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(Miraculous) Marvelous Fairy Raili


AbstractEdit

This page helps to address issues on how to choose the best cards for your new 7+5 card raid frontline, factoring the skills from raid cards which deal additional damage to bosses.


BodyEdit

  • Changes to the Raid system:


The raid system has moved from the standard 5 card frontline to a 7 card frontline and 5 card supportline.

The 5 card support line:

The supportline works to boost the over all damage of your front line based on the 5 card's total defence value. I don't know the exact calculations for this but choosing this is too straight forward for me to bother anyway. Just filter your deck for highest def power and choose the top 5 def cards. By def cards I mean cards with higher def than atk. Don't blindly choose as u don't want to end up choosing a 14K+ atk card with 12K+ def for your support just cause it is top 5 def.

The 7 card front line:

This is the line up that does the actual damage to the boss. The power consumption for the 7 cards has switched to a new formula given by:

(PWR sum of your 7 cards +5)/2.7 Rounded off to the nearest whole number. 

Because there is a rounding off to the nearest whole number. Sometimes replacing a pwr 14 with a pwr 15 with slightly higher attack may end up loosing effeciency as ur pwr consumption may go up by 1. The reverse is also true. Hence it is important to take note of that. 

If u calc the efficiency of a single card based on the new formula, it becomes:

Attack PWR of card/(PWR+5/7) 

Because of the new formula, high power cards with atk ratios just slightly lower than low power ones may end up becoming much better. for example:

Xerxes (8890 ATK, PWR 11) with an old efficiency of 808 drops to 759 for raids

Eostre (12775 ATK, PWR 16) with an old efficiency of 798 drops to 764 for raids

And becomes better than xerxes in terms of efficiency.


  • Raid Boss Battle System:


With your 7 cards you will attack the boss together. And the boss will strike back, killing at random any of the 7 of your cards. You will then attack the boss with your 6 remaining cards. The boss strikes back again untill u are left with no cards or the boss dies. You will deal less damage with each subsequent attack as you are left with fewer and fewer cards.


  • Managing PWR consumption:


Using reference to the most recent Starless & Bible Black Bosses, Stealing the boss list and giving credits to the publisher... Cheers:

Type Name Level Hit Points Time Allotted Damage
Main Lusa, Hades' Flutist 1 100 2 hours
Main Lusa, Hades' Flutist 2 600 2 hours
Main Lusa, Hades' Flutist 3 900 2 hours
Main Lusa, Hades' Flutist 4 1000 2 hours
Main Lusa, Hades' Flutist 5 1500 2 hours
Main Lusa, Hades' Flutist 6 3000 2 hours
Main Lusa, Hades' Flutist 7 6000 2 hours
Main Lusa, Hades' Flutist 8 10,000 2 hours
Main Lusa, Hades' Flutist 9 15,000 2 hours
Main Lusa, Hades' Flutist 10 20,000 2 hours
Main Lusa, Hades' Flutist 11 30,000 2 hours
Main Lusa, Hades' Flutist 12 40,000 2 hours
Main Lusa, Hades' Flutist 13 50,000 2 hours
Main Lusa, Hades' Flutist 14 56,000 2 hours
Main Lusa, Hades' Flutist 15 62,000 2 hours
Main (Interference) Lusa, Hades' Flutist 1 68,000 2 hours
Main (Interference) Lusa, Hades' Flutist 2 74,000 2 hours
Main (Interference) Lusa, Hades' Flutist 3 80,000 2 hours
Main (Interference) Lusa, Hades' Flutist 4 86,000 2 hours
Main (Interference) Lusa, Hades' Flutist 5 92,000 2 hours
Main (Interference) Lusa, Hades' Flutist 6 98,000 2 hours
Main (Interference) Lusa, Hades' Flutist 7 110,000 2 hours
Main (Interference) Lusa, Hades' Flutist 8 130,000 2 hours
Main (Interference) Lusa, Hades' Flutist 9 160,000 2 hours
Main (Interference) Lusa, Hades' Flutist 10 180,000 2 hours
Main (Interference) Lusa, Hades' Flutist 11 200,000 2 hours
Main (Interference) Lusa, Hades' Flutist 12 250,000 2 hours
Main (Interference) Lusa, Hades' Flutist 13 300,000 2 hours
Main (Interference) Lusa, Hades' Flutist 14 400,000 2 hours
Main (Interference) Lusa, Hades' Flutist 15 1,000,000 2 hours
End Greedy Goblin King 1 1,400,000 2 hours
End (Oneself) Greedy Goblin King 1 1,700,000 2 hours
Special (Avatar) Shadow Minister Ganymeda 1 35,000 20 minutes
Special (Birth) Irene, Life Giant Subduer 1 160,000 20 minutes
Special (Zone) Lorentz, Ruler of Space-Time 1 600,000 20 minutes
Special (Strangling) Deathbringer Welina 1 60,000 20 minutes
Hidden The Shadow King 1 10,000,000 2 hours
Hidden (Nought) The Shadow King 1 12,000,000 2 hours
Secret The Shadow King's Core 1 18,000,000 2 hours
Secret (Last) The Shadow King's Core 1 21,000,000 2 hours 2x

