This guide will talk about the optimal skills distribution for high level players.
There is a section on how to extend this to low levels, and the changes needed in assumptions.
Here's a remainder of what each skill is, from the wiki: Skills page[gemcraft.fandom.com]

To start, the skills that depend on playstyle and preference, that don't have a rigid distribution:
Max around WL 1k-10k: Strike spells
Max around WL 25k: Mana Stream (this one could be included, but it's easier to just max it at this point)
Utility only, raise/max at convenience: Bolt, Barrage, Lanterns, Demolition
Useless: Beam, Pylons, Components other than orange/yellow

The rest of the guide will deal in SP, which is the number of skill points you leave free to be allocated in the rest of skills, after you've filled the skills above and left enough for initial mana.

The guide is divided in 2 parts:

• High level = 25 talisman bonuses to skills, WL > 500
  
• Low level = 0 talisman bonuses to skills, 100 < WL < 1000

If you find yourself in the middle, take inspiration from both.

The guide assumes you're using the optimal endgame arsenal. You can find details in the https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=2105632516 but for the purpose of this guide it just matters that the monsters meet, in order:
blue lantern, orange amped traps, red amped lantern, yellow amped traps

All capped skills will reach the cap before Mana Stream does, so they'll be at 50 eventually.
For the uncapped ones, if you prefer having a general hint rather than a list of precise numbers,
there is a skill hierarchy and we can rank the skills from higher to lower optimal level:
Leech>>TColors>Traps>>>>CritHit>>Reson
The Amps skill starts out as the worst one and progressively rises to be as good as TC.

Next sections will talk about the theory behind the optimal skill distribution, if you just want optimal numbers head to the "High level/Low level skills table" sections.

Most of the work presented here has been done by Bill Wilson, thank him if you see him around.
A lot of text has been lifted from the corresponding GCCS guide, the author of that guide gave me permission to do so when I saw him in the mirror this morning.

First of all we need to figure out how many skill points every skill level costs, it's pretty straightforward, to buy up to the Nth level of a skill you need:

Then we need to understand which skills are important to raise, given a defined playstyle.
As written above, the monsters meet the following gems, let's see which uncapped skills help:

• Blue lantern -> TC (only helps duration), Slow (only helps duration)
  
• Orange amped traps -> TC, Leech, Traps, Amps
  
• Red amped lantern -> TC (only helps duration), Bleed (only helps duration), Amps
  
• Yellow amped traps -> TC, Resonance, Crit, Traps, Amps

True Colors, Resonance, Critical Hit, Leech, Amplifiers and Traps and the best choices.
Bleed and Slowing are not needed, at high level TC gets you all the duration you could ever want.

Then there are static bonuses to mana, damage and exp:

• Static mana bonuses -> Fusion (effectively gives more mana), Orb of Presence
  
• Static damage bonuses -> Fury (effectively gives more damage)
  
• Static exp bonuses -> Fury, Seeker Sense

We add Fusion, Orb, Fury and Seeker Sense to the list

At this point we need to see what effect those skills have on the game stats, so let
be the level of every skill (name got from their initial) and 'ta' be the bonus granted by your talismans (hopefully 25).

The raw bonuses look like:

I assume the gems are at the speedcap (all the decent amped trap gems get to the speed cap before g30, easily reached from WL 3k), so we don't bother with it.

Now let's consider what we want to maximize, we'll divide the problem in more parts:

The benefit the amps skill gives is more complicated than all the other skills, because it depends on how much mana is in the amps respect to the gems, how many amps you have, how many gems each one sees and what special we're optimizing.

For 1D amps (leech, bleed) it's possible to give an analytical solution that gives out what is the ideal amp/gem cost ratio and the associated benefit:

where Qa is the number of amps per gem, Ga is the average number of gems seen by each amp and g is the growth of the gem.

Now, with some reasonable assumptions we can get:

For yellow gems, the problem isn't analytically solvable, but can be solved numerically.
We have 2 competing formulae with similar result but different derivation.
Use the ratio formula you like (or remember) best, they give extremely similar results:

We'll use the power formula for traps here, but I leave the one for a killtower if someone needs it.

Manapower

In this game the best mana gems are pure orange gems, whose leech power is influenced by skills this way:

So the quantity we need to optimize for mana gaining is:

if we were to maximize this with respect to {tc,l,a,t, fs, o} over the constraint of a maximum expendable SP amount, we'd get the best setup for mana farming.

But then we need to kill monsters, too, so let's understand

Killpower

In this game the best killgems are pure yellow gems, whose power is its displayed max damage times its displayed crit (times 0.8 times 0.5, which are constants so we never care about those).
They can be helped by a pure red gem applying bleeding on everything.

