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Math Help - This might be too hard, but...

  1. #1
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    This might be too hard, but...

    Hey guys,

    Random Excel Data.xlsx here I think this is the link to my Excel sheets I made if I did it right.

    If anyone wants to try to help me tackle this I would appreciate it. I need to give you an Excel file I made up in order to show you what I did. But what I've got is 6 different races for a game my friends and I are making up to play around with. We all agreed the Warlock class was the most 100% of where we thought the characters should be. So using the Warlocks damage Armor and Hit Points, I balanced every other class around him. I made up 6 sheets in Excel featuring each class against the other classes. Some come out balanced ok but others have a very distinct advantage.
    Last edited by mr fantastic; May 31st 2010 at 01:29 AM. Reason: Deleted email address.
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  2. #2
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    Quote Originally Posted by JasonGaln View Post
    Hey guys,

    Random Excel Data.xlsx here I think this is the link to my Excel sheets I made if I did it right.

    If anyone wants to try to help me tackle this I would appreciate it. I need to give you an Excel file I made up in order to show you what I did. But what I've got is 6 different races for a game my friends and I are making up to play around with. We all agreed the Warlock class was the most 100% of where we thought the characters should be. So using the Warlocks damage Armor and Hit Points, I balanced every other class around him. I made up 6 sheets in Excel featuring each class against the other classes. Some come out balanced ok but others have a very distinct advantage.
    A few points. Making people download an attachment for your question decreases the chance you will get a helpful response. If you don't have time to type out the relevant questions in an easy-to-access manner, why would we have time to give a good response? Also, attachments can contain viruses, etc.

    Furthermore, .xlsx is not a very universal format. I don't own Microsoft Office and am viewing instead with OpenOffice.org software (free), and it doesn't seem to render 100% right, although most of it seems okay.

    Moreover, I don't even know what I'm looking at. What are all these numbers?

    I suggest you ask more specific questions.
    Last edited by mr fantastic; May 31st 2010 at 01:30 AM.
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  3. #3
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    Quote Originally Posted by undefined View Post
    A few points. Making people download an attachment for your question decreases the chance you will get a helpful response. If you don't have time to type out the relevant questions in an easy-to-access manner, why would we have time to give a good response? Also, attachments can contain viruses, etc.

    Furthermore, .xlsx is not a very universal format. I don't own Microsoft Office and am viewing instead with OpenOffice.org software (free), and it doesn't seem to render 100% right, although most of it seems okay.

    Moreover, I don't even know what I'm looking at. What are all these numbers?

    I suggest you ask more specific questions.
    I'm sorry I tried to get as specific as I could. I spent almost 4 hours doing calculations for that Excel sheet. I'm trying to balance all the numbers and make the damage health and armor relevent to every other race. So that they are all equal, but sitll make sense in the game world. Without making them the exact same all the way around. I guess to answer your question I will amend this to reflect what I have and what I'm looking for, windy post coming...
    Melee damage is half vs armor, range damage is half vs health
    It's Armor,Health,Melee,Range, MeleeVsArmor,RangeVsHP for stats

    Code:
                 Armor      Health         Melee         Range       Melee vs Armor              Range vs Health
    Hunter        125          125          25           25                10                          10
    Warlock       150          0            15           15                15                          15
    Werewolf        0         300           50           0                 20                           0
    Demon           90         90           60           0                 30                           0
    Undead         125        125          2^x           2^x              2^x                          2^x
    Vampire        195        200           25           25                10                           10
    So here is my proposed stats, I figured them out based of how each class would do against a Warlock. Warlock does 15 damage to both HP and Armor at the same time and has a 10 damage fire aura and regenerates 2 armor, each other class would do just either range or melee depending on the situation. Werewolf regenerates 5 Health each of his turns, Vampire regenerates 14 armor/health each of his turns. I modified the regen's ,health and armor versus how long it would take to fight the Warlock. So for example the Hunter does 25 damage to armor so it takes him 6 turns to kill a Warlock, so in turn it should take 6 turns for the warlock to kill him. So I did 10 * 6 to figure in the fire aura, then 30*6 points of total damage to figure in his attacks. Which makes it 240 / 2 for Health and Armor gave 120 each. But it ended up finishing unevenly so I added 5 more to each so that both would end up dieing at the same time. Now I did this all the way through for each of the proposed classes and made it to within 1 turn of each other dieing. Then I went through and tested to see if each of the other classes were balanced vs each other like the warlock was balanced against all of them. And some of them were significantly weaker. The Hunter for instance, if you stack him up against the Vampire or the Werewolf. It takes 21 turns for him to kill a Vampire and only 8 turns for the Vampire to kill him. The Werewolf is 14 turns to kill a Hunter and 8 turns to kill a Werewolf. It just seems that if the Warlock is balanced everything else should be balanced. The Hunter is an easy fix, because story wise you could just say that the Hunter does more damage against the supernatural beings. But I don't know I think it would be better to figure out a way to make them all balance without having multiply powers vs specific classes.
    Last edited by JasonGaln; May 31st 2010 at 01:43 AM. Reason: took a bit of doing but I got it lined up right
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  4. #4
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    I just saw your newest post and haven't read it all yet, but I see you're having trouble lining things up. You can use [ code] [ /code] tags (without spaces) to enter data with spaces so things line up. For example,