You will realize from the table above that there are a few free frag bosses like the low lvl Lusas, Gany & Welina.

A strong line up with PWR consumption above 40 can easily kill irene in 1 attack. Thats 160K worth of damage. You will not want to waste 40 PWR to kill a 100 HP flutist or 35K Gany. Hence it is good to customize a few line ups to conserve power. I personally saved a low PWR line up specially to deal just enough damage for Welina & Gany, and one more lame 1 single power 2 common card line up just to "poke" my guildie's low HP boss to share repel counts XD.
(Flare) Flitting Firelight Fernanda

The important thing to note here is when designing a low PWR line up, one does not simply reduce the number of cards used. Line ups with less than 7 cards are very inefficient due to the boss battle system as mentioned above. With 7 cards you will hit the boss for 7x,6x,5x,4x,3x,2x,1x damage for a total of 28x. A 6 card line up reduces that to 23x and a 5 card line up to 17x and so on, cutting the efficiency significantly. The key is to swap your high power cards out for low power rares/commons, and maintain the 7 card line. A few cards I can recommend are those PWR 5 rares with 700 ATK efficiency with 2 of them from each element, and a total of 6 for you to work with. If you are too lazy for that, just use pwr 2 commons like lost angel like what I do to act as fillers for your 6 or 5 main ATK cards.


  • Optimizing PWR Consumption:


As mentioned above the formula for PWR consumption of your 7 card FL is:

(PWR sum of your 7 cards +5)/2.7 Rounded DOWN to the nearest whole number. Yes rounded down as I have comfirmed. Means 39.99 will still be rounded to 39, and 40.01 will end up with 40 pwr. 

Because of the rounding off feature, there are certain ranges of total PWR of your 7 cards where the PWR consumption remains the same. You will want to look for the optinum number which is just before the next increase in PWR consumption. Below is a table to of values, from 70 to 119. You cant go above 119 as 119 is 17*7 and there are no PWR 18 cards.... yet.......

7 card total PWR Raid PWR consumption
70 27
71 28
72 28
73 28
74 29
75 29
76 30
77 30
78 30
79 31
80 31
81 31
82 32
83 32
84 32
85 33
86 33
87 34
88 34
89 34
90 35
91 35
92 35
93 36
94 36
95 37
96 37
97 37
98 38
99 38
100 38
101 39
102 39
103 40
104 40
105 40
106 41
107 41
108 41
109 42
110 42
111 42
112 43
113 43
114 44
115 44
116 44
117 45
118 45
119 45


My personal recommendation is to aim for total PWR of your 7 cards to be 105 or 108, where your PWR used is just nice 40 & 41 respectively before jumping by 1. The individual break down of individual card PWR I would recommend for most casual players is:

40 PWR Break down 41 PWR Break Down
Raid 14 Raid 14
Raid 14 Raid 14
Raid/High 14 Raid/High 15
High 15 High 16
Raid/High 15 Rehnskold 16
Lisa 16 Lisa 16
Dragon Child 17 Dragon Child 17


Why such a breakdown?

