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Video Game / Exponential Idle

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The game's base formula for progress. Don't worry, it's playable even if you don't get it.

Exponential Idle is an Idle Game for smartphones released in 2020. In it, you play as a talented undergraduate student who gets asked by his professor to converge a formula which is an exponential recursive equation into a finite value. Not knowing how to solve it, you make a small program that calculates it for you. As you progress, you start upgrading and using more variables to make numbers grow faster and progress with your research. The game also has some of the largest numbers seen in idle games, with them having the ee notation later on (for example, ee54.129 means 10^(10^54.129)).

This game provides examples of:

  • 15 Puzzle: You can play the 15-puzzle minigame to earn stars, with its size depending on difficulty (3x3 on easy, 4x4 on medium, and 5x5 on hard).
  • Ad Reward: You can watch an ad to temporarily increase the value of dt by 50% or buy the Permanent Ad Reward and all achievements related to them.
  • A.I.-Generated Economy: You can buy autobuyers for variables and upgrades, with each one pressing the Buy All button at the max setting every second, though it can be sped up. Due to the speed, this may make purchasing upgrades difficult if you have a variable autobuyer and vice versa, though there should be no problems if you have both and you can always turn them off.
  • Arc Number: Euler's number (approx. 2.718), also known as e, shows up multiple times due to it being a well-known constant. It's in the app icon, your current amount of money is multiplied by it to a certain power every tick, and it's used while calculating costs for star bonus levels.
  • Are You Sure You Want to Do That?: If you try to activate Supremacy before the point where you would have accumulated enough mu points to buy the next upgrade, the game will ask "You will not have enough mu to buy the cheapest Supremacy upgrade. Are you sure you want to continue?" This is to make sure that players don't waste progress for nothing.
  • Boring, but Practical: The first three ψ parameter upgrades are more effective than the latter three (at least before the ee11000$ mark), even if their formula is not nearly as complex.
  • Cap: The game defines infinity as its cap. At first, it's ee200$, or 10^10^200$. However, doing a Supremacy lets you increase the infinite value, with the highest possible score going above ee59,999.9$.
  • Cash Gate: To progress the story, often a certain amount of money or db must be reached. For instance, to get to the "Some Hope" chapter, you have to get more than 1.0000=e20 db.
  • Cool Teacher: The professor, who is supportive of your project and gives you the Prestige currency that can be spent on permanent upgrades.
  • Deliberately Monochrome: The game has absolutely zero colors other than grey and white (or black and white if you're playing with Dark Theme on), as a game heavily centered on math wouldn't really need color.
  • Dump Stat: Don't be surprised when the boost from x gives 0% profit when compared to other variables, as even if it's free trying to boost something that mostly relies on y and higher variables (like x=64y+2^3*100, when y=15z+2^6*128 which is clearly much higher and there are variables above that) isn't going to work well. The game even gives you the "Why Are You Doing This?" achievement for upgrading it 1000 times.
  • Experienced Protagonist: Your character starts off as a talented undergraduate student with professors who see a promising future ahead of him.
  • Export Save: You can export the approx. 20KB save into the clipboard and paste it into the game or a document.
  • Game Within a Game: The theories are described as small idle games. They have their own formulas, upgrades, and prestige mechanics, and the largest amount of currency reached in them is used for a main-game multiplier.
  • Harder Than Hard: The arrow puzzle is the only one with expert difficulty. It gives more stars than hard upon completion, but it also has six possible arrow positions instead of two, making direction management far more finicky. To put it in perspective, the fastest clear time for hard as of August 2021 is 0.44 seconds. For expert? 22.34.
  • Leaning on the Fourth Wall: The player character mentions after the second Prestige that the function value growing at an increasing pace is beginning to feel like an idle game.
  • Loads and Loads of Loading: Not initially, but after getting Auto-Prestige and doing it and Supremacy a lot, your super high profits and frequency of Prestige-ing turns so high that it can take several minutes for the phone to calculate how much money you've earned while the game was off and ultimately finish loading. An update added a button that lets you speed up the process by up to 50 times to cut down on the loading time greatly (though there's still a few seconds of loading before that), at the cost of the calculations becoming slightly less accurate.
  • Low-Level Advantage:
    • Oftentimes in theory 9, buying certain upgrades a lot is going to make progress next to impossible due to each purchase raising the power of q which acts as a divisor in lemma 2 for instance. It's why a minus button for each upgrade is always available.
    • The Arrow minigame boasts an Expert difficulty; completing the minigame on said difficulty awards more stars than any other minigame or difficulty. However, it's notoriously difficult, completing the Arrow minigame on Hard twice awards more stars, and it's far quicker.
  • Magikarp Power: ψ upgrades 4, 5, and 6 are initially inferior to 1, 2, and 3, but their effects start to outweigh those by the time you reach ee11000$.
  • Mini-Game: There are three minigames you can play to earn stars with selectable difficulties - a 15 Puzzle, a torus puzzle in which you have to slide rows and columns of tiles so they're in their intended places, and an arrow puzzle which has you make all arrows turn upwards by tapping them while affecting those around them.
  • New Game Plus:
    • Doing a Prestige makes you lose all upgrades but gives you a Prestige currency for new upgrades, labeled as μ. An upgrade lets you perform it automatically after a certain time or a certain ratio of db to b is reached, even when the game is off.
    • A long time after that you can eventually do a Supremacy, which makes you restart the game at b=0.001 without prestige upgrades, but it allocates a Supremacy currency for more new upgrades named ψ, making it a New Game+^2.
    • Even later after that you can do a Graduation to reset all normal, Prestige, and Supremacy upgrades, but it grants a new currency named σ that can be spent on upgrades for the ψ parameter or formula modifications that greatly speed up progress, making it a New Game +^3.
    • Once you unlock theories, you can publish a paper in a theory that resets currency earned and upgrades bought while making progress faster, but only inside the theory, making it a New Minigame +.
  • Not-Actually-Cosmetic Award: Every achievement earned gives you stars which can be spent at a shop.
  • Not Completely Useless: All the lemmas you prove in theory 9 don't appear to boost anything and are likely to be skippable for most players who don't care for the story. Nevertheless, you still need to finish them if you intend to reach the extreme postgame, as money will be capped at ee50000$ if they're not done.
  • Number of the Beast: You get the Devil's Advocate achievement for gaining ee666 dollars.
  • Player Creation Sharing: An update adds the custom theory feature, which lets players create their own small idle games with JavaScript and upload them into the game. The ones that receive approval from the developers are marked with a star and progress in them affects the main game theory multiplier.
  • Player Nudge: Tapping the acceleration button ten times in a row makes the game give you the "Hold, Not Tap" achievement, making it clear that it should be held to be used properly.
  • Rare Random Drop: There's a 0.04% chance that tapping the equation will give you a star. Every tick also has a chance for getting a star starting from 0.04%.
  • Shout-Out: Some achievement names are references.
  • Skill Point Reset: You can respec Stars and Graduation upgrades, receiving all of their respective currency back.
  • Your Princess Is in Another Castle!: The chapter called "The End" (that comes after your graduation and Master degree) is not the last one, there are at least four more after it where you earn further honors.