The killgem killing power is influenced by skills this way:

On top of that our bleed gem also helps, but bleed is influenced by no skills aside from amps, so:

So the quantity we need to optimize for killing power is:

if we were to maximize this with respect to {tc,r,c,a,t,fr} over the constraint of a maximum expendable SP amount, we'd get the best setup for killing monsters with no manafarming.
This is kinda useful (with minor adjustments) for talisman farming at high level, but not what we need here.

In this game most of the exp comes from the enraging bonus, you should aim to keep your enraging gem as high as possible all the time, and stop the field once you need to degrade it too much to keep up with the monsters.

A typical endurance is split in 2 phases:

• Mana phase: you set up the mana farm and you can make a killgem to kill anything that comes at max enrage, with a cost much smaller than your mana gems, the enrage gem is limited by max mana
  
• Kill phase: monsters start getting big enough that the needed killgem is as costly as the manafarm, so you sell the latter, finish upgrading the enrage gem and the killgems and start slowly degrading the enrage gem to keep up, the enrage gem is limited by max killpower

There are actually 2 more phases: Instakill and Peak Kill, but they don't change the effect of the skills on XP and are ignored here, you can find more details in the https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=2105632516

The transition point comes when:
it's possible to solve the above by iteration to find waveT.

We can now compute the total exp before the transition, by summing up the exp of each wave:

The total exp before transition can be approximated by the integral of the above from 0 to waveT, which is:

Now after the transition we have for each wave:

The total exp after transition can be approximated by the integral of the above from waveT to infinity, which is:

The final exp power is then the sum, multiplied by the static exp bonuses, so:
this final function depends on M and K, which depend on the skill values, this is the formula we need to maximize to have the best skill setup.

I report here just some selected rows from the skills table, a full list is available at this link:
https://gist.github.com/12345ieee/cabb04da5e60b3bf08ddc8635ec7c916

The table assumes +25 bonus from talismans, so in the first line TC will be at 39+25=64 total points.

For low wizard levels (100-1000) some assumptions change, so we offer a different distribution, that can be used for the endurance runs that are mixed with talisman farming in that level range.

Once the talisman skills bonus reaches +20, you should switch to the high level one.

Basics

The orb skill is extremely weak, and at low level it's very easy to leak, making it even less effective, therefore we recommend it's kept at 0.

The gems are not at the speedcap, so we also need to consider all the bonuses to speed.

Traps and amps give a speed bonus, that now helps, so now:

The speed of gems grows now, so their growths raise (we ignore the grade nerf, because, again, low level).
We also assume low level players use U instead of combines, so we have:

Amps

The amps now have to consider the speed benefit amps give to gems, for mana and killgems (bleed just needs to be applied once, speed does not help).
The easiest way to evaluate that is to use the approximate averaging formulae, so we have:


M and K, exp model

Nothing changes here.

I report here just some selected rows from the skills table, a full list is available at this link:
https://gist.github.com/12345ieee/458f7c0b4ec8be41a6b2c92c50521f8e

The table assumes +0 bonus from talismans, so in the first line TC will be at 16+0=16 total points.

Gem growth
Given a combine scheme, we know its power increment (P) and its length (N).
E.g. for leech gems an U upgrade has P=1.38 and N=2

If we have a certain amount of mana (Nt base gems) to spend on a gem and many combine schemas, which one do we choose? And how strong is the resulting gem?

It's possible to define a quantity, called growth that is a measure of the goodness of a combine:
g only depends on the properties of the combine schema, and the bigger it is, the stronger a gem becomes for a given initial mana, so it's the ideal number to rank combines.
The last equation also gives how spending mana on a gem affects its power, which is used multiple times throughout the guide.


Proof of the total_mana[wave] formula

Proof of the 1D amps metrics
we use Lagrange Multipliers to do so, and when we eliminate lambda from the first 2 equations we are left with:

Exp_power approximation

It turns out that at high enough level (>10k) the relative exp power is well approximated by:

Looking at the exponents we see that improving mana is 10 times more important than improving killpower, and that's why mana skills are a ton higher than the equivalent damage skills.

At higher levels (> 1M) well after the capped skills are maxed, the kill skills become less and less impactful, as their scaling is logarithmic, leaving only the mana skills to matter.

High level skills approximation

At high level, once the constant terms are negligible, one can find that the SP invested in each skill should be:
where e_i is the exponent with which each skill level appears in the approximated expression of Relative_exp_power. They are:

The exp growth

Given the above approximation, we can substitute back in and get:

Considering that appr_exp_power is proportional to the amount of exp we expect to get on the next field, its exponent is the growth of exp.

It being less than 1 means the game converges, and we can't get infinite Wizard level, but it allows one to estimate how our level will progress as we complete fields and get stronger.

Estimation of max wizard level

By the approximation above, we expect to get:
one can estimate the maximum amount of exp obtainable in the game as
estimation of Ce is a work in progress.