The feeling when everything clicks smoothly:
Great job as always @Zack 
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Indeed the 933 MP was not sufficient and based on the gap on the final turn that charged him I would say about 67 MP was approximately remaining.
As predicted he fired in 10 turns
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@Zack I see what you’re doing so I’m going to run my own test and see if I can find that make or break point and cancel out speeds trying your different methods and different formulas to see which ones fit.
Can you show me your formula again that you’re currently using
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Sure, bro! That new defense-formula I’m using is:
Multiply the mana_points_on_offense with the rarity_factor and round down to whole number
The rarity_factor starts at 1 for 1*. For the next higher rarity you (1) multiply with 1.04 and (2) round down to 3 decimal places. Repeat for each higher rarity.
Required mana points on defense = floor(mana_points_on_offense x rarity_factor; 0)
mana_points_on_offense =
490 MP for charge 1
490 MP for charge 2 = 980 MP total
490 MP for charge 3 = 1470 MP total
550 MP for magic 1
680 MP for magic 2 = 1230 MP total
600 MP for styx 1
300 MP for styx 2 = 900 MP total
300 MP for styx 3 = 1200 MP total
650 MP for very fast
800 MP for fast
1000 MP for average
1100 MP for slayer
1200 MP for slow
1350 MP for very slow
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 result is then something like this table:
| base value | 3* | 4* | 5* | |
|---|---|---|---|---|
| factor | - | 1,081 | 1,124 | 1,168 |
| very fast | 650 | 702 | 730 | 759 |
| fast | 800 | 864 | 899 | 934 |
| average | 1000 | 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 | 680 | 735 | 764 | 794 |
| Styx 1 | 600 | 648 | 674 | 700 |
| Styx 2 | 300 | 324 | 337 | 350 |
| Styx 3 | 300 | 324 | 337 | 350 |
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New data on very fast 5* and for fast 4* on defense:
Strong expectation from our formula: very fast 5* charge with exactly 759 mana points
Here are the two tests for 758 MP and 759 MP.
Test 1 with a Malosi 4-80 with 16% mana generation bonus from mana troops level 21 (11%) and the bard Zhabog (5%) getting mana from 3 regular turns and 5 turns with -34%.
758 = 300 x 1.16 + 500 x (1.16 - 0.34)
=> as expected Malosi is not charged yet with 758 MP.
Test 2 with a Malosi 4-80 with 7% mana generation bonus from mana troops
759 = 300 x 1.07 + 600 x (1.07 - 0.34)
=> Malosi is charged with 759 MP as predicted.
Now for the 4*.
We strongly expect that the 4* charge exactly with 899 mana points
So let’s see what happens with 898 and 899 mana points.
Test 3 with a Caedmon 4-70 with 9% mana generation bonus from mana troops level 11 (+9%)
898 = 700 x 1.09 + 300 x (1.09 - 0.64)
=> Caedmon is not charged yet with 898 MP.
Test 4 with a Mist 4-70 with 7% mana generation bonus from mana troops level 7 (+7%)
899 = 600 x 1.07 + 100 x (1.07 - 0.64)
=> Mist is charged with 899 MP as predicted.
It looks like there’s a trend. All predictions are spot on. 
Well, initially I wanted to check on every speed (except slayer) for 5*, 4* and 3* to verify the exact amount of mana required to charge the heroes on defense, but this new formula works just perfectly, so that now I’m inclined to only go for the remaining 5* speeds of magic 1 and styx 1 and finish the fast 3*.
Maybe I’ll find a way for the elusive slayer speed to be checked precisely nonetheless. I just got an idea on how to do this…
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I am so glad i started playing another gem game because the new owners and developers have destroyed the game. 2017 this game was going places. 2024 it will be a ghost town. Good luck trying to fix it.
Okay, so with these two tests we have verified that 5* get exactly 75 mana points from each combo1 tile (assuming that each tile from a combo gives the same amount of mana).
We know that fast 5* are charged with 934 MP, while 933 MP are not enough.
That Ranvir with 0% mana generation got mana from 7 regular turns, 3 combo1 tiles and 3 turns with -64% and it wasn’t enough to charge Ranvir.
933 MP – 600 – 300 x (1 – 0.64) = 225 MP
225 / 3 = 75
Ranvir could have received a maximum of 75 MP per tile, otherwise he would have been charged.
Marjana with 12% mana generation got mana from 4 regular turns, 3 combo1 tiles and 3 turns with -34% and she was charged.
[934 MP – 400 x 1.12 – 300 x (1.12 – 0.34)]/1.12 = 225
225 / 3 = 75
Marjana received a minimum of 75 MP per tile, otherwise she wouldn’t be charged yet.
