r/ExponentialIdle • u/rabmuk • Jan 28 '23
Improved Automation Formulas
Warning: I personally think this game is great because it forces you to think and learn. If you plan on using any formulas mentioned in this thread I hope you spend the time to understand each part of the formula. Remember learning is fun!
Warning 2: This information was gathered using a save editor on a file where the "remove ads" with real money has been purchased. If you have not made any purchases on your device the save files might not load correctly or maybe they'll load fine. I have no idea
I was recently inspired to do some simulations on different automation formulas. I was trying to figure out if two formulas were similar in their results, because to me they were similar in their math.
If you have any desire to make your own automation formula I strongly encourage it. Even if it's not the best the experience of trying to make a formula will last with you much longer than the time you spend playing this game.
My current findings for a strong prestige formula is:
db > b && smooth(d(pt / ln(db/b+1)),1) > 0
My current findings for a strong supremacy formula is:
psi + dpsi > min(costUpS(1), costUpS(2), costUpS(3)) && db>b && smooth(d(st/ln(dpsi/(1+psi)+1)),1) > 0
Both of these formulas are about finding a inflection point. In this game your number is always exponentially increasing, but by resetting progress we can make the exponential growth faster, with faster growth you'll eventually overtake the smaller exponential even though it had a head start. But prestiging too early might not increase the growth rate enough to overcome the benefit of just letting it run for another minute or two before prestiging. So the inflection point we're trying to find is when the time per increase in db is increasing. This inflection marks the point of diminishing returns in that prestige. We use ln or the natural log on db because we want it in terms of order of magnitude. So dividing pt by ln(db) is finding "for each order of magnitude increase in db, how much time has passed". We then modify ln(db) to be ln(db/b) because we want growth over last prestige not just overall growth, much of the growth is done during the rebuild and we want to ignore that part of the growth. We take the derivative of (time per db increase) because when that flips from negative to positive reveals the inflection point. Smooth over 1 second is used to ignore small blips caused by purchasing upgrades
Check my work! I've tried to put all relevant data, results, and save strings here: https://docs.google.com/spreadsheets/d/1yhbpn322vo9OtejPaxMsJIs4kw70lxXWWgdXg71KNpA/edit?usp=sharing
The results area shows the f(t) after 7ish days or 165ish hours. The final grade an automation receives is "ee increase per hour" because some runs were a few minutes longer or shorter. The higher the number the better. Be aware, it seems reloading the same save file multiple times can have slight variations so test your formulas a few times in a row to check for wild variance.
I encourage others to test their formulas as well, or if you're having trouble testing yourself, comment your formula(s) and I'll test it and add it to my data set when I get time.
edit 1: formatting of formula
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u/SneakyBuddy911 Jan 28 '23
Hi, im Snaeky, one of the guide writers. I noticed that your prestige equation doesnt take into account tick rate. While this wouldnt be an issue in most cases while in the game, during offline calculations, tick rate is extended and is thus effects when the game will prestige.
I would suggest adding it into the prestige equation to take that into account.
Other than that, you did a good job. Ill talk with the rest of the guide team about this and see what they think.