Editing Poison (section)

== Mathematics ==

=== Single poisons ===
The formula entropy posted for poison damage was...
<pre>P = 1 + (D-30)/30</pre>
... where '''P''' is the damage from poison, taken every 10 seconds, and '''D''' is the remaining duration in seconds. See the ''[[#General information|General information]]'' section above for the initial duration values.

However, this produced results that were slightly inaccurate, so we have to take rounding (in this case, truncating) into account. The derived formula that will produce accurate results is:
<pre>P = 1 + Truncate[(D-30)/30]</pre>

''Truncate'' means that if the result inside the square brackets is a fraction, always round down. By expanding the fraction, the 1's will cancel out, and we can simplify this with a few exceptions. For example, ...
<pre>P = Truncate(D/30)</pre>

... works, except for when D is between 0 and 30. Therefore, we must create a piecewise (multi-part conditional) function to account for all scenarios. The final formula for the amount of poison damage every 10 seconds is:
<pre>P =
     Truncate(D/30), when D = 0 or D >= 30
     1, when 0 < D < 30</pre>

From that formula, the remaining duration can be ''estimated'' by multiplying the interval damage (P) by 30. Even though this estimate will be distorted by the truncation of decimals and when P = 1, this formula is short and allows you to find the remaining duration (D) of the poison simply from watching how much health you are losing (P) every 10 seconds:
<pre>D (estimated) = 30P</pre>

=== Simultaneous poisons ===
Another formula can be used to calculate the total damage yielded from a given amount of ''simultaneous'' poisons. This expression returns the total damage from k poisons:
:[[File:Poison sum 1.png|none|alt=Two plus the summation of n from 1 to k of the quantity 51 plus 108 times the quantity k minus n]]
<!-- :[[Summation.gif]] -->

This can also be written as follows:
<!--
*k*51 + 108* (k-1)*k/2 + 2 = k * (51 + 54*(k-1)) + 2
Got a typo in the file name below, sorry :-/
-->
:[[File:Posion sum 2.png|none|alt=Two plus 51 times k plus 108 times k times one half times the quantity k minus 1 equals two plus k times the quantity 51 plus 54 times the quantity k minus 1]]

The graphs of damage from single and cumulative poisons look like this:
[[File:Poison1.png|none|alt=Total damage increases linearly as long as each poison is suffered separately. Total damage increases exponentially if the poisons overlap.]]

The main observation we can make from this is that it is beneficial to have as few overlapping poisons as possible at any given time.

=== Remaining damage ===
This table helps to estimate the remaining damage you will receive during a poison interval. For example, if a 5 was the last damage value received, look across from the 5 on the table to find the total remaining damage you will receive. Since the formula is based on truncating a fraction with 30 as a denominator, each damage value will repeat for 3 hits except for the initial amount and the final amount of 1. In the table, each damage value is assumed to be the first of the 3 hits for that value. Also, the total remaining damage in the table ''includes'' the current hit. So, subtract 1, 2, or 3 intervals, depending on if it is the first, second, or third hit of that value, respectively.

{| class="wikitable sortable" cellpadding="3" cellspacing="0"
|-
!scope="col" | Last Damage Value Received
!scope="col" | Approximate Total Remaining Damage
|-
|scope="row" style="text-align:right;" | 30
|style="text-align:right;" | 1395
|-
|scope="row" style="text-align:right;" | 29
|style="text-align:right;" | 1305
|-
|scope="row" style="text-align:right;" | 28
|style="text-align:right;" | 1218
|-
|scope="row" style="text-align:right;" | 27
|style="text-align:right;" | 1134
|-
|scope="row" style="text-align:right;" | '''26'''
|style="text-align:right;" | '''1053'''
|-
|scope="row" style="text-align:right;" | 25
|style="text-align:right;" | 975
|-
|scope="row" style="text-align:right;" | 24
|style="text-align:right;" | 900
|-
|scope="row" style="text-align:right;" | 23
|style="text-align:right;" | 828
|-
|scope="row" style="text-align:right;" | 22
|style="text-align:right;" | 759
|-
|scope="row" style="text-align:right;" | 21
|style="text-align:right;" | 693
|-
|scope="row" style="text-align:right;" | 20
|style="text-align:right;" | 630
|-
|scope="row" style="text-align:right;" | 19
|style="text-align:right;" | 570
|-
|scope="row" style="text-align:right;" | 18
|style="text-align:right;" | 513
|-
|scope="row" style="text-align:right;" | 17
|style="text-align:right;" | 459
|-
|scope="row" style="text-align:right;" | 16
|style="text-align:right;" | 408
|-
|scope="row" style="text-align:right;" | 15
|style="text-align:right;" | 362
|-
|scope="row" style="text-align:right;" | 14
|style="text-align:right;" | 317
|-
|scope="row" style="text-align:right;" | 13
|style="text-align:right;" | 275
|-
|scope="row" style="text-align:right;" | 12
|style="text-align:right;" | 236
|-
|scope="row" style="text-align:right;" | 11
|style="text-align:right;" | 200
|-
|scope="row" style="text-align:right;" | 10
|style="text-align:right;" | 167
|-
|scope="row" style="text-align:right;" | 9
|style="text-align:right;" | 137
|-
|scope="row" style="text-align:right;" | 8
|style="text-align:right;" | 110
|-
|scope="row" style="text-align:right;" | 7
|style="text-align:right;" | 86
|-
|scope="row" style="text-align:right;" | 6
|style="text-align:right;" | 65
|-
|scope="row" style="text-align:right;" | 5
|style="text-align:right;" | 47
|-
|scope="row" style="text-align:right;" | 4
|style="text-align:right;" | 32
|-
|scope="row" style="text-align:right;" | 3
|style="text-align:right;" | 20
|-
|scope="row" style="text-align:right;" | 2
|style="text-align:right;" | 11
|-
|scope="row" style="text-align:right;" | 1
|style="text-align:right;" | 5
|-
|scope="row" style="text-align:right;" | 0
|style="text-align:right;" | 0
|}

[[Category:Guides]]