As these tests show the max and min for combo1 tiles to be 75,
=> the combo1 tiles must provide exactly 75 MP per tile.
@G_H_O_S_T Is this also the case for 4* and 3*?
Test 4: fast 4* getting hit by 3 combo1 tiles to charge with exactly 899 mana
Requirements:
• target = fast 4*, wing position
• sturdy, not dangerous healer next to target
• 3 squishy, not dangerous heroes to complete the defense team
• 24% mana generation bonus for the target
Get an ally member to set up a friendly battle with this defense team. No additional, unplanned mana effects, cleansing or protection against mana debuffs must occur during the battle.
Go for 5 regular turns for the target to charge and let exactly 3 combo1 tiles hit the target during these 5 regular turns.
The target should be charged with the resulting 899 mana = 500 x 1.24 + 3 x 75 x 1.24
=> Is the fast 4* target charged with this amount of mana?
Test 5: fast 4* getting hit by 3 combo1 tiles to not charge with exactly 898 mana
Requirements:
• target = fast 4*, wing position
• sturdy, not dangerous healer next to target
• 3 squishy, not dangerous heroes to complete the defense team
• 4% mana generation bonus for the target
Get an ally member to set up a friendly battle with this defense team. No additional, unplanned mana effects, cleansing or protection against mana debuffs must occur during the battle.
Go for 6 regular turns for the target to charge and let exactly 3 combo1 tiles hit the target during these 5 regular turns, then fire Mist for 1 turn of -64%. Ana-Belle could help to quickly end the debuff after 1 turn for more flexibility for when to use Mist’s special.
The target should not be charged with the resulting 898 mana = 600 x 1.04 + 100 x (1.04 – 0.64) + 3 x 75 x 1.04
=> Is the fast 4* target charged with this amount of mana?
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Awesome I want to run it with multiple formulas but I want to find values that hit the make or break spot of around 100 or a number that ends in 99 MP and be able to hit both values even on different levels to verify it’s correctness.
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@Zack Magic, Styx and Tides are not confirmed yet, correct?
Are you going to test only first or also higher charges?
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Yup, it might be tricky for magic charge 2 and Styx charge 2 and 3 because it seems every charges need the same amount of mana (550mp and 600mp respectively) but their is a charged mana multiplier (-22% for magic and +100% for styx) and the issue is that the mana gain that overflows from charge 1 to charge 2 doesn’t get this multiplier applied onto the leftover mp after filling the first charge.
It was kind of analyzed and explained there:
The Styx family(Hypnos, Nyx)’s mana charge is not working as expected
Already discussed this issue with @CrazyChemist3891 on Line and I gave this example:
The problem lies, I believe, in the fact that charges 2 and 3 still need 600 mana points but mana generation is doubled when the first charge is reached. However if 50 (for example) mana points is missing to fill the first charge and you ghost one tile for your hero, it gives 200mp so charge 1 is filled and charge 2 starts with 150mp/600, two other (non ghosted) tiles will give 2*100mp*2 (for the generation bonus) which makes it up to 150+400=550mp, charge 2 not filled.
Even though we could have expected charge 2 to be filled with a ghosted tile (worth 2 tiles) and two other normal tiles although less than a tile worth of mana was missing to fill charge 1.
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Correct, the exact values have not been verified for those.
Well, I guess we can check on tides, too, just to make sure.
We’ll need to find a setup with mana debuffers that is flexible for fast and average speed.
The first charges I will do for sure. The second charges I’ll give a try.
If they would behave normally, I can calculate exact values with the new formula. Then I “just” need to find a suitable setup with mana debuffers that works for reaching exactly the first charge and then also exactly the second charge, as well as one mana point less.
Well, that sounds like a mess then 
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Update on the fast 3* on defense with 863 mana points:
Jack with 3% mana generation bonus from his family bonus gets mana from 8 regular turns and 1 turn with -64%.
863 MP = 800 x 1.03 + 100 x (1.03 - 0.64)
Jack is not charged yet with 863 MP.
=> fast 3* charge with 864 MP on defense, as predicted
I got some data now for offense that shows the magic 2 is charged with 5 tiles with +34% mana generation bonus:
=> so my 680 MP for magic 2 are definitely incorrect
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Firstly, it’s great you could get 10% mana generation bonus on your Magic hero to exactly reach the first charge and avoid the spill-over issue. I also think it’s easier to first try to decipher it on offense as there is one less factor to consider 
(even though I think we can say we are pretty confident that that extra factor on defense just increases the max mana / amount required to charge but does not change the mana generation in absolute value).
