Death Ward

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Release date	30 March 2020 (Update)
Unlocked by	Ring of Solomon
Chronote cost	3,000
Monolith energy	150
Level	81
In-game description
5% damage reduction when your life points are below 50%; 10% damage reduction when they are below 25%.
Infobox • Talk page

A player with the Death Ward relic power active surviving the hard typeless entry hit at Vorago. The hit normally deals 12,500 damage to the player (only one player joined the challenge to enter the encounter), but since the player's current and maximum life points are both 12,090, the player takes 12,006 damage, leaving 84 life points.

As the player does not have more life points than the original entry hit damage, the player does not enter the encounter.

Death Ward is a relic power that players can activate at the mysterious monolith. Once activated, players receive reduced damage at certain life points thresholds. When a player is below 50% of their lifepoints, they will receive 5% less damage, and when they are below 25% of their lifepoints, they will receive 10% less damage. It reduces all types of damage, including hard typeless. It costs 3,000 chronotes to activate and uses 150 monolith energy.

Obtaining

• Give a restored aviansie dreamcoat artefact to Armadyl at the top of Armadyl's Tower and you'll receive a Ring of Solomon relic. If Armadyl is not there, check if you have an ongoing replay of Sliske's Endgame and finish it.
• Use the Ring of Solomon on the mysterious monolith to unlock the relic power.

Mechanics

Though the in-game description states that the damage reduction happens when the player's life points are below 50% and 25%, the effect occurs even if the player's current life points are above 50% provided the base damage brings the player's life points under 50% (or 25%) of the player's maximum life points.

Analysis

Let the player's current life points be defined as ${\text{LP}}_{\text{current}}$, the player's maximum life points be ${\text{LP}}_{\text{max}}$, and the base damage taken by the player be $D$. Define the half life point threshold as ${\text{LP}}_{50\%}=\lfloor {\text{LP}}_{\text{max}}/2\rfloor$ and the quarter life point threshold as ${\text{LP}}_{25\%}=\lfloor {\text{LP}}_{\text{max}}/4\rfloor$. The damage taken by the player due to the Death Ward relic power, $D_{\text{DW}}$, is then

${\begin{aligned}D_{\text{DW}}&=H\left({\text{LP}}_{\text{current}}-{\text{LP}}_{50\%}\right){\text{min}}\left({\text{LP}}_{\text{current}}-{\text{LP}}_{50\%},D\right)\\&+H\left({\text{LP}}_{\text{current}}-{\text{LP}}_{25\%}\right)\times \\&\qquad \qquad {\bigg \lceil }{\text{min}}{\bigg [}{\text{min}}\left({\text{LP}}_{\text{current}},{\text{LP}}_{50\%}\right)-{\text{LP}}_{25\%},{\text{min}}{\bigg (}D,{\text{max}}{\big (}0,D-\left({\text{LP}}_{\text{current}}-{\text{LP}}_{50\%}\right){\big )}{\bigg )}{\bigg ]}\cdot 0.95{\bigg \rceil }\\&+{\text{max}}{\bigg (}0,{\bigg \lceil }{\big (}D-{\text{max}}\left(0,{\text{LP}}_{\text{current}}-{\text{LP}}_{25\%}\right){\big )}\cdot 0.90{\bigg \rceil }{\bigg )}\end{aligned}}$

where $H(x-a)$ is the Heaviside step function with the step occurring at $a$, with

$H(x-a)={\begin{cases}0&{\text{for}}~x<a\\1&{\text{for}}~x\geq a\end{cases}}$

Calculator

template = Calculator:Template/Combat/Death_Ward form = deathWardCalcForm result = deathWardCalcResult param = currenthp|Player's current life points|9000|int|1-32767|| param = maxhp|Player's maximum life points|10600|int|1-32767|| param = damagetaken|Base Damage Taken|9000|int|1-32767||

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Update history

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• update 30 March 2020 (Update):
  • Added to game.