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

Update on magic heroes overspill:

We now know that each tile gets treated separately, which should help us with our understanding.

In Post 157 2 Lucys with 0% and 2% mana generation bonus were tested. The 2% Lucy was charged with 5+2(1)+5 tiles, and the 2(1) was a ghosted tile.

If each tile gets treated separately here, Lucy+2% shouldn’t have been charged, if that wasn’t a ghosted tile.
5 tiles at 2% = 500 x 1.02 = 510 MP
1 tile at 2% = 100 x 1.02 = 102 MP, total of 612 MP, so this would push the mana bar to magic2
1 tile at 2% = 100 x (1.02 - 0.22) = 80 MP, total of 692 MP
5 tiles at 2% = 500 x (1.02 - 0.22) = 400 MP, total of 1092 MP, so magic2 shouldn’t be charged.

Let’s test this:
Test 1: Magic hero Milena with 2% mana generation bonus from class gets charged from 4+5+3 regular tiles.
This is a large overspill of 5 tiles into magic2. If all of them would add some extra mana, Milena’s magic2 should be easily charged.
If only a single tile can provide overspill mana, then she shouldn’t be charged.

=> Milena’s magic2 is not charged
=> overspill only applies to a single tile

Let’s do some more tests to see, if they comply with this understanding.

Test 2: Milena with 0% mana generation bonus charging with 12 tiles at once.
Well, in case that all 12 tiles would get treated as part of the magic1 mana bar, they would give 1200 MP and Milena would be supercharged.

=> Milena’s magic2 is not charged
=> no overspill from all 12 tiles, as expected

Test 3: Milena with 0% mana generation bonus charging with 13 tiles at once.
This is basically just for information, to verify that 13 tiles are enough to charge magic2.

=> Milena’s magic2 is charged from 13 tiles, as expected

Test 4: Magic hero Milena with 2% mana generation bonus from class gets charged from 3+4+5(2) tiles, including 2 ghost tiles at the end.
Just a test to verify that only the ghost tile is special, that cross into the next mana bar
Expectation: Magic2 won’t be charged and this will give exactly as much mana as test 1.

=> magic 2 is not charged, as expected
=> The 2 ghost tiles at the end gave exactly as much mana as 4 regular tiles

Ok, so far so good. Let’s go for a detail check.

Test 5: Milena with 10% mana generation bonus from mana troops level 1 (+5%) and Phenexa (+5%) charging with 4 tiles, 1 ghost tile and 5(2) tiles for 1100 MP.
1100 = 400 x 1.1 + 200 x 1.1 + 500 x (1.1 - 0.22)

Expectation: magic2 will be charged

=> magic2 is charged, as expected

Test 6: Milena with 7% mana generation bonus from class (+2%) and mana troops level 1 (+5%) charging with 3+6(3)+1 tiles and 1 tile with +10% for 1099 MP.
1099 = 300 x 1.07 +200 x 1.07 + 200 x 1.07 +200 x (1.07 - 0.22) + 100 x (1.07 - 0.22) + 100 x (1.07 + 0.1 - 0.22)

Expectation: magic2 will not be charged

=> magic2 is not charged, as expected
=> even with 3 ghosted tiles for overspilling the extra mana was insufficient to charge magic2, therefore this confirms again that only a single ghost tile gets to overspill

@CrazyChemist3891 Any further open issues with the overspill mechanic for magic heroes?

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Okay Zack it’s been a minute but it looks like you’ve been busy My friend. Can you give me the breakdown cuz there’s a lot of information here and I just I’m trying to catch up. Did the factors end up working out for all the speeds including the ones with the tiers? And I see you’ve made some serious progress on calculating tiles. I’ve been working on a chart to display all this information in a way that is user-friendly. I can get back in to help now so let me know what you need from me and this is what my chart looks like so far.

I’m also going to be adding in in the troop requirements as well I just haven’t gotten there yet

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After we found the refined formula and the mana modifiers basically everything worked out as expected.

Mana bars and mana gains on defense:

• the mana bar depends on the mana speed and the hero stars
• at the end of each turn each hero gets 100 MP
• mana modifiers and mana bonuses and debuffs get added and subtracted, respectively
• mages, styx and tide heroes: the mana modifier applies as soon as as the respective mana bar is reached
• mana is only gained as whole numbers, and gets rounded down

Rarity_factor:
1* hero = 1
2* hero = 1.04
3* hero = 1.081 = floor(1.04 x 1.04; 3)
4* hero = 1.124 = floor( floor(1.04 x 1.04; 3) x 1.04; 3)
5* hero = 1.168 = floor( floor( floor(1.04 x 1.04; 3) x 1.04; 3) x 1.04; 3)

