What is fun? – a rather mathematical outlook

Games are meant to provide fun and/or entertainment. I think that’s a statement that a lot of people would agree on. But what is fun? How would one calculate the amount of fun that one has in a game? What’s needed for a game to be successful or for a game to be considered “great” or “entertaining”?

Taken from Ori and the Blind Forest – a rather challenging but very sweet game that I spend hours upon hours with.

Now, for that question, we should first take a look at the definition of fun.

Something that provides mirth or amusement


Fun-damentally (oof), all games are there to have fun or amusement. Exceptions would be games designed to be provoking or even just frustrating

I personally define “fun” as something entertaining or something that lets my time go by faster. Work can be fun. A challenge can be fun.

Grinding gear can be fun just like solving a puzzle or finally climbing in a competitive ladder. Even rather challenging games like the Dark Souls series are fun as they provide the player with that certain edge and suspense that they can die at any time if they are too reckless. Finally overcoming that challenge, results in joy, pleasure, amusement, mirth, ecstasy or just… fun. 

Taken from Borderlands 1When I first stumbled across the Borderlands series, I ended up neglecting my friends completely as I wanted to complete the first game, the pre-sequel and the second game as soon as possible. I just couldn’t put them down!

In game-terms, grinding is something that requires you to put in a certain amount of work and effort to hone your skills and/or get better at a certain activity. Once you achieved that goal, your effort will be rewarded and you proceed in the activity. Therefore there does not only have to be some sort of challenge that can be found in a grind or a great difficulty but also some sort of sense for progression and reward. Challenging games punish you for mistakes but reward you for perseverance. Competitive games punish misplays and bad calls while also rewarding good players that handle certain situations well. Good players have the ability to turn the tides of battle and win off their enemies’ mistakes or further their own advantage and win off their lead. That can be fun. It’s the edge that is needed for a game to be considered fun. 

Then there’s also replayability. There are longer games that can be played for hours and shorter games that can be played for days. The Binding of Isaac, to bring in another example, is rather short when it comes to its runs. You eventually defeat the boss and start anew or you die trying, resulting in a bit of frustration but also a new chance of winning the game. 

Oh, how I loved the puzzles in Pool Panic! And then there’s the humour and the presentation…. just awesome! And bizarre!

Meanwhile, there are other games, like Beyond Good and Evil, that can be completed in about twenty hours (maybe less) that I personally found fun but would only replay for nostalgia’s sake. There aren’t many alternative parts to take, there aren’t many collectives to collect and overall, you just have the same game over and over again without any alternations. 

Games have to maintain a certain amount of freshness that lets you experiment with new styles and improve your skills while also advance in certain ways that you haven’t tried yet, once you complete the game for the first time. 

Even after you unlock everything in The Binding of Isaac, you have still the option of trying your best at the challenges, trying to get all achievements or compete in the rather challenging Eden runs that provide you with shuffled stats, items and lives on every run in contrast to the other characters. 

Kind Words has been such a great game! Really lovely and atmospheric and the perfect title for rainy days.

Destiny 2 is a class-based shooter that combines a great story, presentation and satisfying gunplay with interesting mechanics, a variety of enemies and constant updates to its game. Here, again, there’re classes to master, weapons to find, missions to complete, competitiveness in form of different ladders and in the end, rewards at the end of the season for completing the season pass and honing your skills. A while back I reached a light level of 913 and started doing raids with a few friends of mine. Those raids opened a whole new world to me with scripted events, new mechanics and a certain amount of edge and suspense to them that basically made every challenge seem manageable despite the difficulty. 

Last Sunday, we spent hours trying to complete the Spire of Stars raid and were struggling with the last part that required you to communicate with your team and strategize on a whole different level than what I’m used to from League of Legends. I loved it to bits, especially because of the time and effort that we put in. In that raid, I received the tractor cannon, a power-weapon that pushes enemies away and suppresses their abilities, which is really fun to use in Crucible (PvP) matches!

So, to put it into a formula, I’d say we need to summarize what I’ve mentioned so far:

I only just got into Destiny 2 and I’m having a blast with it. There’s so much to do and the newly added Corridors of Time offer such a unique experience as well!

We need a challenge or an achievement – a goal that you want to reach:

This can be called “progression” or Π (“Pi” -> the greek “P”) and should be calculated by the reward you receive from an activity in a game divided by the time/effort it requires. 