    Code:
    This line is enclosed in code tags.
               This line has a lot of leading spaces.
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    I've read your post and unfortunately it's still not all clear. Possibly I could figure it out from context, but it would take a while since I'm not familiar with the rules of the game (even though I've played RPGs many years ago).

    I just need to know the rules you are using to determine how many turns it takes for character A to kill character B, based on the stats. Maybe you should step me through an example with some specific numbers. Also, the 2^x entries stand out as different from the rest, please explain what that means.

    It seems that if each pair of characters kills each other in roughly the same number of turns then we have success.

    For onlookers, if you're wondering what meelee is, I looked it up and will save you the time of doing the same: it means hand-to-hand combat, either with fist, sword, axe, teeth, or whatever.
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  6. #6
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    Quote Originally Posted by undefined View Post
    I've read your post and unfortunately it's still not all clear. Possibly I could figure it out from context, but it would take a while since I'm not familiar with the rules of the game (even though I've played RPGs many years ago).

    I just need to know the rules you are using to determine how many turns it takes for character A to kill character B, based on the stats. Maybe you should step me through an example with some specific numbers. Also, the 2^x entries stand out as different from the rest, please explain what that means.

    It seems that if each pair of characters kills each other in roughly the same number of turns then we have success.

    For onlookers, if you're wondering what meelee is, I looked it up and will save you the time of doing the same: it means hand-to-hand combat, either with fist, sword, axe, teeth, or whatever.
    Basically we want freedom of choice. But in order to do that A has to = B.
    Otherwise one variable would be quickly be found to be "easier" to use, and no one would use anything else.

    Ya I thought of the 2^x after I had went to bed. It's going to be 2 to the power of whatever turn. It's a stacking damage. So if an Undead character hits someone 5 times then it'd be 2^5 which is 32.

    Ok so lets run through the Undead vs Demon, one of the first flaws.

    Code:
    Undead versus Demon
           AC   HP
           125   125
            95    65
            65    5   
            35   -55   
            5    -115    
          -25   -175   
          -55   -235
    So this is the Undead character being hit by the Demon. The Demon has only melee. It's modified damage against armor(AC) (since melee doesn't do full damage on armor) is 30. So each line under armor represents a hit. There are 4 positive numbers after the initial base value. Now that the armor is destroyed the Demon can hurt the Health. His full damage for Health is 60. So each line represents a hit for Health under HP. There are 2 positive numbers. So that brings the Demon up to a count of 6 to be able to eliminate the Undead (I actually think it would be 2 more since he would have to swing again on both sides to bring the Undead to 0 or below, but we'll stick to counting positive numbers)

    Undead vs Demon
    Code:
        AC   HP   
        90   90    
        88   88    
        84   84    
        76   76     
        60   60   
        28   28    
       -36   -36     
      -164   -164
    And this is the damage the Undead does against the Demon. Each successive hit is the previous line - 2^x (x being whatever # after the initial base damage counting down the chart)We didn't lower the Undead's damage against any specific type, we just stuck with the power of whatever hit it was on. So in 5 hits on each side the Undead brings the Demon down. Which is 10 total hits vs 6 total hits. Which means the Demon would win every time it went against the Undead
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  7. #7
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    I saved the file in an Open format. Here's the link to the new file. I use NOD32 Eset Smart Security. I have never had a problem with viruses. I guarantee it is a safe file I just assume that anyone on the internet uses some type of virus protection, otherwise they aren't really using the internet very long before there stuff is messed.

