Thursday, November 30, 2023

The stealth math of ‘Hearthstone’

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The situation in in front of me looks disastrous. Four servants are seated on the tray, none of whom are mine. They have a range of attack points, an assault that will surely deplete my remaining health points. A rope flies in the middle of the screen, ignites on the left and burns on the right, signaling the imminent end of my turn. I need to go fast. Suddenly, the answer becomes clear: the health points of these minions are factors of two. I throw Parade out of my hand, dealing damage to all minions and putting the lowest health within knockout range. There is just enough time to play Lord Godfrey, which deals two damage to everyone else, repeating this over and over again until all minions on the board are destroyed. I live to see another turning point.

“Well done,” admits my friend, also my current opponent, and my pride swells.

The game we play is Fireplace, a digital card game based on the long-popular MMORPG World of warcraft. We are currently in the middle of a 1: 1 battle, pitting our decks against each other. It’s a habit that takes time and is definitely a lot of fun. I appreciated Fireplace since its launch in March 2014, languishing in the escape it offers during my busy days. With new expansions and collectibles released every year, the game stays fresh and entertaining. But something else has come to my attention lately, and I think I completely blame this game.

I’m not just a seasoned gamer, I’m a stronger mathematician.

As someone who sometimes struggles with math, this is huge. I would rather open a calculator on my phone than struggle with a problem. Now, however, I find that I am able to do all kinds of calculations in my head. Mathematics that previously seemed out of reach. Lots of resolution for X. And when I went to look for a possible reason for these new skills, all the signs pointed to the candy-colored deck of cards on my screen.

Fireplace is full of stealth math, and players might not even realize it.

The gameplay is quite simple: each player has an allotted number of mana (resources) to play a selection of cards in their hand. However, in a typical 75 second round, players calculate several combinations of the following: addition and subtraction, multiplication and division, value statistics, percentages, probability, and logic problems. It’s a lot of math in a short period of time, but the game succeeds without ever feeling like it’s working. Kind of like performing a fancy skateboarding trick – you don’t actively think about the complicated mechanics involved, but they’re still there.

“For us, it’s about trying to find fantasies that match the mechanics of the card,” says Fireplace chief game designer Alec Dawson. The animations and sounds cover up the boredom of math. For example, the map Rolling fire ball Deal eight damage to a single minion. However, if the minion takes only two damage before dying, the excess rolls over to the minions on the right or left. The animation is exactly as you imagine it in your own mind. “Seeing a large fireball on the screen makes it easier to understand how damage spreads from minion to minion,” Dawson explains. It’s visuals like these that so cleverly cover up the work you just did in your head.

Technically my first edge trim moves were just basic subtraction issues. Written down, the equation for doing this would look like H (health) – 1 – 2 x 4 = 0 (clear table). Let’s move on to more complicated things.

The Battlefield mode has a completely different set of rules, the most similar to that of automatic failures. Each lobby begins with eight players eliminating themselves until there is a winner. There is a lot of random luck in this mode, but there is also a ton of probability involved. In order to strategize for a win condition, players must already be thinking about turns five, six, and seven. And if your plan doesn’t materialize, you need to be able to pivot quickly. Add to all this the unique special powers of your chosen character, strategic positioning, and tiered minion levels, and players develop a sunk cost error every turn.


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