechanics

1 year ago

My greetings, and welcome to the second edition of Boiling it Down, with yours truly, HardBoiled! In this weekly column, I find the mathematical value of Hearthstone mechanics, then use them to analyze cards! Last week, we took a look at vanilla minions and their stat distributions and found that each minion must have a Mana cost equal to half of Attack and Health added up minus one. Today, I planned on doing direct damage from Spells or Battlecries, but I’ve changed heart in honor of the new expansion announcement. Chillblade Champion, the 4 mana 3/2 with Charge and Lifesteal, is set to become the only non-Basic/Classic card in Standard, besides our good friend Patches, that has Charge with no conditions or downsides. So, let’s find out - WHO’S IN CHARRRRRRGE NOW? There are a LOT of cards that simply won’t work for us, due to the low amount of card mechanics we’ve examined. I have the math worked out for some other stuff, but until I get it on paper we can’t use it. So, I will be forced to use cards with no other keywords besides Charge, which surprisingly narrows it down quite a lot.


There are 7 only Charge minions, or 8 if you count Druid of the Claw. I’m not counting duplicates created by Druid transformations, by the way. However, I think I’ve discovered a formula that lines up quite cleanly with all the cards. For reference, H = Health, A = Attack, and M = Mana Cost.


M = ½(1.5A + 2/3H)


Complicated, right? Well, the Attack of Chargers generally is the most important aspect, since it’s their immediate effect. However, Health doesn’t matter, since the Charger doesn’t need to survive to have an impact, and probably won’t anyway when used for trading. After running through the math with a few cards, I uncovered a spicy Hearthstone secret that works with all cards - most cards are mathematically balanced. The thing that decides how good they are is whether they round up or down.


Now, obviously, this doesn’t work with some cards. Cards like Reckless Rocketeer, Magma Rager, Silverback Patriarch, and others are just so unbelievably bad that they most likely exist to teach new players a lesson about value. However, with this knowledge, we can do some amazing things.


It was my pleasure bringing you all some Numberstone - Heroes of Mathcraft. Next time, on Boiling it Down with HardBoiled, we’ll be analyzing some more, less complicated keywords, like Divine Shield, Poisonous, and Stealth! If we’re feeling crazy and ambitious, maybe we’ll even cover Taunt.