    Download Balance Issue Open Format.ods for free on uploading.com
    Last edited by JasonGaln; May 31st 2010 at 02:18 AM. Reason: misspelled a word
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  8. #8
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    Quote Originally Posted by JasonGaln View Post
    I saved the file in an Open format. Here's the link to the new file. I use NOD32 Eset Smart Security. I have never had a problem with viruses. I guarantee it is a safe file I just assume that anyone on the internet uses some type of virus protection, otherwise they aren't really using the internet very long before there stuff is messed.

    Download Balance Issue Open Format.ods for free on uploading.com
    Hehe, I'm not really worried about viruses, but some people are, so I was just saying that to let you know about what kind of response to expect. Also, thanks for the .ods, but for the record I never use .ods because then potentially Microsoft people will have a hard time viewing (go figure). So I would go with .xls (Microsoft Excel 97/2000/XP) instead of .xlsx or .ods.

    Anyway I think I follow everything now. I'd rather count Demon killing Undead as 8 turns rather than 6, since it doesn't make things harder and is more correct.

    I think it would be best instead of saying Demon vs Undead, to say rather Demon against Undead and Undead against Demon, so that way there's no confusion about which direction you're talking about in any circumstance (you could always look at the numbers, but why bother when there's a clearer way to specify?).

    Also we might as well introduce a shorthand. Say f(X, Y) is the number of turns it takes character X to kill character Y; that is, X against Y. If we use abbreviations

    H = Hunter
    Wa = Warlock
    We = Werewolf
    D = Demon
    U = Undead
    V = Vampire

    then

    f(D, U) = 8
    f(U, D) = 12

    So obviously we want f(X,Y) \approx f(Y,X) for all X, Y.

    As for solving your problem, it might help to use equations. If you're not familiar with the ceiling function, it looks like this: \lceil x \rceil and means the least integer greater than or equal to x. So

    \lceil 4 \rceil = 4

    \lceil 4.02 \rceil = 5

    \lceil 4.9998 \rceil = 5

    \lceil 5 \rceil = 5

    Excel has the ceiling function, Ceiling(). Then, suppose we choose the following labels

    A = Armor
    H = Health
    M = Meelee
    R = Range
    M2 = Meelee vs Armor
    R2 = Range vs HP

    So now, ignoring the special things like regeneration, and assuming we're only dealing with meelee, we can write

    f(X,Y)=\left\lceil\frac{Y_A}{X_{M2}}\right\rceil + \left\lceil\frac{Y_H}{X_M}\right\rceil

    For the 2^x stuff, we can use the fact that 2^1 + 2^2 + \cdots + 2^n = 2^{n+1}-2 (how I got the equation is easy if you know binary, there are various ways to show it's true, anyway it works). So then we can write

    f(U, Y) = \lceil \log_2(Y_A+2) \rceil - 1 + \lceil \log_2(Y_H+2) \rceil - 1 = \lceil \log_2(Y_A+2) \rceil + \lceil \log_2(Y_H+2) \rceil - 2

    Anyway it's not too hard to make modifications to account for regeneration and whatnot.

    I'm still a little unclear as to when you want to consider meelee and when you want to consider range. If we wanted, we could define f_M(X,Y) means meelee and f_R(X,Y) range. It looks like you always use meelee for your calculations.

    Well it's taken me a while to write this up, I'll go take a break and come back later.
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    When to use range.

    I started anything that had only melee attack next to the target. So that it would be easy to compare. So V against H, they both use range until A is gone then switch to melee. H against D however is both of them using melee because D doesn't have a attack for range so wouldn't give an advantage. Which meant H is dealing 10 while D is dealing 30.

    What is log2 in the equation. I've only taken algebra, I have trig next semester though (woe is me), so far and that was about 10 years ago =)~ I think I can find a solution of x still, but that might be the limit of my memory.
    Last edited by JasonGaln; May 31st 2010 at 09:54 AM. Reason: said something backwards from what I meant
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    Can it take all of the x y values into account?

    Just thought of something. Are we comparing only Undead against Demon in this formula? When I figured it my way I compared only Warlock against Y. If we follow this formula are we doing what I already did with the Warlock? Because all of the values should be close to = not just 2 sets, if that makes sense.
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    Quote Originally Posted by JasonGaln View Post
    I started anything that had only melee attack next to the target. So that it would be easy to compare. So V against H, they both use range until A is gone then switch to melee. H against D however is both of them using melee because D doesn't have a attack for range so wouldn't give an advantage. Which meant H is dealing 10 while D is dealing 30.
    Okay, I'm pretty sure that answers my question. So we'll want to be using the max() function in some places.

