ForumsGamesGemCraft CS: gem combining schemes competition

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daniil_sizov_98
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daniil_sizov_98
30 posts
Farmer

Some of you could have read my post on reddit (http://www.reddit.com/r/Gemcraft/comments/2385eg/sc_about_gem_combining_mechanics_and_why_we/) in which I explain how does gem combining works. But one of conclusions I've made â" "Try to avoid combining one color gems of different grades" â" is correct only in theory, since if you combine one color gems of different grades your gem's attack speed will suffer a lot. But in practice attack speed is capped by 30 shots per second.

So, in practice you can get some gain in specials (if your gem's attack speed is greater than 30 sps) by using special combining schemes, e.g. (((G20 + G20) + G20) + G20) instead of ((G20 + G20) + (G20 + G20)). By this post I want to start new funny competition â" for best combining scheme for Black and Orange! To set the new record you can post your G60 gem analogue (i.e. gem with the same cost as G60 gem), but since your scheme may not allow you to make G60 gem analogue, it will be better to post your ~G60 gem and a special value (let call it "growth speed&quot, which is:

log(result_gem_special / base_gem_special) / log(n) (n is number of identical base gems combined into resulted gem)

Let say you have base pure gem x and combining scheme g(x1, x2, ..., xn) (g(x1, x2, ..., xn) combines n input gems into one resulting gem). Then "growth value" will be (log(special(y) / special(x)) / log(n)), where y = f(x) = g(x, x, ..., x). You need to find such a scheme g(x1, ..., xn), which has maximum "growth value". Since G7+ gems have extra bonuses and gems lower than G7 have not, please, use only G7+ gems as your base gems to calculate "growth value".

Why I'm starting such a competition?

Because optimal combining schemes for Orange and Black is Holy Grail for all Gemcraft SC players. Growth values for standard combining are ~0.4647 for orange and ~0.1243 for black for total ~0.589 for Black/Orange. That means, that if you grade your B/O gem up, it's manaleech power will be 2 ^ 0.589 = 1.5042x, and after 80 grading ups it will be ~152'913'823'388'742x. But if we could find schemes, which will show even e.g. 0.51 and 0.14 growth values, if you grade your B/O gem up according to those schemes, it's manaleech power will be 2 ^ 0.65 = ~1.57x per grade, and after 80 grading ups it will be ~4'503'599'627'370'509x. So, G81 gem will leech 30x more mana and it will be 30x less time to get G100 gem and beat the endurance even without WoE and shrines

I will start:

Orange G61 analogue
http://i.imgur.com/qm19DGE.png
Orange growth value
http://i.imgur.com/h0fPVqZ.png

Black G61 analogue
http://i.imgur.com/3SOPW1A.png

Black growth value
http://i.imgur.com/sqWIZGV.png

Total groth: 0.62851
scheme_G81_manaleech / standard_G81_manaleech = 2 ^ (0.62851 * 80) / 2 ^ (0.589 * 80) = 8.94x

  • 89 Replies
daniil_sizov_98
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daniil_sizov_98
30 posts
Farmer

@cronos51, @thunderrider, @ConnerC, you had combination schemes that outperform standard ddddd...dd grading. Would you like to try to find optimal scheme?

psorek
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psorek
447 posts
Jester

I'm working on the best scheme for single-color gems. Some numeric methods if you care.

daniil_sizov_98
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daniil_sizov_98
30 posts
Farmer

@psorek, very nice! Numerical solution seems to be very difficult problem to me, since combining result depends on combining stones grade difference, but it will be great if someone will find it. I'm thinking about heuristic search

psorek
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psorek
447 posts
Jester

I just check every combination up to grade I wish. Dynamic programming method if you know what it is.

psorek
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psorek
447 posts
Jester

0.495 is max growth speed for pure orange gem when it's combined from 64 base gems.
0.49 is max growth speed for pure orange gem when it's combined from 16 base gems.