Also in your example 5x100x(1.34-0.22) = 560mp > 550mp which, so far, matches my statement that every charges need the same amount of mp, just that there is a mana generation modifier to apply 
But it’s only one situation, I wouldn’t bet it’s 100% the correct formula yet.
However, I called that modifier multiplier in my previous post but if we do 5x100x1.34x(1+ -0.22) = 522mp < 550mp so it seems it’s actually additive and not multiplicative, as you actually did. Just wanted to write it down to eliminate one candidate (even if it wasn’t really the most obvious one).
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@Zack and @Elioty33 I’m going to try to start working multiple formulas on that magic/charge problem. I’m going to see if I can find any mathematical method in which we can obtain exactly the man that we need for charge 1 or magic 1.
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I just saw this. I must have missed it somehow.
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You know that computers don’t “naturally” works with real numbers. Actually, they usually works only with integer numbers, and, with a time and power (and thus heat dissipation) cost with floating numbers. Also turning a floating number into an integer number usually always rounds towards zero, hence the all rounding downs we notice.
I know and understand your feeling. We also thought at first it was just floor(1.04^(rarity-1)) because it seems more natural (and I got the 1.04 value directly from the game so this one is correct for sure) but we noticed a few errors here and there and we then figured it out the way it actually is.
On what combo were the tiles Nemesis received? 
Also, what does this mean exactly?!
Between 1300 and 1350?
I’ll say it again though, every styx charge, for a 5* hero on defense, is 700mp. It’s just that once charge 1 is filled, there is an hidden +100% mana generation bonus. Also, it seems the first tile to hit her was before charge 1 was filled so you fell in the left-over issue I described earlier with one turn giving 100mp even though less than 100mp is missing to fill charge 1 and the left-over mp are charging towards charge 2 but without the hidden mana generation bonus.
Got data on a 5* slayer hero on defense, a Rian with +7% mana generation bonus from mana troops level 9.
According to the formula a 5* slayer will charge with 1284 mana points, 1283 shouldn’t be enough.
With 7% I could go for the 1283 MP by letting Rian get his 10 stacks first so that he has a fixed mana generation bonus of 57%.
The he gets charged from 2 regular turns, 3 turns with -50%, 3 turns with -34% and 3 turns with -64%.
1283 = 200 x 1.57 + 300 x (1.57 - 0.50) + 300 x (1.57 - 0.34) + 300 x (1.57 - 0.64)
=> as predicted, Rian is not charged with 1283 MP
Here’s a test to check for the mana generation modifier for the styx heroes on offense.
First, charge styx 1 with 600 MP, then activate +24% mana generation bonus from a special, go for 3 or 5 more tiles and check the mana bar.
If there is no +100% modifier, then styx 2 and styx 3 need 300 MP each.
With 3 tiles you should end up with the styx3 being filled by 24%, because the 3 tiles give 300 x 1.24 = 372 MP, which fills styx 2 and 72 MP end up on styx 3, which is 24% = 72/300.
With 5 tiles you should end up with styx3 charged, because the 5 tiles give 500 x 1.24 = 620 MP, which fills up styx 2 and the remaining 320 MP also fill styx 3.
If there is a +100% modifier, then styx 2 and styx 3 need 600 MP each.
With 3 tiles you should end up with the styx3 being filled by 12%, because the 3 tiles give 300 x 2.24 = 672 MP, which fills styx 2 and 72 MP end up on styx 3, which is 12% = 72/600.
With 5 tiles you should end up with styx3 at 86.7%, because the 5 tiles give 500 x 2.24 = 1120 MP, which fills up styx 2 and 520 MP end up on styx 3, which is 86.7% = 520/600.
The 12% and 24% filled mana bar can be compared to a 12% and 24% filled mana bar from a different speed, like average speed where you can charge a hero with +20% mana generation bonus with 1 tile or 2 tiles.
1 x 1.2 / 10 = 12%
2 x 1.2 / 10 = 24%
Test with styx hero charging with 6 tiles, then 3 tiles with +24%:
Test with styx hero charging with 6 tiles, then 5 tiles with +24%:
Test with an average hero charging with 1 tile with +20%:
Test with an average hero charging with 2 tiles with +20%:
We can zoom in for the mana bars to compare:
With the 3 tiles the styx 3 bar is charged by 12% and not 24%.
With the 5 tiles the styx 3 bar is clearly not charged yet, but in the 80-90s range.
=> should be good support for a 100% mana generation modifier for styx
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Great work again as usual @Zack. I hope you’re enjoying it seeing how things turn out and click/match predictions 
After running some more tests to confirm this, only tiles hitting the defense are left to fully figure out. Especially the “10” reduction for each combo. Is it an absolute -10mp per combo per tile or -10% per combo on the base 75mp given by a tile.
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