Most PWR 16s and 17s have poorer ratios than power 14s and 15s, even after considering raid efficiency, with the exception of special evolved cards which most players cannot afford. The PWR 16s and 17s used here are the 5/11 Stage Evolutions that is being given out for FREE^^

The terminology i believe should be pretty self explainatory. Raid 14,15 refers to a raid card with 14,15 PWR and High 14,15 refers to a PWR 14,15 card with high attack ratio. Raid/High just means either a raid or HIGH card whether u feel 2,3 or 4 raids does better for you. 


  • Raid Skill Cards


Raid Skill Cards are cards with skills that deal additional damage to raid bosses, or block raid boss attacks. Their skills are set to activate during 1 of the 7 hits you deal the boss, or 1 of the 7 hits the boss hits your cards.

Block attack cards:
(Fortunate) Brightly Kindled Future

Set to trigger during 1 of the attacks your frontline gets attacked by the boss, preventing the boss from killing 1 of your cards. hence allowing your entire frontline to attack 1 more time, for example, if the skill triggers during the 3rd attack when u have 5 cards left, your attack sequence from 7x,6x,5x,4x,3x,2x,1x becomes 7x,6x,5x,5x,4x,3x,2x,1x, increasing your effiiency from 28x to anywhere from 29x to 35x, depending on the skill level of the card. The special evolution card that comes with the current raid event does just that, greatly boosting your damage output ontop of his already extremely high atk ratio. Block atk cards are however seldom use as the special evolved UR is just too darn expensive for most players and the commons have too low efficiency to justify their use, so I shall not go into too much depth here.

Boss Damage cards:
(Revival) Kingsaver Tracy

Boss damage cards are set to have their skill activate anywhere between the 7 attack phases. A skill 10 for example multiplies the attack by 1.7x for that phase. increasing your attack efficiency from 28x to anywhere between 28.7x if triggered on the last attack to 32.9x if triggered on the 1st attack. Obviously you will pray that your raid skill triggers on the 1st few attacks. The average gain in efficiency here is 2.8, from 28 to 30.8, which is just the average of the 2 values above.

There is also however a chance that the raid boss gets killed by the boss before the skill has a chance to trigger.


  • Maximizing Overall Damage/PWR consumption.


Damage output/PWR consumption is not just a simple equation of your: 

Total ATK/[(Total PWR of your 7 cards +5)/2.7] rounded off

This equation holds true only if you do not use any raid skill cards. When raid skill cards have to be considered, I would like to propose a new formula as below:

Total ATK*EFF/[(Total PWR of your 7 cards +5)/2.7] rounded off

Where EFF is a coefficient for your raid efficiency depending on the type of raid cards you use. I shall now attempt to quantify this value.

I first start to introduce a base value of 28 for EFF when no raid cards are used. How I derive at 28 is a simple analogy of the boss battle system, where by your first attack phase attacks with all 7 cards and hence 7x efficiency. When the boss strikes back and kills one of your cards, you attack back with the remaining 6 at 6x efficiency. This goes down to 5,4,3,2,1 for a total of 28 efficiency, and hence the value. With this I expand my equation to:

Damage/PWR consumption = Total ATK*(28+REFF)/[(Total PWR of your 7 cards +5)/2.7] rounded off

Where REFF is the Gain in Efficiency when u use a certain number of raid cards at certain skill levels. The Challenge now is to quantify REFF. 

Skill Trigger Effect:

Cheers to my friend in the game programming who proposed a logical algorithm for boss battling and skill triggering effect. It made more sense than my otherwise unexplainable observation of the raid cannibalization effect.

There are 7 battle slots in your raid line up. The LOC system randomly arranges the numbers 1 to 7 in 2 seperate strings. 1 for sequence of boss attack, and 1 for sequence of skill activation. So for example for a simple analogy the system for one of your attacks generates 2 strings: 7,6,5,4,3,2,1 for boss attack sequence and 1,2,3,4,5,6,7 for skill activation sequence. This means that after the 1st attack phase, the boss will attack the card in slot 7 first, then 6,5,4 and so on. And the card in slot 1 has a chance of activating its skill 1st. As skill activation comes 1st before boss attacks, this means that at all times only 4/7 of the cards will have a chance for their skill to activate, and the remaining 3/7 of them will get killed before their turn in the sequence. 

