Editing Noman's Friend/Template:NomansFriendLoss

<!--Calculator Template for Total Noman's Friend Required to get a Tattoo, or to last a certain period of time

NOTE0: THIS CALCULATOR IS NOT AND HAS NEVER BEEN BASED ON IN GAME FORMULAS; IT ESTIMATES BASED ON OBSERVATIONS AND CANNOT BE TREATED AS RELIABLE FACT
NOTE1: DATA BASED ON OBSERVATIONS IN EARLY 2022; MAY NOT BE EXHAUSTIVE
NOTE2: [REDACTED]
NOTE3: ABRIDGED FORMULA CANT INTERMEDIATE ROUND; MIGHT EVENTUALLY CAUSE ANSWERS TO BE SLIGHTLY WRONG
NOTE3A: NOT, LIKE, SUPER WRONG. OFF BY 1 OR 2 PER MONTH.
NOTE4: DATES UP TO WHITSUN HAVE PROVEN RELIABLE, BUT ANYTHING BEYOND MAY 15 IS NECESSARILY COMPLETELY GUESS WORK

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INPUT BY FORM, OR YEAR:
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"start" refers to how much Noman's Friend one begins with
-->{{#vardefine: start | {{{start| 100}}} }} <!--

leap year check; will be reviewed if necessary in 2099
-->{{#vardefine: leap | {{#ifexpr: {{CURRENTYEAR}} mod4 = 0|1|0}} }} <!--

Assigning start day (month1, day1) and end day (month2, day2) 
-->{{#vardefine:month1|{{{month1|1}}} }} <!--
-->{{#vardefine:day1|{{{day1|5}}} }}<!--
-->{{#vardefine:month2|{{{month2|2}}} }}<!--
-->{{#vardefine:day2|{{{day2|14}}} }}<!--

Defining the next TtH as "day", which is how many days since Dec 31
-->{{#vardefine: day | {{#switch: 1
| {{#expr: {{#var:month1}} = 2 }} = {{#expr: 31 + {{#var:day1}} }}
| {{#expr: {{#var:month1}} = 3 }} = {{#expr: 31 + 28 + {{#var:day1}} + {{#var:leap}} }}
| {{#expr: {{#var:month1}} = 4 }} = {{#expr: 90 + {{#var:day1}} + {{#var:leap}} }}
| {{#expr: {{#var:month1}} = 5 }} = {{#expr: 120 + {{#var:day1}} + {{#var:leap}} }}
| {{#expr: {{#var:month1}} = 6 }} = {{#expr: 151 + {{#var:day1}} + {{#var:leap}} }}
| {{#expr: {{#var:month1}} = 7 }} = {{#expr: 181 + {{#var:day1}} + {{#var:leap}} }}
| {{#expr: {{#var:month1}} = 8 }} = {{#expr: 212 + {{#var:day1}} + {{#var:leap}} }}
| {{#expr: {{#var:month1}} = 9 }} = {{#expr: 243 + {{#var:day1}} + {{#var:leap}} }}
| {{#expr: {{#var:month1}} = 10 }} = {{#expr: 273 + {{#var:day1}} + {{#var:leap}} }}
| {{#expr: {{#var:month1}} = 11 }} = {{#expr: 304 + {{#var:day1}} + {{#var:leap}} }}
| {{#var:day1}}
}}
}}<!--

"extra" adds 1 week if you're unlucky enough to suffer a TtH before noon on the day the Parlour opens, otherwise adds 0
-->{{#vardefine: extra | {{{extra| 0 }}} }}<!--

"goal" is how many days into the year the Parlour opens. 2023's value is 40 (February 9th), but [REDACTED]
-->{{#vardefine: goal | {{#switch: 1
| {{#expr: {{#var:month2}} = 2 }} = {{#expr: 31 + {{#var:day2}} }}
| {{#expr: {{#var:month2}} = 3 }} = {{#expr: 31 + 28 + {{#var:day2}} + {{#var:leap}} }}
| {{#expr: {{#var:month2}} = 4 }} = {{#expr: 90 + {{#var:day2}} + {{#var:leap}} }}
| {{#expr: {{#var:month2}} = 5 }} = {{#expr: 120 + {{#var:day2}} + {{#var:leap}} }}
| {{#expr: {{#var:month2}} = 6 }} = {{#expr: 151 + {{#var:day2}} + {{#var:leap}} }}
| {{#expr: {{#var:month2}} = 7 }} = {{#expr: 181 + {{#var:day2}} + {{#var:leap}} }}
| {{#expr: {{#var:month2}} = 8 }} = {{#expr: 212 + {{#var:day2}} + {{#var:leap}} }}
| {{#expr: {{#var:month2}} = 9 }} = {{#expr: 243 + {{#var:day2}} + {{#var:leap}} }}
| {{#expr: {{#var:month2}} = 10 }} = {{#expr: 273 + {{#var:day2}} + {{#var:leap}} }}
| {{#expr: {{#var:month2}} = 11 }} = {{#expr:  304 + {{#var:day2}} + {{#var:leap}} }}
| {{#var:day2}} <!--
-->}} <!--
-->}} <!--

