This guide is for nerds who want to know a little about the maths dictating the game. I hope some people find it interesting or useful for analyzing different strategies.

How much experience do you gain in a given time? At the start of the game you get one XP every second, but the longer the game goes on, the more generation and instinct levels you get, accelerating your growth. The interplay of generations and instincts makes it hard to give a precise closed formula, but we can approximate under a few simplifying assumptions. When we simplify by saying that instincts and tool modifier does not change in a given run, we obtain the approximation:


Here

• X(t) is the experience obtained in the time t in seconds spent in one skill.
  
• x is the experience requirement for your first generation. Without New Game Plus perks, you have x = 9.9 and every generation XP perk multiplies this by 0.95.
  
• E is roughly 1.88.
  
• m is the product of the multipliers from your instincts and tool modifier - it does not include the generation modifier.

This formula does not work well at the very beginning of the game (low instinct modifier, small time) or if you gain a lot of instincts in a run. Also note that this is only the experience gained in one skill for the time spent in that skill in a single run.

The inverse of this function gives an approximation for the time you need to spend in a skill to get to a certain amount of experience:

Here is an (again approximate) formula for how much time you require to get n additional instinct levels in a run:

Here

• y is the experience requirement for your first instinct. Without New Game Plus perks, you have y = 25 and every instinct XP perk multiplies this by 0.95.
  
• n is the number of additional instinct levels you want to have in a run.
  
• i is the number of instinct levels at the start of your run.

Combining this formula with the above formula for how much time you need for a given amount of XP, we can obtain an estimate how much time we need to get additional instinct levels in a run. Here is a quick example without using tools. The tool multiplier would just divide the time by the modifier.

Some takeaways:

• Experience is roughly quadratic as a function of time. That means you get four times as much experience if you double your time spent in that skill or nine times as much if you triple your time.
  
• You want to spend your time in as few skills as possible to maximize your XP gain, with a priority to the skill you can spend the most time in.
  
• Experience is also roughly quadratic as a function of the tool or instinct modifier - if you can spend the same amount of time in the skill.
  
• The time you need to spend to get to a certain point in a run gets divided by your tool and instinct modifier (assuming that the time spent in the skill before the tool is negligible).

The generation XP perk

The generation XP perk has the same effect as an additional tool modifier of roughly 2.4% per perk level (multiplicative), i.e. it divides the time you need to get to a given point by 1.024. In a 35 minute run this means you free up roughly 50 additional seconds to spend. This is especially good if you can spend the additional time in a skill you want to prioritize.


How does the generation XP perk compare to the instinct XP perk?

Except at the very start of the game, one level in the instinct XP perk roughly translates to 2.6 additional instinct levels. You can again think of this as having an additional tool modifier of roughly 1.026. With that reasoning, the instinct XP perk should be slightly better than the generation XP perk, although the difference is not great.

Here I'll give a quick sketch of how to obtain these formulas. The first observation is that the XP required to get to the n-th generation is given by a geometric sum, which has a closed form:

Similarly, the time required to get the n-th generation is also given by a geometric sum (assuming your instinct modifier and tool modifier is constant), but with a base of 1.11/1.05 and additional multipliers.
Solving for n, approximating the formula a bit and reinserting into the other geometric sum you obtain the formulas from the section above.

The XP required to get to a certain instinct level is also a geometric sum, with base 1.02. Multiplying the XP requirement for the first level with 0.95 is the same as having 2.6 additional levels in the limit.