The resulting mana bars for heroes on defense are then:

base value 1* 2* 3* 4* 5* mana modifier
factor - 1 1.04 1.081 1.124 1.168
very fast 650 702 730 759
fast 800 800 832 864 899 934
average 1000 1000 1040 1081 1124 1168
slow 1200 1297 1348 1401
very slow 1350 1459 1517 1576
slayer 1100 1189 1236 1284
Charge 1 490 529 550 572
Charge 2 490 529 550 572
Charge 3 490 529 550 572
Magic 1 550 594 618 642
Magic 2 550 594 618 642 -22%
Styx 1 600 648 674 700
Styx 2 600 648 674 700 +100%
Styx 3 600 648 674 700 +100%
Tides fast 800 864 899 934
Tides average 800 864 899 934 -25%

Example calculation for the “average” charge of a tide hero on defense with

• 4% mana generation bonus from class,
• 15% mana generation bonus from troops and
• (1) +24% mana generation bonus from special skill
• (2) -64% mana generation bonus from special skill

for the 100 MP at the end of the turn:
case (1): mana at end of turn = 100 MP x (1 + 0.04 + 0.15 + 0.24 - 0.25) = 118 MP
case (2): mana at end of turn = 100 MP x (1 + 0.04 + 0.15 - 0.64 - 0.25) = 30 MP

Mana on defense from tiles:

• each tile gets treated separately for the calculation
• tile mana gets rounded (75 x 0.9 = 67.5 = rounded up)
• tiles give mana as follows

combo 1 = 75 MP = 75 MP x 100% (and rounded) (verified)
combo 2 = 68 MP = 75 MP x 90% (and rounded) (verified)
combo 3 = 60 MP = 75 MP x 80% (and rounded)
combo 4 = 53 MP = 75 MP x 70% (and rounded)
combo 5 = 45 MP = 75 MP x 60% (and rounded)
combo 6 = 38 MP = 75 MP x 50% (and rounded)
combo 7 = 30 MP = 75 MP x 40% (and rounded)
combo 8 = 23 MP = 75 MP x 30% (and rounded)
combo 9 = 15 MP = 75 MP x 20% (and rounded)
combo 10 = 8 MP = 75 MP x 10% (and rounded)
combo 11 and higher = 8 MP = 75 MP x 10% (and rounded) (approximately correct)

Miscellaneous:

• offense: mana from minor mana potions gets rounded up, if it wouldn’t result in a whole number. For example, for mages and ninjas with 0% mana generation bonus the 25% minor mana potions give slightly more mana because of rounding
mages: 25% of 550 MP = 137.5 MP = 138 MP (rounded up)
ninjas: 25% of 490 MP = 122.5 MP = 123 MP (rounded up)
• offense: mana steal % apply to the defense’s mana bar. That means for all fully charged fast 5* target that R&N’s 50% mana steal take 93 MP for each hero = 934 x 50% / 5 heroes
• mana steal: the stolen mana gets rounded down
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Thanks buddy I’ll apply the differences to my stat sheet and add troop requirements to it as well.

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With our current understanding of the overspill mana for mages I prepared an overview for the required tiles for various mana generation bonuses:

mana generation bonus required regular tiles with ghost tile ghost tile is No.
1 13 12 6
2 13 12 6
3 12 12 6
4 12 12 6
5 12 12 6
6 12 12 6
7 12 12 6
8 12 11 6
9 12 11 6
10 12 11 5
11 12 11 5
12 11 11 5
13 11 11 5
14 11 11 5
15 11 11 5
16 11 11 5
17 11 11 5
18 11 11 5
19 11 10 5 (yes)
20 11 10 5
21 10 (semi-nope) 10 5
22 10 10 5
23 10 10 5
24 10 10 5
25 10 10 5
26 10 10 5
27 10 10 5
28 10 10 5
29 10 10 5
30 10 9 5
31 10 9 5
32 9 9 5

According to this table you should be able to charge magic2 with 10 tiles and +19% mana bonus if you get a ghost tile for tile No. 5.
400 x 1.19 = 476 MP
200 x 1.19 = 238 MP
400 x (1.19 - 0.22) = 388 MP
1102 MP = 476 + 238 + 388

For the test I went with a Dölgöön+20 with mana troops level 29.

=> magic2 is charged with 1102 MP from 4+1gh+4 tiles, i.e. 10 tiles in total.

According to this table you would also charge magic2 with any 10 tiles with +21%, but it is already known that it depends on the sequence on how you charge these 10 tiles.
With 4+3+3 and with 3+4+3 tiles magic2 is charged, but with 3+3+4 tiles it is NOT charged.

So far we have no explanation for this behaviour yet.

With each tile being treated separately, the sequence shouldn’t make any difference, but it does in this case.

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Outstanding work @Zack

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@Elioty33 any idea, why the sequence matters?

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@Zack @Elioty33
Each combo can consist of more than 3 tiles, correct?
If I match 6 tiles as 3+3 in my one move, do 3 tiles give 75 MP and the other 3 68 MP, or they all 6 give 68 each?

I would expect all of them to give 68MP since they are all part of combo x2 but @Zack would probably have a more definitive answer than me.

