This is my first post in the evony forums and yes, it is a guide. This is not a gameplay strategy guide, just a mathematical analysis on the cheapest way to upgrade star levels.

If you are not interested in the math used you may just skip to the conclusion

But first i will explain the formulas used to draw these conclusions:

The average upgrade cost per level=(the cost to upgrade to previous level+Gems used) /Success Rate

So if you use 1 delicate gem to upgrade to level 1 then the average cost to get to level 1 is:

1/.65 = 1.538 Delicate Gems

level 2 is:

(1.538+1)/.6 = 4.231 Delicate Gems

Starting at level 4 it gets a little more difficult, you must do the same thing then subtract level 1 cost * fail rate:

(9.51+4)/.8 - (1.538*.2) = 16.578 Delicate Gems

This is to account for not losing the average amount invested on that level down each time you fail

You stop doing this after level 8. Delicate and Flawless Gems must be calculated separately.

Here are my results:

note that after level 3 it is cheapest to use 4 Gems each time you are upgrading.

I Chose to recommend using flawless gems at level 7 because the ratio of flawless to delicate is more consistent with drop rates, but feel free to change this slightly as needed. I would suggest saving up 2x as many as needed to upgrade an item to level 15 and then try because this is only an average, your results may vary.

If anyone could take some time to confirm the validity of my approach and the correctness of my calculations i would appreciate it, thanks

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