There is no proof, it's just result of my calcullations. I will check the exact algorithm for one or both and post it here.

daniil_sizov_98
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daniil_sizov_98
30 posts
Farmer

@psorek, oh, I thought you were talking about exact solution in general case For some reason I abandoned using dynamic programming approach for combining, and as I can see now probably I was wrong.

psorek
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psorek
447 posts
Jester

@daniil_sizov_98
May we talk on some chat? Google talk, some IRC, whatever you want.

psorek
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psorek
447 posts
Jester

I will describe sub-optimal combining scheme for 16 base gems for orange and black, basing on daniil reddit math about gems combining mechanisms. Optimal ones are little different for these colors, but the difference is very small and doesn't changes overall result alot. I don't know (but can compute if needed) what is optimal for other color gems and there is big chance that it won't be the same.

The method is as follows:

(g1+g1) + ((g1+g1)+g1) - gives g3 call it ONE with value of 5 basic gems.

(((((g1+g1)+g1)+g1)+g1)+g1)+g1 - gives g2 call it TWO with value of 7 basic gems.

(g1+g1) - gives us g2 call it THREE with value of 2 basic gems.

((TWO+THREE)+THREE)+ONE - gives us g4 call it FINAL with value of 16 basic gems.

FINAL is our resulting gem.

psorek
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psorek
447 posts
Jester

My g58 equivalent. I started from grade two orange/black and upgraded gem with recipe one post above every time I've 16-ed my mana. Gem I've created gives 4.35 times mana than plain upgrade one.


Supergemmed and standard one for comparision
https://dl.dropboxusercontent.com/u/64607958/g58%20supergemming.pnghttps://dl.dropboxusercontent.com/u/64607958/g58%20standard.png

Astroshak
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Astroshak
268 posts
Peasant

Psorek, do you mean that you took a basic grade 2 OB, duplicated it 15 times, and then followed that recipe? And each time you could, you took the resulting gem and duped it 15 more times, repeating the recipe?

psorek
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psorek
447 posts
Jester

Yeah, you can get used to it

psorek
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psorek
447 posts
Jester

It seems like there is no universal combining scheme. I was looking for optimum schemes while manipulating parameters (for example different colors, damage etc) and it behaves just like chaos generator. I am pretty sure that my solution is very close to optimal and nobody will be able post something better than for example 1.5 of mine @g60.

cronos51
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cronos51
108 posts
Nomad

daniil, when I saw your results, I was stunned. Fortunately I don't have to try to beat these stats, as apparently - accoeding to psoreks results - it is not possible For a guy like me that approached all this purely empirical it would have been impossible to get even close.

You and psorek impress me. I don't know how the best methods for dual and triple gems (O/Bla, R/O/Bla) will look like. Applying psoreks method in a roughly adapted quick first try for R/O/Bla already doubled the manaoutput in relation to the old method I was using (just the basegem).

Given the fact that for my last run I had reached a 1,4*G91 (with amps already 3,2e+21 mana per hit) before my notebook liked to produce its first ever bluescreen, it seems we won't wait too long till we see G100 and till endurance has been beaten. One of the two you should go for it!

Thanks, psorek, btw for sharing this.

borthelcash
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borthelcash
104 posts
Peasant

Are the raw specials compared using a baseline of 45+15 to True Colors, Orange, Black, and Fusion? I assume so, so if it is the case, it might be helpful to add that to the main post, or clarify it in another if the edit time limit is passed.

Astroshak
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Astroshak
268 posts
Peasant

Psorek, I'm impressed. I'm trying your technique right now, and in this (admittedly lowest difficulty level) Y1 I'm doing, I'm able to bomb the waves to e22 levels of HP - for wave 12.

Now, a question. Is it better to start with 16 G2 OB gems, or to start with 16 G1 gems, in the color distribution desired? IE - 9 Orange, 1 Red, 6 Black? And if the latter, does combination order matter much (beyond just "insert G1 gem here into recipe&quot?

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