Its basically just everything we already know, combined into ONE general equation. I don't want to scare everyone off with how I got it, so I'll leave the explanation of it in a spoiler which you can choose to see if you want.
Click here to see proof
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The formulas depends on 6 unknowns which I have abbreviated them as:
CL = Current level (the level your character is now)
FL = Final level (a target level of your character. More explanation in examples later)
CHP = Current Base HP (your BASE hp that your character has at the moment)
FHP = Final Base HP (a target hp that you want to have / get)
INT = amount of int you level with (round DOWN if you know your int gear, but round UP if its the answer.
More explanation in examples later)
CMP = Current Base MP (amount of BASE mp your character currently has)
The formulas also only works based on these assumptions:
1. You will HP wash until you reach your minimum MP (ie. wash as MUCH as you can with your mp)
2. You are only doing NORMAL HP washing (ie. no MP washing / double washing / saving ap or w/e)
3. You are level 30+ (this is because the minimum MP formula only applies to level 30+)
4. We assume average numbers. You gain 1 extra MP every level (even with no int) You gain 18 hp per
wash. You gain 22 hp per level.
5. You are either a thief or a bowman.
There are three versions of my formula. You will ALWAYS know what CL, CMP and CHP is. The three different versions of the formula is to work out what FHP, INT and FL are if you only know what 2 of them are.
Be warned. If you do not like maths, you make look at the formula and go "asldkjaewiojfsklfslf! WTF IS THIS?!" Being honest here, it DOES look really confusing that, I'm not sure it will help anyone. I just want to post it anyway because if it helps at least 1 person, then I have helped someone :)
The three formulas:
You know FL and INT. You want to know what your FHP will be when you reach "final level" with this much INT:
FHP = [CMP - CL(15 + [INT/10]) + FL(1 + [INT/10]) - 148]*1.5 + (FL - CL)*22 + CHP
You know FHP and FL. You want to know how much INT is needed to reach that much HP (FHP) at that Level (FL):
INT = {(20/3)*[FHP - CHP - 23.5*FL + 44.5*CL] - 10*CMP + 1480}/(FL - CL)
Finally, you know FHP and INT. You want to know CL (what level you need to reach FHP with that much INT):
FL = {FHP - CHP - 1.5*CMP + CL*[44.5 + 0.15*INT] + 222}/(23.5 + 0.15*INT)
I know the formulas look horrible...thats why I will now do some examples. They will all be based on my bowman when he was level 148.
We will take: CL = 148, CMP = 3305 and CHP = 3985 for the following examples
EXAMPLE 1
Using the first formula:
FHP = [CMP - CL(15 + [INT/10]) + FL(1 + [INT/10]) - 148]*1.5 + (FL - CL)*22 + CHP
Now this formula lets you calculate what FHP is. Therefore you need to know what INT and FL is. INT will obviously be your total int that you level up with, and FL is what level you want to check your hp at. In this example, I want to know what FHP I will have at lv200, so FL = 200 in this case. I will also assume I level up with 86 int all the time, but you need to round down to INT = 80, since 10 int = 1mp, the extra 6 int does nothing.
So now you know:
CL = 148, CMP = 3305, CHP = 3985, FL = 200, INT = 80, its time to work out FHP by subbing in ^^
FHP = [3305 - 148*(15 + [80/10]) + 200*(1 + [80/10]) - 148]*1.5 + (200 - 148)*22 + 3985
FHP = [3305 - 148*(15 + 8) + 200*(1 + 8) - 148]*1.5 + (52)*22 + 3985
FHP = [3305 - 148*(23) + 200*(9) - 148]*1.5 + (1144) + 3985
FHP = [3305 - 3404 + 1800 - 148]*1.5 + 1144 + 3985
FHP = [1553]*1.5 + 5129
FHP = 2329.5 + 5129
FHP = 7458 (rounded the 0.5 down)
That answer means, if I level with 80 int every level, at lv200 I will have 7458 hp.
EXAMPLE 2
Using the second formula:
INT = {(20/3)*[FHP - CHP - 23.5*FL + 44.5*CL] - 10*CMP + 1480}/(FL - CL)
This formula is to calculate how much INT you need to get FHP by FL. We will use the same numbers for all examples, to show they are all EQUAL, and therefore, CORRECT.
Imagine you are lv148, with 3985 hp, 3305 mp. You want 7458 hp by lv200, and so you want to know how much INT is needed to reach this.
In this example: CL = 148, FL = 200, CHP = 3985, FHP = 7458, CMP = 3305
INT = {(20/3)*[7458 - 3985 - 23.5*200 + 44.5*148] - 10*3305 + 1480}/(200 - 148)
INT = {(20/3)*[7458 - 3985 - 4700 + 6586] - 33050 + 1480}/(52)
INT = {(20/3)*[5359] - 33050 + 1480}/52
INT = {35726.666... - 33050 + 1480}/52
INT = 4156.666.../52
INT = 79.93
This answer, is telling you, in order to reach 7458 hp at lv200, you are going to need 80 int to reach it. This answer is ALWAYS rounded up. This is because the answer is telling you how much you "at least" need, but since 10 int = 1 mp, the extra part, above 70 is "useless" till it reaches the next block of 10 int. You need to get to 80 int, till it adds anymore MP. Therefore when using this formula, ALWAYS round the answer up.
EXAMPLE 3
Using the third formula:
FL = {FHP - CHP - 1.5*CMP + CL*[44.5 + 0.15*INT] + 222}/(23.5 + 0.15*INT)
This formula tells you what level you need to achieve the FHP levelling with the INT you have. As the previous examples, we will use the same numbers and show that they match, to show the formula works.Imagine you are lv148, with 3985 hp, 3305 mp. You level with 80 int everytime and you want to know what level you will be in order to reach 7458 hp.
