Defensive Mana - Troops/Differences/Turn- Based Mana Calculations and it's Discovery

Was about to say this. The game has to round up in this case. Otherwise everyone would cry out loud and complain (for a very good reason I can get behind here) that four 25%-mana pot didn’t charge their hero.

For the rest of your post, I will read it later after some sleep. You did ■■■■ ton of work again but it’s too late to read all of that :rofl:

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I think the overspill effect cause this. I think the overspill mechanism is more complicate than we think.

  • Case 1 : 5 tiles, then 2 tiles, then 5 tiles. → 2nd Charge
  • Case 2 : 3 tiles, then 4 tiles, then 5 tiles. → Not 2nd Charge
  • Case 3 : 4 tiles, then 3 tiles, then 5 tiles. → Not 2nd Charge

In Case 1, Lucy gain 2 tiles during the change from 1st charge to 2nd charge
In Case 2, Lucy gain 4 tiles during the change from 1st charge to 2nd charge
In Case 3, Lucy gain 3 tiles during the change from 1st charge to 2nd charge

I think the gaining tiles during the change from 1st charge to 2nd charge cause this. And it is possible the -22% Mana Generation Debuff isn’t totally correct. Also the round effect might cause that as well.

I think this same thing happen to the ninja test.

I don’t understand “no bard” and what is the different between “Cobalt with Sapphire, no bard” and “Cobalt with Sapphire and Phenexa”.

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Yeah, it makes total sense, but it is very good to have some evidence and be certain about this as it may help us in understanding some of the other features :grinning:

So there are no decimals for mana points, only whole numbers.
(some of my testing for the small mana gain from Yang Mai’s link was based on the 25% from minor mana potions, so I ended up with approx. 0.3157 tiles/turn instead of 0.32…)

With that I just wanted to point out that I had a setup without mana generation bonus from a bard since and then with a non-working bard, since this might have influenced the mana gain due to a bug, but it doesn’t look like it did.

Well, since we are quite sure that ninjas and mages get slightly more mana from the 25% minor mana potions due to rounding up, I wanted to test this and set up a Willow 4-73 with 0% mana generation bonus.
If I give her 5 minor mana potions she should get additional 2.5 MP from the rounding up for each minor mana potion. 5 more tiles with +4% mana generation bonus from Kingston should then charge her magic2.
A single minor mana potion gives 138 MP = 25% x 550 = 137.5

5 x 138 MP + 500 x (1.04 - 0.22) = 1100 MP or
5 x 137.5 MP + 500 x (1.04 - 0.22) = 1097.5 MP
So let’s see, if her magic2 will be charged from that:


=> the 25% from minor mana potions indeed get rounded (up) (here 137.5 MP get rounded up to 138 MP) and provide slightly more mana than just 25%

Next test: Milena with +2% from class, so any minor mana potions will give
25% x 550 MP x 1.02 = 140.25 MP which will either get rounded up or rounded down

If I charge this Milena with 7 minor mana potions and then increase her mana generation bonus to +36% (with +24% from Phoenicus and +10% from Delilah) and get her one tile, then her magic2 will be either charged (with rounding up) or not charged (with rounding down)
7 x 141 MP + 100 x (1.36 - 0.22) = 1101 MP = charged
7 x 140 MP + 100 x (1.36 - 0.22) = 1094 MP = not charged


=> Milena’s magic2 is not charged yet, so there was rounding down of the decimal mana points in this case (140.25 MP get rounded down to 140 MP)

Let’s make sure. Next test is to confirm the 140 MP for each minor mana potion. So my Milena with +2% gets 4 minor mana potions again, then 3 tile with 26% (additional +24% from Phoenicus) and another 2 tiles with 36% (additional +10% from Delilah) and then her magic2 should be charged.
4 x 140 MP + 300 x (1.26 - 0.22) + 200 x (1.36 - 0.22) = 1100 MP



=> Milena’s charge2 is full

=> mana points get rounded to whole numbers, i.e. rounded up or rounded down, depending on the decimal

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@Zack were you able to rerun that test as Elioty33 suggested without ghosting?

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After we verified that on offense styx heroes charge with 600 mana points for each charge and get a +100% mana generation bonus for styx2 and styx3 let’s see how this holds up on defense.

5* styx heroes should require 700 MP for each charge and for styx2 and styx3 there should be a +100% mana generation bonus.

