# Death Ward

 This article has a calculator here.Calculators determine experience and costs based on real-time prices from the Grand Exchange Market Watch.
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.

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

{\displaystyle {\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 ${\displaystyle H(x-a)}$ is the Heaviside step function[1] with the step occurring at ${\displaystyle a}$, with

${\displaystyle H(x-a)={\begin{cases}0&{\text{for}}~x

## Calculator

template  = Calculator:Template/Combat/Death_Ward
form      = deathWardCalcForm
result    = deathWardCalcResult

param     = hpgroup|Player life point values||group|currenthp,maxhp
param     = currenthp|Player's current life points|9000|int|1-32767
param     = maxhp|Player's maximum life points|10100|int|1-32767

param     = damagegroup|Base damage value(s)||group|damagetoggle,damagetaken,damagetakenLow,damagetakenHigh
param     = damagetoggle|Select output||buttonselect|Single,Range|Single=damagetaken;Range=damagetakenLow,damagetakenHigh
param     = damagetaken|Base damage taken|9000|int|1-32767
param     = damagetakenLow|Base damage taken (lower bound)|8000|int|1-32767
param     = damagetakenHigh|Base damage taken (upper bound)|10000|int|1-32767

param     = plotgroup|Plot Options||group|outputType
param     = outputType|Select output|Percent damage reduction|buttonselect|Percent damage reduction,Life points remaining

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## Update history

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