6. Reign of Dragons Enhance and Evlove Strategy (MATH!)

I burned through alot of Cards and Dorri trying to nail down exactly what was happening
during the enhancement and evolution of cards in Reign of Dragons. You can feel free to do the same in order to test my results.

You may have noticed that I gave a little math in the Enhancement section but none in
the Evolution section. The good news is that the Evolution math is really pretty simple.
The bad news is that in Reign of Dragons you will be both Evolving AND Enhancing cards at the same time, and the math for doing that gets very complicated very quickly.

First, here is the simple part... Evolution Statistics without enhancement.
All cards gain exactly the base increase when being evolved:

Base Card = Base Card stats x 1.0 (ex. 1000 ATK)
Evolution1 = Base Card stats x 1.2 (ex. 1200 ATK)
Evolution2 = Base Card stats x 1.4 (ex. 1400 ATK)
Evolution3 = Base Card stats x 1.8 (ex. 1800 ATK)

At least one person out there has already pulled out a calculator and discovered that
these ratios dont match what it says on their cards. Never fear there is more math to
come, and then some boiled down explanations for the math challenged.

When Evolving a card, there is a message on the screen right before you hit the evolve
button. I will type out that message so you don't have to go look.

"Half of the base Cards lvl will be carried over"
"5% of the ATK/DEF will be carried over"
"If the card is at max lvl, the rate will be 10%

The reason that the numbers I gave above may not exactly match your calculator is that
5% part. Factoring in the 5% carry over will make the math match what your card says, but once again its a little more complicated than that. Depending on how many cards you used in the Evolution process, and in what order you used them, that 5% gets applied between 6 and 14 times! your going to hate me for saying this but once again, its a little more complicated than that. (you see why it cost me so many cards and Dorri to nail this down!)

Its pretty easy (ok maybe not THAT easy) to go through all this math and miss something that I find absolutely critical. Those 5% bonuses get added to the next cards base, and then 5% of that cards power gets carried over to the next evolution, and then 5% again to the Final Evolution. I'm going to give you a mathematical progression of a REAL LIVE Reign of Dragons Card now, instead of just theoritical "Card-X"
(I haven't said the critical thing yet, so don't worry you didn't miss it)

Card info
Werewolf: [Melee] Chaos (Common)
lvl 1/20
Attack: 590
Defense: 540
Cost: 3

Using a 4 card evolution will net you the following stats:
evo(0) 590/540
evo(1) 769/704
evo(2) 898/812
evo(3) 1154/1048

Mathematical formula of that evolution (ATK only)
evo(0) 590
evo(1) [590 x 1.2]+[590 x 0.05]+[590 x 0.05] = [708]+[30]+[30] = 768
evo(2) [590 x 1.4]+[768 x 0.05]+[590 x 0.05] = [826]+[38]+[30] = 894
evo(3) [590 x 1.8]+[894 x 0.05]+[590 x 0.05] = [1062]+[45]+[30] = 1137

Comparing these numbers to actual game numbers you can see that there are some minor differences, but using this formula I have been able to calculate and confirm combined evolution and enhancement mechanics with a very small margin for error.

You probably remember from earlier that you can use up to 8 cards to evolve to a final
state, as opposed to just 4. Using 8 cards would change the end of the lines to look
like this.
[708]+[30]+[30] = 768
[826]+[38]+[38] = 902
[1062]+[45]+[45] = 1152

It should be pretty obvious that 1152 > 1137 because the 5% carryover in the last 2
evolutions was larger. The same thing happens if we Enhance the cards at each step.
The "Perfect Evolution" that will result in the strongest card of a given type is.

8x base cards, enhance to max level
evolve into 4x card+, enhance to max level
evolve into 2x card++, enhance to max level
evolve to final card, enhance to max level

I'm not going to bother to do the math on this, because you are never going to do it.
Doing a "Perfect Evolution" card would be so expensive and use so many feeder cards
that I am not certain it is even possible for anything above a common 1 star card.
for a 1 star card perfect evolution I estimate that it would cost a few hundred thousand
Dorri several hundred feeder cards. for a 2 star card that cost would go up 500-1000% since you have to enhance all those cards 10 more levels to get to max enhancement. When you start talking about doing this to 3,4,5, & 6 star cards, you are talking about Billions of Dorri and Cards... good luck with that.

Now that I've Crushed your dreams, lets get back to reality and talk about Combination
Enhacement and Evolution Strategies for Reign of Dragons. To keep this simple lets
just redo that Werewolf evolution from above, but with an Enhanced card thrown in the
mix. (We are really close to that Critical thing now!)

Card info
Werewolf: [Melee] Chaos (Common)
lvl 1/20
Attack: 590
Defense: 540
Cost: 3

Using a 4x lvl 1 Werewolf cards will net you:
evo(0) 590/540
evo(1) 769/704
evo(2) 898/812
evo(3) 1154/1048

Instead of 4x lvl 1 Werewolf cards, I now have 3x lvl 1 and a lvl 8 Werewolf card with
the following stats.

906/874 (8)

I can use this card during Evolution 1, 2, or 3.
If I use it during Evolution 1, I will get the following progression (ATK only)

evo(1) 878 = 784 + 94 (the +94 is because this card will be lvl 4, half lvl carried over)
evo(2) 957 = 903 + 54 (the +54 is because this card will be lvl 2, half lvl carried over)
evo(3) 1051 (lvl 1)

In this example, using that card in the first stage evolution brought the ATK of the final
card up by a whopping 3 points, from 1048 to 1051. The reason that this is such a small increase (Critical thing immediately ahead!!!) is that the bonus from that card was multiplied by 0.05, and then by 0.05 again, and then by 0.05 AGAIN! If we had used that lvl 8 card in the LAST evolution step instead of the FIRST we would lose MUCH less of that bonus, giving us a card that looks like this.

evo(3) 1191 = 1063 + 127 (the +127 is because this card will be lvl 4, half lvl carried over)

Finally, the point of all of this rambling is this.

1. You will never make a perfect card, but feel free to try.
2. Using more cards in the Evolution process will result in a stronger final card
3. Using Enhanced cards in the Evolution process will result in a stronger final card
4. Using Enahnced cards FIRST in evolution will result in a weaker final card
5. Using Enahnced cards LAST in evolution will result in a stronger final card

You can tailor this process to you needs and budget, but I will now give you the card
building strategy that I try to use most often.

Base card----
------------------- \
Base Card-------- Base card(+)--
------------------------------------------ \
Base Card -------------------------- Base card(++)[ENHANCE]--
-------------------------------------------------------------------------------- > Final Card
Base Card--------------------------- Base card(++)[ENHANCE]--
-------------------------------------------- /
Base Card-------- Base Card(+)--
------------------- /
Base Card----

Maybe not my best picture, but I think it conveys the Idea. I will pretty much never enhance a non evolved card unless I need it my deck RIGHT NOW and I only have one of them. If I do need that base card enhanced to use, I will try to save it for the 2nd stage of evolution so that more of its bonus can carry forward. I do sometimes Enhance (not above lvl 10) during that 2nd stage of (+) cards, but only If I have alot of extra feeder cards clogging up my inventory. I ALWAYS enhance the last two cards that will be combined to make the final card, even if I cannot
manage to get 2x (++) cards.

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