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INTERMEDIATE: VARIABLES USED TO REDUCE CLUTTER DOWNSTREAM
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"weeks" refers to how many times TtH will take Noman's Friend. This could just be written out three times in the equation proper, but why not save space? Don't change this unless it's misbehaving.
-->{{#vardefine: weeks | {{#expr:trunc (1 + {{#var:extra}} + ( {{#var:goal}} - {{#var:day}} - 1 ) / 7 )}} }} <!--

##### 
EXPERIMENTAL NON LINEAR APPROXIMATION
two variables approximate one possibility for the cumulative "bonus melt factor" that becomes noticeable around mid-April. Their error is the LESSER of 1 point, or 1.15%, from one possible formula. Necessarily an estimate based on limited observations in 2024 and the declaration that it will be "over 50,000" "around day 300 or so". Less than 50 total for any reasonable Whitsun run.
"bonusMeltEnd" approximates cumulative melts attributable to the new, non-linear growth up to and including the last expected melt.
"bonusMeltStart" approximates cumulative melts attributable to the new, non-linear growth up to and including the melt PRIOR to the first expected melt.
Their difference approximates the non-linear component to the cumulative melt beginning with the first expected melt and ending on the last expected melt (including both ends)
#####
-->{{#vardefine: bonusMeltEnd | {{#ifexpr: {{#var:goal}} < 80 | 0 | {{#ifexpr: {{#var:weeks}} > 0 | {{#expr:  1.75 * ((( {{#var:day}} - 5 + 7 * ( {{#var:weeks}} + {{#var:extra}} ) )/100)^10.85) | 0}} }} }} }}<!--
-->{{#vardefine: bonusMeltStart | {{#ifexpr: {{#var:day}} < 80 | 0 | {{#ifexpr: {{#var:weeks}} > 0 |  {{#expr: 1.75 * ((( {{#var:day}} - 12)/100)^10.85) | 0}} }} }} }}
<!--

"lower" is the lower bound of NF required; every week you get the lowest loss possible
-->{{#vardefine: lower | {{#expr:trunc ({{#var:bonusMeltEnd}} - {{#var:bonusMeltStart}} + {{#var: weeks}} * ( 1.75 * ( {{#var:day}} + 3.5 * ( {{#var:weeks}} - 1) ) - 5.75) ) }} }}<!--

"upper" is the upper bound; every week you get the highest loss possible
-->{{#vardefine: upper | {{#expr: 1 + trunc({{#var:bonusMeltEnd}} - {{#var:bonusMeltStart}} + {{#var: weeks}} * ( 1.75 * ( {{#var:day}} + 3.5 * ( {{#var:weeks}} - 1) ) + 28.25) ) }} }}<!--


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OUTPUT:
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-->If your next Time the Healer with a Noman falls on '''<!--

set the start month

--> {{#switch: 1
| {{#expr: {{#var:month1}} = 2 }} = February
| {{#expr: {{#var:month1}} = 3 }} = March 
| {{#expr: {{#var:month1}} = 4 }} = April 
| {{#expr: {{#var:month1}} = 5 }} = May 
| {{#expr: {{#var:month1}} = 6 }} = June 
| {{#expr: {{#var:month1}} = 7 }} = July 
| {{#expr: {{#var:month1}} = 8 }} = August
| {{#expr: {{#var:month1}} = 9 }} = September
| {{#expr: {{#var:month1}} = 10 }} = October
| {{#expr: {{#var:month1}} = 11 }} = November
| January
}} {{#var:day1}}''', to survive until at least '''<!--

set the end month

--->{{#switch: 1
| {{#expr: {{#var:month2}} = 2 }} = February
| {{#expr: {{#var:month2}} = 3 }} = March 
| {{#expr: {{#var:month2}} = 4 }} = April 
| {{#expr: {{#var:month2}} = 5 }} = May 
| {{#expr: {{#var:month2}} = 6 }} = June 
| {{#expr: {{#var:month2}} = 7 }} = July 
| {{#expr: {{#var:month2}} = 8 }} = August
| {{#expr: {{#var:month2}} = 9 }} = September
| {{#expr: {{#var:month2}} = 10 }} = October
| {{#expr: {{#var:month2}} = 11 }} = November
| January
}} {{#var:day2}}''' it will have '''{{#var:weeks}} Melts''' costing between ''' <!-- 
--> {{#var: lower}} <!--
-->''' - ''' <!-- 
--> {{#var: upper}} <!--
-->''' total {{IL|Noman's Friend}} <br />
<br /> <!--


This next paragraph converts Noman's Friend into Taste of Lacre and then into Pails of So-Called Snow. 