    Quote Originally Posted by JasonGaln View Post
    What is log2 in the equation. I've only taken algebra, I have trig next semester though (woe is me), so far and that was about 10 years ago =)~ I think I can find a solution of x still, but that might be the limit of my memory.
    It means logarithm base 2. So basically, when we say

    y=\log_2x

    this means that

    2^y = x

    I could explain it more a bit later, but anyway you'll just need to know how to do logarithms in Excel, I can show you.

    Quote Originally Posted by JasonGaln View Post
    Just thought of something. Are we comparing only Undead against Demon in this formula? When I figured it my way I compared only Warlock against Y. If we follow this formula are we doing what I already did with the Warlock? Because all of the values should be close to = not just 2 sets, if that makes sense.
    I'm not sure what you mean by this. We'll consider each pair (X,Y) where X can be anything and Y can be anything (we'll not consider X=Y because that would be trivial; of course a Hunter versus a Hunter is going to be evenly matched, etc.).

    So what I'm envisioning is a new excel sheet where it just has a table for all the stats near the top, and then below it somewhere it will consider each pair {X,Y} by placing f(X,Y) and f(Y,X) near each other for comparison. Then whenever we change the stats, the values for f(X,Y) and f(Y,X) will update automatically. I can work up a prototype in Excel in the next few hours, but I have some things to attend to. If you decide to work on it yourself, let me know so that I don't duplicate your work.

    If we want to we can try to work with things like setting f(X,Y) = f(Y,X) but this might be more complicated than simply playing around with numbers.
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    Okay so I made a prototype, meaning it gives you the idea of the spreadsheet I have in mind but isn't complete. See attached.

    Questions:

    1) I don't understand fire aura. In your spreadsheet I notice you have each Warlock hit count for 20, which is 15 + 5. Where does 10 come in?

    2) About regeneration. Say a Hunter is fighting a Warlock and Warlock has 24 HP left, and Hunter makes a hit. Does Warlock die because it is unable to regenerate, or does Warlock live and end up having 1 HP left?

    By the way, even though I saved it as Excel, I'm not sure OpenOffice works compatibly (sometimes I really dislike OpenOffice, although I mostly like it). Tell me if anything seems off.
    Attached Files Attached Files
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    Sorry I haven't replied sooner, I have been doing homework almost all day. Since about 11am until I took my family to see the new Shrek movie. Just now finished up my programming assignment. Shrek was good by the way.

    Quote Originally Posted by undefined View Post
    Okay so I made a prototype, meaning it gives you the idea of the spreadsheet I have in mind but isn't complete. See attached.

    Questions:

    1) I don't understand fire aura. In your spreadsheet I notice you have each Warlock hit count for 20, which is 15 + 5. Where does 10 come in?
    Picture it as a ball of tar or pitch thrown at something. If there is a smaller target in front, it will first hit that then kind of flow like water around to the other. So I divided the 10 up to armor and health to try to simulate that.

    2) About regeneration. Say a Hunter is fighting a Warlock and Warlock has 24 HP left, and Hunter makes a hit. Does Warlock die because it is unable to regenerate, or does Warlock live and end up having 1 HP left?
    That would depend on who went first. In the way we're doing it played out someone has to go before the other character. So if the Warlock started first then he would indeed live with 1HP left.

    By the way, even though I saved it as Excel, I'm not sure OpenOffice works compatibly (sometimes I really dislike OpenOffice, although I mostly like it). Tell me if anything seems off.
    It all seems to be formatted correctly I think. There is a spreading triangle of figures flowing towards the right. They are currently unassigned.
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  14. #14
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    Quote Originally Posted by JasonGaln View Post
    Sorry I haven't replied sooner, I have been doing homework almost all day. Since about 11am until I took my family to see the new Shrek movie. Just now finished up my programming assignment. Shrek was good by the way.

    I'll check that out.

    Quote Originally Posted by JasonGaln View Post
    It all seems to be formatted correctly I think. There is a spreading triangle of figures flowing towards the right. They are currently unassigned.
    The Hunter figures should be assigned. See attached screenshot (partial, to save space).
    Attached Thumbnails Attached Thumbnails This might be too hard, but...-rpgtable1ss.png  
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    If you can't see what's in the screenshot on your computer, then maybe I should dig out a copy of Excel so that we're using the same program and there are no issues. (Let me know.)
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