The Stealthy Mathematics of Hearthstone
The situation in front of me looks dire. Four minions sit on the board, none of which are my own. They have a range of attack points, an onslaught that will surely deplete my remaining health points. A rope flies across the middle of the screen, igniting on the left and burning toward the right, signaling the impending end of my turn. I need to move fast. Suddenly the answer becomes clear: The health points of those minions are factors of two. I fling Defile out of my hand, dealing one damage to all minions, and putting the lowest health within elimination range. There’s just enough time to play Lord Godfrey, who pops off two damage to all others, repeating this over and over until all minions on the board are destroyed. I live to see another turn.
“Well played,” acknowledges my friend, also my current opponent, and my pride swells.
The game we’re playing is Hearthstone, a digital card game based on the long-popular MMORPG World of Warcraft. We’re currently in the middle of a 1:1 battle, pitting our decks against each other. It’s a time-consuming habit that’s admittedly a lot of fun. I’ve been enjoying Hearthstone since it first launched in March 2014, languishing in the escape it provides during my busy days. With new expansions and collectibles released each year, the game remains fresh and entertaining. But something else has come to my attention lately, and I think I have this game completely to blame.
I’m not merely a seasoned player, I’m a stronger mathematician.
As someone who occasionally struggles with math, this is huge. I’d sooner pull up a calculator on my phone than wrestle with a problem. Now, however, I find I’m capable of doing all sorts of calculations in my head. Maths that felt previously out of reach. A lot of solving for x. And when I went searching for a possible reason for these new skills, all signs pointed to the candy-colored card game on my screen.
Hearthstone is full of stealthy math, and players might not even realize it.
Gameplay is simple enough: Each player has an allotted number of mana (resources) to play a selection of cards in their hand. However, in the span of a typical 75-second turn, players calculate multiple combinations of the following: addition and subtraction, multiplication and division, value statistics, percentages, probability, and logic problems. That’s a lot of math in a short amount of time, yet the game pulls it off without ever feeling like you’re doing work. Sort of like executing a fancy skateboarding trick—you’re not actively thinking about the complicated mechanics involved, but they’re still there.
“For us, it’s about trying to find fantasies that match the card mechanics,” says Hearthstone lead game designer Alec Dawson. Animations and sounds cover up the tedium of the math. For example, the card Rolling Fireball deals eight damage to a single minion. However, if the minion only takes two damage before perishing, the excess rolls to the minions on either the right or left. The animation is exactly how you would imagine it in your own mind. “Seeing a big rolling fireball on screen makes it easier to understand how the damage is carrying over from one minion to the next,” explains Dawson. It’s visuals like these that so cleverly disguise the work you just did in your head.
Technically, my earlier board-clearing moves were merely basic subtraction problems. Written out, the equation to pull that off would look like H (health) – 1 – 2 x 4 = 0 (board clear). Let’s move on to more complicated stuff.
The Battlegrounds mode has a completely different set of rules, most similar to that of auto chess. Each lobby starts with eight players who eliminate each other until there is one winner. There’s a lot of random luck in this mode, but there’s a ton of probability involved too. In order to strategize a win condition, players need to already be thinking about turn five, six, and seven. And if your plan doesn’t pan out, you need to be able to pivot quickly. Add to all of this the unique special powers of your chosen character, strategic positioning, and multileveled tiers of minions, and players are cranking out sunk cost fallacy with every turn.