--> Once you have your Noman, you'll need an additional total of '''<!--
-->{{#ifexpr: {{#var:lower}} < {{#var:start}} | 0 | {{#expr: ceil ( ( 1 + {{#var: lower}}-{{#var:start}} ) / 3 ) }} }}&#160;-&#160;<!--
-->{{#ifexpr: {{#var:upper}} < {{#var:start}} | 0 | {{#expr: ceil ( ( 1 + {{#var: upper}}-{{#var:start}} ) / 3 ) }} }}''' <!--
-->x {{IL|Putting the Pieces Together: the Taste of Lacre|Appearance = Taste of Lacre}} to increase its Noman's Friend, which could be achieved with '''<!--
-->{{#ifexpr: {{#var:lower}} < {{#var:start}} | 0 | {{#expr: ceil ( ( 1 + {{#var: lower}}-{{#var:start}} ) / 9 ) }} }}&#160;-&#160;<!--
-->{{#ifexpr: {{#var:upper}} < {{#var:start}} | 0 | {{#expr: ceil ( ( 1 + {{#var: upper}}-{{#var:start}} ) / 9 ) }} }}''' x {{IL|Unusual Pail of So-Called Snow}}.<br />
<br /><!--


This next paragraph incorporates Tears of the Bazaar. It assumes 30% of Taste of Lacre comes from your Pails, and 70% from your Tears.  The base case pretends that each Tear gets 6 Taste of Lacre before breaking (5 × +1, and 1 × +2 when it breaks), which is the expected result and should be the average over longer experiments. The user must always assume their own level of risk, so the "zero risk" option follows which assigns 2 Lacre to each Tear, which is the worst outcome and should never consistently happen when more than 10 Tears are used, but does provide an upper-bound to err towards for additional caution.


-->
If you'd prefer to minimise Pails, you can instead use '''<!--
-->{{#ifexpr: {{#var:lower}} < {{#var:start}} | 0 | {{#expr: ceil ( ( 1 + {{#var: lower}}-{{#var:start}} ) / 30 ) }} }}&#160;-&#160;<!--
-->{{#ifexpr: {{#var:upper}} < {{#var:start}} | 0 | {{#expr: ceil ( ( 1 + {{#var: upper}}-{{#var:start}} ) / 30 ) }} }}''' x {{IL|Unusual Pail of So-Called Snow}} and  '''<!--
-->{{#ifexpr: {{#var:lower}} < {{#var:start}} | 0 | {{#expr: ceil ( ( 1 + {{#var: lower}}-{{#var:start}} )  * (7/180) ) }} }}&#160;-&#160;<!--
-->{{#ifexpr: {{#var:upper}} < {{#var:start}} | 0 | {{#expr: ceil ( ( 1 + {{#var: upper}}-{{#var:start}} ) * (7/180) ) }} }}''' x {{IL|Tears of the Bazaar}}, or '''<!--
-->{{#ifexpr: {{#var:upper}} < {{#var:start}} | 0 | {{#expr: ceil ( ( 1 + {{#var: upper}}-{{#var:start}} ) * (7/60) ) }} }}''' x Tears if the bottle breaks every time.<br />
<br /><!--


This next paragraph gives a count of how many Tears, Night-Whispers, and Storm-Threnodies should be stockpiled.  It only appears if the end-goal is past February 14th.  It does not account for free pails, which can either be internalised as part of the original Noman cost, or by adding extra Noman's Friend to the "start" value.


-->{{#ifexpr: {{#var:upper}} - {{#var:start}} > 0
|Before December (or as soon as possible) you may want to have the following:
* '''{{#ifexpr: {{#var:lower}} < {{#var:start}} | 0 | {{#expr: ceil ( ( 1 + {{#var: lower}}-{{#var:start}} )  * (7/180) ) }} }}&#160;-&#160;<!--
-->{{#ifexpr: {{#var:upper}} < {{#var:start}} | 0 | {{#expr: ceil ( ( 1 + {{#var: upper}}-{{#var:start}} ) * (7/180) ) }} }}''' x {{IL|Tears of the Bazaar}}
*'''{{#ifexpr: {{#var:lower}} < {{#var:start}} | 0 | {{#expr: ceil ( ( 1 + {{#var: lower}}-{{#var:start}} ) / 30 ) }} }}&#160;-&#160;<!--
-->{{#ifexpr: {{#var:upper}} < {{#var:start}} | 0 | {{#expr: ceil ( ( 1 + {{#var: upper}}-{{#var:start}} ) / 30 ) }} }}''' x {{IL|Night-Whisper}}
*'''{{#ifexpr: {{#var:lower}} < {{#var:start}} | 0 | {{#expr:7 *  ceil ( ( 1 + {{#var: lower}}-{{#var:start}} ) / (30) ) }} }}&#160;-&#160;<!--
-->{{#ifexpr: {{#var:upper}} < {{#var:start}} | 0 | {{#expr:7 * ceil ( ( 1 + {{#var: upper}}-{{#var:start}} ) / (30) ) }} }}''' x {{IL|Storm-Threnody}}
}}
<noinclude>[[Category:Calculator templates]]</noinclude>