This means CL = 148, CHP = 3985, CMP = 3305, FHP = 7458, INT = 80
FL = {7458 - 3985 - 1.5*3305 + 148*[44.5 + 0.15*80] + 222}/(23.5 + 0.15*80)
FL = {7458 - 3985 - 4957.5 + 148*[44.5 + 12] + 222}/(23.5 + 12)
FL = {7458 - 3985 - 4957.5 + 148*56.5 + 222}/(35.5)
FL = {7458 - 3985 - 4957.5 + 8362 + 222}/35.5
FL = {7099.5}/35.5
FL = 199.98
This answer is telling you what level you will need to be, in order to achieve FHP by levelling up with the INT you put into the formula. Once again, like the 2nd example, you should always round UP using this equation.
I hope you understand how to use the formulas through the 3 examples, and I hope it is useful to you.
Everything in this page is written by me, Waiget, and all calculations / formulas are created by me too. I do not wish to see people "copy&pasting" this anywhere else. If you wish to use this / post this somewhere (possibly sleepywood, idk) Please leave me a comment, I will probably let you use it that way.
Proof:
It basically starts off from you knowing the basic things about HP washing, and instead of plugging numbers in, you replace them with letters and keep them as letters till the end, and you will end up with my formula.
You need to know:
Minimum MP formula (for thief / bowmans) is lv*14 + 148
10 int = 1 MP when level up
12 MP = 1 wash
And finally, the average stats. On average, you get 1 MP extra per level naturally, meaning even with no int, you will get 1 MP extra. You get 18 hp per wash, and 22 hp per level.
Next, we need to give out unknowns some names.
CL = Current level (the level your character is now)
FL = Final level (a target level of your character. More explanation in examples later)
CHP = Current Base HP (your BASE hp that your character has at the moment)
FHP = Final Base HP (a target hp that you want to have / get)
INT = amount of int you level with (round DOWN if you know your int gear, but round UP if its the answer.
More explanation in examples later)
CMP = Current Base MP (amount of BASE mp your character currently has)
With that said, we can now start to form the equation.
First thing we need to do is find out how much extra MP you already have. To do this, we need to work out your Minimum MP. That would be: Minimum MP = (14*CL + 148)
The next step to calculating how much extra MP you have, is simply CMP - Minimum MP.
That would be: Extra MP = CMP - (14*CL + 148)
Now to calculate how many washes you can already do, you simply divide extra MP by 12 (since 12 mp = 1 wash)
That gives: Washes available atm = [CMP - (14*CL + 148)]/12
Next, you find out how much more MP you will get, by leveling up. 10 int = 1 mp, and on average, you gain 1 MP naturally when you level up gives: MP gain per level = (1 + INT/10)
The number of times you will level up is simply: FL - CL
So to get the total MP gain by levelling, that would be: (FL - CL)*(1 + INT/10)
And to see how many more washes you can do, you simply divide that by 12 giving:
Number of washes due to levelling up = [(FL - CL)*(1 + INT/10)]/12
Now to get the TOTAL number of washes you can do, you add the both together.
total washes = washes available atm + Number of washes due to levelling up
total washes = [CMP - (14*CL + 148)]/12 + [(FL - CL)*(1 + INT/10)]/12
This can be shortened to: total washes = [CMP - (14*CL + 148) + (FL - CL)*(1 + INT/10)]/12
Each wash gives 18 hp (on average) so to get how much HP you gained from washing, you do:
total washes*18 = HP gained from washing
HP gained from washing = {[CMP - (14*CL + 148) + (FL - CL)*(1 + INT/10)]/12}*18
The "divide by 12", and "multiply by 18" can be joined together, and become *1.5 (same as 18/12)
HP gained from washing = [CMP - (14*CL + 148) + (FL - CL)*(1 + INT/10)]*1.5
That is only the HP you gained from washing, you now need to calculate how much hp you gained for levelling up. Each level up, is 22 hp, and if you recall, the number of times you levelled up is FL - CL.
Therefore: total hp gained by levelling = (FL - CL)*22
Now if you add HP gained from washing + hp gained from levelling, you will get the Total HP gained.
Total HP gained = [CMP - (14*CL + 148) + (FL - CL)*(1 + INT/10)]*1.5 + (FL - CL)*22
and finally, to calculate the final HP, that would be: Total hp gained + Current HP
FHP = [CMP - (14*CL + 148) + (FL - CL)*(1 + INT/10)]*1.5 + (FL - CL)*22 + CHP
This is the general formula for HP washing that I have come up with. All three different forms are just a re-arrangement of this equation.
To get FHP as subject:
The formula above, is already FHP equals, but the stuff inside the bracket at the start is slightly different than what I've written as the formula. All I did was break the brackets, gathered some like terms.
You start with:
FHP = [CMP - (14*CL + 148) + (FL - CL)*(1 + INT/10)]*1.5 + (FL - CL)*22 + CHP
Break the brackets inside the square brackets:
FHP = [CMP - 14*CL - 148 + FL + FL*(INT/10) - CL - CL*(INT/10)]*1.5 + (FL - CL)*22 + CHP
Gathering like terms:
FHP = [CMP - 15*CL - CL*(INT/10) + FL + FL*(INT/10) - 148]*1.5 + (FL - CL)*22 + CHP
Taking a common factor of -CL and also FL gives:
FHP = [CMP - CL(15 + [INT/10]) + FL(1 + [INT/10]) - 148]*1.5 + (FL - CL)*22 + CHP
I will only show you how I re-arranged it to this form, I won't show the working for re-arranging it to INT equals, or FL equals. It takes much working. You can try it out yourself ^_^