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Need math help with optimal base int formula

Discussion in 'Help & Advice' started by Myungsoo, May 16, 2020.

  1. Myungsoo
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    Myungsoo Slimy

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    2:32 AM
    Robinn
    Crossbowman
    Hi,

    I'm working on writing an app that calculates the amount of resets you need to get your desired MP. And I have all the formulas to reach that.

    There is one thing I want to add to my program, and that is to calculate the optimal base int to reach a desired MP by any specified level. Including the int gear that someone wears.

    Example:
    We take in account that you have a Bowmaster who is level 150.
    He typically gets 18 hp per wash. Including the 1000HP ring, he would be at 4500HP by that level. But the hp the bowmaster wants to reach at level 150 is precisely 13000HP given that there are no unique circumstances.

    So facts we know are:
    • Base + ring HP is exactly 4500 at level 150.
    • The bowmaster has leveled with 80 int gear since level 50. (2/3 wash per level)

    TL;DR: What is the formula to calculate the optimal base int for your desired HP goal? And what is the formula to calculate the desired amount of MP Washes vs HP washes?

    PS: I have every formula required to calculate for hp washing / resets you need etc. Ask them if you need it.
     
  2. Selquin
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    Selquin Headless Horseman

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    May 28, 2018
    7:32 PM
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    Bowmaster, Night Lord, Buccaneer
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    Let x be the amount of HP you have at level 150 with all hp equips but without washing
    Let y be your hp goal
    (y-x) is then the amount of hp that you need to gain via washing
    (y -x) *(12/18) would be the amount of total extra mp required to do these washes (assuming no stale washes)
    Calculating the amount of extra mp you have can be a bit cumbersome, so let us make some simplifications to get a first order estimate(you can go through spreadsheets if you want a more accurate value here). Suppose your base int is M, let us assume that you have 0 int before level 30 and M base int from level 30 onwards. Suppose that your total int from all equips is N, let us assume that prior to level 30 you have 0 int from equips and level 30 onwards you have N int from equips. The amount of extra mp you have prior to mp washing is then (M +N) *120
    Now we need to calculate how many MP washes are necessary to reach the amount of extra MP required. The extra mp needed from mp washing is given by the expression ,
    (y -x) *(12/18) - (M+N)*12
    and thus the amount of MP washes necessary will be ((y -x) *(12/18) - (M+N)*12) * (10)/(M-20)
    Now let us compute the total number of AP resets required to finish all washing process (including resetting ing), this is given by
    total # of AP resets = # to reset base int + # to mp wash + # to hp wash = (M-4) + ((y -x) *(12/18) - (M+N)*12) * (10)/(M-20) + f(x,y)
    Note that the 3rd term associated with the number of AP resets to reset points out of the MP pool as you HP wash is independent of M.
    We can then differentiate this expression with respect to M(your base int) and set it to 0 in order to solve for the global minimum.
    d/dm (total # of AP resets) = 1 + 10 (-12(M-20) - (y-x)*(2/3) + (M+N)*12) / (M-20)^2 = 0
    (M-20)^2 =10 * ((y-x)*(2/3) - 12N - 240 )
    M = sqrt (10 * ((y-x)*(2/3) - 12N - 240 )) + 20
    For the parameters you have given, (y-x) ~8500 and N = 80, the solution is then M ~231, which would mean your optimal base int is somewhere around 230.

    For a slightly more general formulation, suppose you wanted the goal to be met at level L instead of 150, the formula would then be
    M = sqrt (10 * ((y-x)*(2/3) - (L-30)N/10 - 2(L-30) )) + 20


    If you wanted a more accurate estimate, you would have to take into account the fact that characters don't receive all of their base int/equip int instantly at level 30. This could also be slightly off if you are doing a lot of stale washes (the ratio would shift from 12:18 to 12:16).
     
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  3. Alcor
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    Alcor Stone Golem

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    6:32 PM
    Alcor
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    Where can I get access to calculator. for HP washing, MP washing or double washing etc. It for every jobs? You are awesome <3
     
  4. OP
    OP
    Myungsoo
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    Myungsoo Slimy

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    Robinn
    Crossbowman
    I will write an application very soon. I never created a calculator app so I'm not sure how long it's going to take but definitely not later than June. There will be a guide thread soon.

    The app will calculate optimal base int solution along with basic hp washing calculations. If you have recommendations or wish to see other formulas, feel free to share.
     
  5. Chew
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    Chew Headless Horseman

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    If you cant wait for someone to write an application, then have a look at the calculator in my signature.
     
  6. Alcor
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    Alcor Stone Golem

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    6:32 PM
    Alcor
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    Hp & mp wash calculAtor is same thing?
     
  7. Chew
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    Chew Headless Horseman

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    No. Well, it's the same pool of ability points, so the calculator does calculate the MP at a certain level in order to calculate how much MP can be washed into HP.
     
  8. OP
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    Myungsoo
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    Myungsoo Slimy

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    Robinn
    Crossbowman
    My application will consist of multiple formulas. HP wash and MP wash will be both taken account for.
     

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