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That is my expectation as well, because it skips combo1 and immediately shows combo2, so this should apply to both triplets.

Also, there is @G_H_O_S_T 's experience with such mana gain for the defense:

Up to now I didn’t have any evidence available for it, so I thought of a test now with an available defense team:

4*Woolerton on defense without mana generation bonus
=> 899 mana points required.

3+3 combo2 with 4 tiles hitting Woolerton, then mana from 6 turns. It turned out that 4 tiles of this 3+3 hit Woolerton in my actual test.
6 x 100 + 4 x 75 = 900 MP => charged
6 x 100 + 4 x 68 = 872 MP => not charged

So, which one happens then?

=> Woolerton is not charged
=> the 4 hitting tiles didn’t give 75 MP each
=> each of the 4 hitting tiles should give 68 MP, i.e. the mana for combo2 tiles

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To be absolutely clear about the mana on defense for combo2 tiles that get 3+3 comboed another test should help.

As an average 4* hero Ptolemy requires 1124 MP on defense.

If we charge a Ptolemy 4-75+20 with 15% mana generation from class (+4%) and mana troops level 19 (+11%) with 4 tiles from a 3+3 combo2 and 7 turns he will have one of the following mana points:

2 x 75 x 1.15 + 2 x 68 x 1.15 + 700 x 1.15 = 1133 MP => charged
4 x 68 x 1.15 + 700 x 1.15 = 1117 MP => not charged

=> Ptolemy is not charged
=> all of the 3+3 combo2 tiles give only 68 MP
=> we can extrapolate that this applies to all such combos:
When the game indicates a combo, each of the tiles that were activated for that combo give only as much mana as corresponds to this combo.

Example: if a combo1 has triggered multiple matches and directly causes a combo 9, then each of the tiles triggered for this combo9 give the defending heroes mana for a combo9 tile, i.e 15 MP

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Thx for the hard work, @Zack . Not sure if I understood… So what you’re saying is that, say in our first move all in one combo, we manage to match 2x3 tiles, it would automatically be moved to combo2’s mana, instead of combo1 like we’d expect? Does that mean if in theory we did 3x3 tiles in our first move within a single combo (I assume this is impossible, right?), the mana for each tile would be at combo3’s rate? Thanks.

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Correct! When you match 3+3 tiles with your first match, the game deems all 6 tiles as combo2 tiles and the defense gets only 68 mana points for each hitting tile.

Yes, if the first move could activate 3 combos, then the game would immediately indicate “combo3” and all hitting tiles from these combos would give the defense only 60 mana points, i.e. mana for a combo3 tile.

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Thanks, @Zack . This is good stuff.

Also, I heard somewhere that defensive tile mana works differently for PvE vs PvP. I don’t recall reading which it was here, but I assume all the stuff above applies (the 75 mana per tile hit, the 100 turn-based mana, etc.) to PvP only? Or are they both the same? Thanks for the enlightenment.

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It all works the same in PvE. The only difference might be in the actual amount of mana points enemies/bosses need to fully charge their mana bar but the mechanics are the same.

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Thanks, @Elioty33 . Any news on when the solstice summon will be?

Edit:

### Solstice Summon

Jun 18, 07:00 UTC – Jun 24, 07:00 UTC

NVM.

Thanks, @Zack . Just to be crystal clear, the 75 mana from a tile on defense mentioned above actually means .667 worth of a tile on offense? And the 100 turn based mana is actually .8667 worth of an offensive tile? I think most people are used to thinking of tile speeds based on attack heroes. It would actually be less confusing (and easier to compare) if everything was based on offensive mana. Having the defensive tile hit based on turn-based mana doesn’t really help most people, I think. Just my opinion. Thanks for reading.

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Don’t know where you are trying to get but it’s actually a lot easier to talk and do the maths in term of mana points. Or a hundredth of a tile if you prefer. Like the game actually does.

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On offense 1 tile gives 100 MP (mana points).
On defense 1 turn gives 100 MP and each combo1 tile gives 75 MP.

75 MP from a tile on defense is 0.75 of a tile on offense, which gives 100 MP.

The rounding of mana that we found in this thread is good evidence that we are dealing with mana points and not with tiles, i.e. a fast hero needs 800 MP on offense and so on…

Please also note, that we also found in this thread that the mana bar of the defending heroes depend not only on hero speed but also on the hero stars - that was one of the first findings in this thread and utterly new to us.

Only the 1* heroes require as little mana on defense as on offense, all others require more mana and the more stars, the more mana they require:

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Thanks a lot, @Zack , for the clarification and summary! You’re awesome.

BTW, is the styx and tides data correct, not a typo? It’s 600, 900, 1200 in offense, but in defense, it’s 700, 1400, 2100 (for 5*s)? That would make styx terrible in defense then.

Also, are defensive tiles also determined in half tiles? Meaning, a 5* fast would only fire after reaching 950? Thanks.

Someone should really consolidate the latest findings in OP.

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