First test has Amphitrite with 0% mana generation bonus getting mana from 7 regular turns, then 7 additional regular turns.
700 = 700 x 1.0
2100 = 700 x 1.0 + 700 x (1.0 + 1.0)




=> Amphitrite’s styx1 is exactly charged with 700 MP, as expected
=> Amphitrite’s styx3 is charged with 2100 MP, as expected

Test 2 checks 1400 MP for styx2 with the same Amphitrite with 0% mana generation bonus, which gets mana from 7 regular turns, then 2 more regular turns with +100% and 2 turns with -50%.
1400 = 700 x 1.0 + 200 x (1.0 + 1.0) + 200 x (1.0 + 1.0 - 0.5)



=> styx2 is charged exactly with 1400 MP, as expected

Test 3 investigates the styx1 charge and 699 MP. Amphitrite with +9% mana generation bonus from mana troops level 11 (+9%) gets mana from 6 regular turns and 1 turns with -64%.
699 = 600 x 1.09 + 100 x (1.09 - 0.64)


=> styx 1 is not charged with 699 MP, as expected

Test 4 investigates 1399 MP and 2099 MP. The same Amphitrite with +9% mana generation bonus from mana troops level 11 (+9%) gets mana from 7 regular turns, 4 turns with +50% and another 4 turns with +66%.
1399 = 700 x 1.09 + 400 x (1.09 + 1.0 - 0.50)
2099 = 700 x 1.09 + 400 x (1.09 + 1.0 - 0.50) + 400 x (1.09 + 1.0 - 0.34)





=> Amphitrite’s styx2 is not charged with 1399 MP, as expected
=> Amphitrite’s styx3 is not charged with 2099 MP, as expected

=> Styx heroes on defense charge with the same +100% mana modifier for styx2 and styx3 as they do on offense
=> as expected :blush:

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Thanks for the reminder. Here you go:

Basically we just want 14 tiles with +5% mana generation bonus and no ghosting.

So I just went with Cobalt and Shale again. Shale outperformed Cobalt again. This is what happened:
Shale with +5% mana generation bonus and then non-ghosted tiles: 3+4+3+3+1 = 14
1470 = 1400 x 1.05




So, ghost tiles do not give as much mana overspill as hitting tiles!? :thinking:
Well, that’s kind of unexpected for me, but it fits with the other data, so :grinning::+1:

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This is very interesting! Thank you! :+1:

Wondering if it is something more general? Maybe a tile cannot give more than 200MP?
Does a Magic hero at +10% charge the first charge with 3 regular tiles and one ghosted?
3×100×1.1+1×200×1.1=550, thus should be charged. :thinking:

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With 3 regular tiles and 1 ghost tile the magic1 is exactly charged.

Test: Willow with +10% mana generation bonus from mana troops level 1 (+5%) and Zhabog (+5%) gets mana from 3 regular tiles and 1 ghost tile:
550 = 300 x 1.1 + 200 x 1.1

=> magic1 is exactly charged
=> ghost tile gave exactly 220 MP with the +10% mana generation bonus

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Proof: no cap for mana per tile :+1:

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@Zack Do I read this correct, that the only ghosted tiles are overspilling from charge 1 to charge 2?

I believe, we can assume, that only ghosted tiles are not behaving as expected? Your rerun with hitting tiles charged the Ninja as predicted by the calculation.

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If I am not mistaken 3 tiles were ghosted in that test, where Ninja Charge 3 was not charged. With 0 ghosted tiles, it was charged.
How about 2 or 1 ghosted tile?

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Hey my friend sorry I’ve been busy starting a new alliance and getting all the moving parts going. How’s the testing going? I can work on something now if you have a task for me. Any new figures or values that we were unaware of? How are the numbers holding?

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I think it cause by total overspill mana from tile regardless if they are ghost tiles or hitting tiles, for example, 2 overspill ghost tiles = 4 overspill hitting tiles.

I think there are something that affect amount of total mana gain when change from 1st charge to 2nd charge or 2nd charge to 3rd charge.

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Correct!

Yes, there is something strange about that.

Will check in detail during the next days after I have finished the 5* ninjas on defense.
A first test showed that 5 + 6 (1 ghost tile) + 3 tiles result in: not charged
Will need to check again and then show screenshots tomorrow or so.

Alliances can be so much work! :sweat_smile:

Testing goes very well, all tests regarding the mana speed on defense show exactly the expected results.
We have left so far:

  • 5* magic speed (will be done in the next post)
  • 5* ninja charge speed (soon)
  • 5* tide speed
  • mana for combo1 tiles for 4* on defense
  • mana for combo2 tiles for 5* on defense

I need your help for the 5* tides speed since I can only go against a Phorcys 1-1, which is a bit awkward with his minions giving 5% mana every turn, so I would have to use Kvasir to prevent his Minions, but he will get the poison DoT and knowing my luck, he’ll die from it because I’ll keep getting cascades.

Test 1:

  • target = tide 5*, wing position
  • sturdy, not dangerous healer next to target
  • 3 squishy, not dangerous heroes to complete the defense team
  • 25% mana generation bonus for the target
  • Mist in the attacking team for -64% mana generation
  • No additional unplanned mana effects, cleansing or protection against mana debuffs must occur during the battle

During the fast tide speed go for 6 regular turns, fire Mist at the target and go for 3 more turns at -64% to reach 933 MP for the target.
933 = 600 x 1.25 + 300 x (1.25 - 0.64)
=> The target shouldn’t be charged.