Assuming 100% chance of skill activation if the slot is triggered, this means that each raid card only has a 4/7 chance of their skill to trigger every battle. At which sequence it triggers also affects its overall damage output. A trigger in the 1st sequence gives the highest damage output. and the least for the last sequence. A simple averaging can be done to calculate the over all increase across many battles. Using a spreadsheet, I computed the increase in EFF a skill 10 at 1.7x multiplier would give on average:

ATK S EFF EFF Gain S Prob A Prob T Prob AVG Gain
1 7 4.9 14.29% 100.00% 14.29% 0.70
2 6 4.2 14.29% 85.71% 12.24% 0.51
3 5 3.5 14.29% 71.43% 10.20% 0.36
4 4 2.8 14.29% 57.14% 8.16% 0.23
5 3 2.1 14.29% 42.86% 6.12% 0.13
6 2 1.4 14.29% 28.57% 4.08% 0.06
7 1 0.7 14.29% 14.29% 2.04% 0.01
REFF 2


Now to explain the parameters:

ATK S: The sequence of the attack, with sequence 1 having all 7 cards attacking for 7 EFF and so on.

EFF: The efficiency of each attack at each sequence, giving a total of 28 for base efficiency.

EFF Gain. The gain in EFF if the Raid skill were to trigger during that phase, for a skill 10 at 1.7x it would give these values accordingly.

S Prob: The probability the skill sequence would assign the raid card to trigger at each attack phase, just a simple 1 in 7 chance.

A Prob: The chance the card would still be alive to trigger its skill at each attack sequence. a simple 6 in 7 chance to survive the first attack, 5 in 6 to survive the 2nd. The table compounds these chances to give the cumulative probability.

T Prob: The chance for the skill to trigger at each ATK sequence. A simple combined probability of S Prob and A Prob.

AVG Gain: A simple product of EFF Gain and T Prob, to give the average gain in EFF at each phase. The sum of these 7 values for each atk sequence will result in a total REFF of 2 to be added on top of the base value of 28 for when a skill 10 raid is used. 

So for the extreme case of using all 7 Skill 10 raid cards, the increase in EFF would be 14 to 42.


  • NOT so fast.......


Thanks to the comments I received below, and having heard an actual example of a person actually using all 7 raid cards, I can safely conclude that the chance for a raid skill to trigger is not 100%, for that be the case she would get 4 skill triggers all the time for each battle, which is not the case as described. The chance of triggering could be:

A simple percentage, if 50% chance would reduce REFF from 2 to 1 for each skill 10 raid card you use

A complex percentage, reducing as more raid cards are used, which I propose to support my observation that for some reason I almost never see my 3rd raid card skill activate at all, where I still constantly see 1 or 2 activations when I use only 2 raids.

As there is no way to compute the percentage for skill activation, I can only stop here and conclude my article. I bring your attention back to the equation:

Damage/PWR consumption = Total ATK*(28+REFF)/[(Total PWR of your 7 cards +5)/2.7] rounded off

Note that the objective is to maximize this equation to achieve highest raid efficiency. I choose to rearrange this equation as follows:

Damage/PWR consumption = Total ATK/[(Total PWR of your 7 cards +5)/2.7] rounded off *(28+REFF)

Note that by introducing a raid card, you are increasing REFF, but reducing Total ATK/[(Total PWR of your 7 cards +5)/2.7]. This is due to the fact that most raid cards are 700 ATK/PWR ratios and below, where as high end cards have Ratios well above 800. The key is to achieve a balance between this 2 values by using the right proportion.

I wish I was able to quantify that but due to the fact the base trigger chance is not 100% and unknown, I am unable to do so. Most people feel that 4/5 High end and 3/2 Skill 10-12 Raids is the best compromise to maximize the equation above.

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