If a game is rewarding, this would result in the player having fun. 

If the time to reach that reward is limitting against 0, that would result in instant-gratification that is great/amusing for you. Examples for this being the case are FPS games where one precise shot from your weapon/one pull from your trigger is able to take down an enemy or clicker games where you get to huge amounts of clicks in a small period of time due to the right upgrades and the use of a auto-clicker program. If the time needed to reach said reward is too high, however, that would result in a small progression-value (0 < Π < 1), resulting in the game feeling too slow and people dropping it. 

Children of Morta has been really great, especially due to the combination of “Slice of Life” and “Rogue-likes”, two genres that I adore!

To put it in simpler words: 

  • If the reward is fixed:

  The smaller the time, the bigger the progression.  

  The bigger the time, the smaller the progression.

  • If the time is fixed:

  The smaller the reward, the smaller the progression.

  The bigger the reward, the bigger the progression.

Note: Reward can be a high rank in a game or you moving on in the story of a game.

This is a screenshot from CrowCrowCrow’s Dr Langeskov! The dev studio’s also behind the Stanley Parable and while their games are short, they offer a lot of replayability as there’s always something to discover after you just completed it!

We also need Replayability to prevent you from growing weary from/getting bored with a game:

“Replayability” or Ρ (“Rho” -> the greek “R”) should just be a constant that gets multiplied into the formula.

I’d also factor in “Perseverance” (aka your ability to play a boring game for hours) into this but in the end, it wouldn’t make too much of a difference, so both “Replayability” and “Perseverance” should be united in Ρ as an addition of sorts. If you’re able to play a game for ages even though said game has a replayability-score of next to 0, then your perseverance for that matter is the factor that should determine Ρ. If the game can be played over and over again but you usually don’t, then you just aren’t the person to replay again, rendering your perseverance-score unnecessary. If you are that person that plays a ton of games no matter how much you’ve already played them and that game offers you a ton of replayability, then that results in a high score Ρ-wise (you may as well be Chris, a friend of mine, who’s got over a thousand hours in Skyrim, mods and DLCs not included, and who usually doesn’t play anything else because of his ability to not get bored with Skyrim).

Dead Cells combined Challenging Rogue-like experiences with fluid combat, astonishing graphics (at least imo) and the right amount of permanent-progression + metroidvania-ness.

And lastly, there’s the presentation:

This basically makes a game nicer. There’s gunplay, lore, graphics, the soundtrack, and other cosmetic aspects in this one. The symbol will be Ψ as I couldn’t think of a different symbol to use.

Therefore, we come to the conclusion that, within one game, fun equals the replayability Ρ times the progression Π times the presentation Ψ, with Π consisting of the reward Δ (Delta – I just like triangles, so I put here) divided by the time t needed to achieve Δ. 

FUN = Ρ * Π * Ψ= P * (Δ/t) * Ψ

Essentially, that’s something I just came up with. This post was inspired by me not playing League of Legends in quite some time as it takes too much time to get into a round of League and as it takes too long to finish one game and as most of the time it’s not even that rewarding to play the game. I don’t have that much time quite often and nowadays I feel like the quality of the game has decreased while the time I put into the game has increased, resulting in less of a sense of progression, less replayability, a lot of salt, and the same presentation as always, resulting in less fun than before. But I didn’t want to rant about League but instead do something THAT IS FUN, so instead, I came up with this and I, indeed had fun with it. Coming closer to a finished joke-formula was nice for a sense of progression. Coming back to this post and working more on it resulted in a lot of “Replayability”. And the presentation of it hasn’t been that bad either as my home’s looking rather cosy nowadays and as my desk is a nice place to work at. Both the soundtrack and the workplace for this post have been nice, resulting in a nice presentation. Hence, writing this post was more fun than ranting about League not being that much fun anymore. 

Risk of Rain 2 is a title that I only just reviewed! I highly recommend it. Insanely fun in multiplayer!

Now, is this formula applicable to everything? 

Nope. Not at all. 


Well, because of personal preferences and other factors, I’d say. But it’s a fun idea to think about and I dare you readers who made it this far to tell me what you think about this formula and changes that could be made to complete it! :)

Until then, have a nice day! :) Cheers!

Note: This post was presented to you by Magi. He’s a math and philosophy student, who should study for his analysis-exams instead of making up formulas and variables like this. Oof.

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