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# Beesafree

## aka Mathew

My favorite wikis
• I live in Flint, Michigan
• I was born on January 3
• My occupation is an Electrician
• I am SMELLING LIKE A ROSE THAT SOMEBODY GAVE ME ON MY BIRTHDAY DEATH BED

## The Recursion Project

### Ryze's Recursion with Serpah's and Rabadon's

v9.23

Mana₀ = Starting Mana before recursive calculations
AP₀ = Starting AP before recursive calculations
Arcane_Masteryₙ = 0.05/100 * APₙ₋₁
Manaₙ = Mana₀ * (Arcane_Masteryₙ + 1)
Seraph's_Embraceₙ = Manaₙ * 0.03
Rabadon's_Deathcapₙ = (Seraph's_Embraceₙ + AP₀) * 0.4
APₙ = AP₀ + Rabadon's_Deathcapₙ + Seraph's_Embraceₙ

The 0.05 is the Arcane Mastery multiplier
The 0.03 is the Seraph's Embrace Multiplier
The 0.4 is the Rabadon's Deathcap Multiplier
The + 1 is to turn the bonus into a multiplier

The final number is rounded to the nearest integer, or 4 decimal places in the case of Arcane Mastery, Thus the answers can usually be determined after 5 or 6 iterations.

Formulas to find the Asymptotes for each of these:
End_AP = (0.000021 * End_AP * Starting_Mana) + (0.042 * Starting_Mana) + (1.4 * Starting_AP)
End_Mana = ((0.000021 * End_Mana) + (0.0007 * Starting_AP) + 1) * Starting_Mana
Arcane_Mastery = (0.0005 * (0.042 * End_Mana + 1.4 * Starting_AP))
Rabadon's_Deathcap = (0.012 * End_Mana) + (0.4 * Starting_AP)
Seraph's_Embrace = End_Mana * 0.03

X = Mana
Y = AP
A = Arcane Mastery
S = Seraph's
Subscript 0 = Starting Value (Only applies to Mana and AP)
Subscript n = End Value (Only applies to Mana and AP)

Yₙ = 0.000021YₙX₀ + 0.042X₀ + 1.4Y₀
Xₙ = (0.000021Xₙ + 0.0007Y₀ + 1) * X₀
A = (0.0005 * (0.042Xₙ + 1.4Y₀))
R = 0.012Xₙ + 0.4Y₀
S = Xₙ * 0.03

Here is a better version with no end values on the right hand side of the equals sign:
End_AP = ((0.042 * Starting_Mana) + (1.4 * Starting_AP)) / (1 - (0.000021 * Starting_Mana))
End_Mana = (0.0007 * Starting_AP * Starting_Mana + Starting_Mana) / (1 - 0.000021 * Starting_Mana)
Arcane_Mastery = (Starting_Mana + (100/3) * Starting_AP)/(47619 - Starting_Mana)
Rabadon's_Deathcap = (19047.6 (0.03 * Starting_Mana + Starting_AP))/(47619 - Starting_Mana)
Seraph's_Embrace = (Starting_Mana * (1428.57 + Starting_AP))/(47619 - Starting_Mana)

X = Mana
Y = AP
A = Arcane Mastery
S = Seraph's
Subscript 0 = Starting Value (Only applies to Mana and AP)
Subscript n = End Value (Only applies to Mana and AP)

Yₙ = (0.042X₀ + 1.4Y₀) / (1 - 0.000021X₀)
Xₙ = (0.0007Y₀X₀ + X₀) / (1 - 0.000021X₀)
A = (X₀ + (100/3)Y₀)/(47619 - X₀)
R = (19047.6 (0.03X₀ + Y₀))/(47619 - X₀)
S = (X₀ (1428.57 + Y₀))/(47619 - X₀)

### Leona: conditioning, Aftershock, Eclipse

V9.23

W = Base Armor
X = Bonus Armor = Conditioning Flat Armor(9) + Armor from items
Y = Eclipse' Flat Armor (20 / 25 / 30 / 35 / 40)
0.2 = Eclipse' Scaling Armor

Leona's Total Armor: Eclipse, with conditioning = (Y + (X * 0.2) + W) * 1.05
Leona's Total Armor: Eclipse then Aftershock, with conditioning =

• (Y + (X * 0.2) + W + (35 + Z)) * 1.05
• Z = (Y + (X * 0.2)) * 0.8)
• Z <= 115

Leona's Total Armor: Aftershock then Eclipse, with conditioning =

• (Y + (X * 0.2) + W + (35 + Z) * 1.05
• Z = (Y * 0.8)
• Z <= 115

Actually pretty simple, she isn't like rammus there is no percentage recursion.
Aftershock can benefit from eclipse, but eclipse can't benefit from aftershock

## Comparisons Between Runes

### Coup de Grace vs Cut Down vs Last Stand

v9.23
Coup De Grace is a catch all, can't use the other 2? use this. Can use the other two but want consistent damage not based on your skill or factors out of your control? use this.
Any champion that Cut Down is active on is the strongest. 10% is the required minimum to activate. The lower the lv18 max health, the better. Yuumi (the champion with the lowest health that isn't modified by a spell/innate) with 1637 base HP can have this active against 95% of the roster as long as she doesn't build health items. Unfortunately she doesn't usually go precision.
Last Stand requires a champion that can survive at low health.They do this by either using protective shields, invincibility, range, or sustain. Darius, Mundo, Kayle, Trynd, Karthus, Jayce.

## Highest single basic attack S1 TFT

Both players are level 9 with 2 force of natures the enemy has: 3x 3-star elise, 2x 2-star elise, and 2x 1-star elise, the elementalist's golem, and Kennen, Anivia, and brand. and 19 spiderlings from the elise.

you have 2 imperial, 8 Assassin's, and a 3-star Draven Equipped with Youmuu's Ghostblade, Deathblade, and Deathblade. Draven gets the imperial buff, and the assassin's buff via Youmuu's.

For the deathblades, draven has participated in killing 3x 3-star elise, 2x 2-star elise, and 2x 1-star elise, the elementalist's golem, and Kennen, Anivia, and brand. He has also killed 17 spiderlings, saving 1.

so each of the 2 deathblades provide 30 (stats from item) + 420 (28 enemies taken down)

Draven also has spinning blades active.

so, when draven attacks the final spiderling:

((Base AD + Deathblade + Deathblade + Youmuu's) * Imperial * Spinning axe * Crit damage (including assassin buff)) * 100 / (100 + armor) ((252 + 450 + 450 + 30) * 2 * 2 * 2.75) * (100 / (100 + 20)) * 100/(100 + 20)

For a grand total hit of 10835 (crit)

If you give up a deathblade, kill one less spiderling, and count runaan's extra hit as part of the single attack: 11502

## Random Formatting/Testing

```{{Do for every champion|Current champion data|p1n=datatype|p1v=title|p2n=output|p2v=custom|p3n=append|p3v=
<br>}}
```

Yields, but is ignoring append, and prepend - and maybe output?

Scorn of the Moon

Value Difference
900
1050
1100
1125.16
735
1002.5
1196.25
843.75
1666.7
1480
1876.7
570
816.67
Item Cost Total Amount Availability
2300 10% - 30% All maps
3100 25% - 73% All maps
3100 20% - 80% All maps
3400 50% Howling Abyss
Active Item CDR
None 0 1 2 3 4 5
None 0% 15% 20% 25% 30% 35% 40%
5% 20% 25% 30% 35% 40% 45%
15% 27.75% 32% 36.25% 40.5% 44.75% 49%
+ 19.25% 32% 36.25% 40.5% 44.75% 49% 53.25%
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