Test2:

  • target = tide 5*, wing position
  • sturdy, not dangerous healer next to target
  • 3 squishy, not dangerous heroes to complete the defense team
  • 18% mana generation bonus for the target
  • Mist in the attacking team for -64% mana generation
  • No additional unplanned mana effects, cleansing or protection against mana debuffs must occur during the battle

During the fast tide speed go for 7 regular turns, fire Mist at the target and go for 2 more turns at -64% to reach 934 MP for the target.
934 = 700 x 1.18 + 200 x (1.18 - 0.64)
=> the target should be charged

Test 3:

  • target = tide 5*, wing position
  • sturdy, not dangerous healer next to target
  • 3 squishy, not dangerous heroes to complete the defense team
  • 10% mana generation bonus for the target
  • Mist in the attacking team for -64% mana generation
  • Ludwig in the attacking team to charge Mist two more times
  • No additional unplanned mana effects, cleansing or protection against mana debuffs must occur during the battle

During the average tide speed go for 9 regular turns, fire Mist at the target and go for 8 more at -64% turns to reach 933 MP for the target. The 8 turns at -64% can be achieved with Ludwig charging Mist
933 = 900 x (1.10 - 0.25) + 800 x (1.10 - 0.25 - 0.64)
=> the target shouldn’t be charged

Test 4:

  • target = tide 5*, wing position
  • sturdy, not dangerous healer next to target
  • 3 squishy, not dangerous heroes to complete the defense team
  • 10% mana generation bonus for the target
  • Mist in the attacking team for -64% mana generation
  • Ludwig in the attacking team to charge Mist one more time
  • No additional unplanned mana effects, cleansing or protection against mana debuffs must occur during the battle

During the average tide speed go for 10 regular turns, fire Mist at the target and go for 4 more turns to reach 934 MP for the target.
934 = 1000 x (1.10 - 0.25) + 400 x (1.10 - 0.25 - 0.64)
=> the target should be charged

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Let’s finish the magic speed.

First, Cristobal with 11% mana generation bonus from mana troops level 22 (+11%) getting mana from 3 regular turns and 4 turns with -34%.
641 = 300 x 1.11 + 400 x (1.11 - 0.34)


=> magic1 is not charged, as expected

Next is Cristobal with 9% mana generation bonus from mana troops level 11 (+9%) getting mana from 3 regular turns and 7 turns with -64%.
642 = 300 x 1.09 + 700 x (1.09 - 0.64)



=> magic1 is charged, as expected

Then we have Cristobal again with 9% mana generation bonus from mana troops level 11 (+9%) getting mana from 6 regular turns, 4 more regular turns, then 3 turns with -24% and 4 turns with -64%.
1283 = 600 x 1.09 + 400 x (1.09 - 0.22) + 300 x (1.09 - 0.22 - 0.24) + 400 x (1.09 - 0.22 - 0.64)





=> magic2 is not charged, as expected

Finally, we have Nadezhda with +18% mana generation bonus from mana troops level 23 (+13%) and Zhabog (+5%) getting mana from 6 regular turns and 6 more regular turns.
1284 = 600 x 1.18 + 600 x (1.18 - 0.22)



=> magic 2 is charged, as expected

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I’ll get on that bro

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So, if we consider Magic heroes on the defence and “only” mana from turns, there is no deviation from the expectation due to unclear overspill?
Great news! :+1:

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I have calculated the following breakpoints for heroes with Styx speed (in offense):

Charge 1, starting with a reduction to 5 tiles at a 20% mana bonus:
20%
50%
100%

Charge 2, starting with a reduction to 7 tiles at a 20% mana bonus:
20%
43%
67%
100%

Charge 3, starting with a reduction to 11 tiles at an 18% mana bonus:
18%
30%
50%
75%
100%
150%

How do your values compare; has anyone perhaps verified some of these breakpoints already?

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Important: These figures apply only to tiles that haven’t been ghosted.

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Here’s the remaining data on the 5* ninjas on defense.

The 572 MP for charge1 have been screenshot verified in my posts 75 (571 MP = not charged) and 82 (572 MP = charged) above, so I’ll only go for charge2 and charge3 now.

Test 1 with 5* Topaz 3-70 with 7% mana generation bonus from mana troops level 7 (+7%) getting 1143 MP from 10 regular turns and 1 turn with -34%:
1143 = 1000 x 1.07 + 100 x (1.07 - 0.34)



=> charge2 is not charged from 1143 MP, as expected

Test 2 with Topaz with 0% mana generation bonus getting 1144 MP from 10 regular turns and 4 turns with -64%:
1144 = 1000 x 1.0 + 400 x (1.0 - 0.64)




=> charge2 is charged from 1144 MP, as expected

Test 3 with Topaz with 5% mana generation bonus from mana troops level 2 (+5%) getting 1715 MP from 14 regular turns, 1 turn with -24% and 4 turns with -64%:
1715 = 1400 x 1.05 + 100 x (1.05 - 0.24) + 400 x (1.05 - 0.64)





=> charge3 is not charged with 1715 MP, as expected

Test 4 with Topaz with 5% mana generation bonus from mana troops level 2 (+5%) getting 1716 MP from 14 regular turns and 6 turns with -64%:
1716 = 1400 x 1.05 + 600 x (1.05 - 0.64)





=> charge3 is charged with 1716 MP, as expected

As a result, (5*) ninjas on defense are verified as well, so only the tide speed is left now.

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