Re: Crit chance word problem

Hey Xodarap777.

Unfortunately I can't understand what you are saying but maybe you could draw a simple graph showing the behaviour for a few points of data (with some notes) which will make more sense to myself and others.

Re: Crit chance word problem

You need to define: "Agility," "investment" in Agility, "Dex," "Damage," "Critical Damage," "AGI," and "critical chance," as we have no idea what any of these terms mean. Then perhaps we will be able to help.

Re: Crit chance word problem

Thank you for the constructive criticism. I figured the actual terms didn't matter as they're just variables. I'll try to make it clearer. The problem is that I couldn't envision the graph of the function or I'd have been able to figure out the function, as I'm not bad at math (I'm just very sleep-deprived lately!). However, it is more obvious to me now that I'm definitely looking for a function, so that's kind-of on the line between algebra and calculus; hopefully I'm in the right subforum.

I'll try this step by step.

Let's say that I can normally jump exactly 100cm into the air.

- I have arbitrary attribute "Dexterity." For each unit of Dexterity (DEX) I possess, I can jump 2% (1.02x) higher on "critical" jumps.
- Currently, my DEX is 100, so when I "critically jump," I jump 200cm high. (At this point, I can only jump either 100cm high or 200cm high.)
- I also have arbitrary attribute "Agility" (AGI), which dictates how
*often* I can jump critically. - My current AGI is 100, and 100 is the baseline, so I have zero chances of jumping critically. At AGI = 100 and DEX = 100, my average jump is 100cm high.
- Finally, my regular jump height (Rj) varies from day to day, but whatever my regular jump height is, my critical jump (Cj) height is (DEX*2)% (or DEX/50 times) higher, and happens AGI(x)% of the time; and for DEX=AGI (both >100), my average jump (Aj) height is [(AGI -100)*2]% higher than Rj. (Could just as easily say Aj is [(DEX - 100)*2]% higher than Rj.)
- ( So Aj = [(AGI*2)/100]Rj when DEX=AGI? )

Hypothetical example for x:

IF each "point" of AGI above 100 equated to a 1% chance to "critically jump," adding a point of AGI while keeping my DEX the same would result in a 1% lift in my *average* jumping height (Aj). 1% of the time, I would jump twice as high: so in 100 jumps, { (99 * 100cm) + (1 * 200cm) } / 100 jumps = 101cm average over 100 jumps, or Aj = 1.01(Rj). In this case [ x = 1+ (AGI - 100) / 100 ] for AGI > 100. ... I think. Or, as I'm looking for a percentage per point of AGI, I would say x = AGI - 100. But that's IF I was keeping DEX = 100 and wanted a 1% lift in my average. Instead, I'm keeping DEX = AGI and I want a 2% lift in my average.

So in other words, what I need: Assuming the multiplier for DEX remains the same: a linear 2% multiplier per point (so 100 = 2x; 200 = 4x), what would the formula (function of AGI?) be to make it so that each matched point in AGI and DEX equals a 2% increase to my average jumping height, factoring in critical jumps x(AGI)% of the time.

That is, assuming AGI=DEX and AGI>100 and DEX>100:

__(AGI-100)*x% of jumps should be critical jumps to = [(AGI-100)*2]% higher Aj than R__j.

- So, at 101 AGI and 101 DEX, if my regular jump is 100cm, my critical jump is 202cm, and my average jump is 102cm.
- At 150 AGI and 150 DEX, if my regular jump is 150cm, my critical jump is 450cm, and my average jump is 300cm.
- At 200 AGI and 200 DEX, my regular jump is 50cm, my critical jump is 200cm, and my average jump is 150cm.

Okay, so there's a pattern... Aj = Cj - Rj

Ugh, I hit my sleep-deprivation wall again. I know I have a bunch of equations here, now, and some might even be wrong. Can someone please point me in the right direction? I think I saw simple substitution and then my brain pooped out.

__Please don't hand me a solution__. If it's not too much to ask, please give me a few hints. I can almost see this, I think.

Re: Crit chance word problem

Aj = [((2AGI)/100)-1]Rj , I mean, forgot the -1

Also, the hard way, I notice that at AGI = 150, x (the percentage solution) = 50; at AGI=200, x = 66.666...; at AGI=400, x=77.7777....

How do I find a function from points? Should I subtract 100 from my points since x=0 at AGI=100, or does that matter?

I think I'm making this way harder than it is :P

Re: Crit chance word problem

I'm actually probably wrong about those last numbers...

Re: Crit chance word problem

You said you can jump 2% higher for every DEX point but this means if DEX = 100 then you should jump 200% higher not 100% higher (i.e. 3x not 2x) as you claimed.

I think what you should do is for variables that involve rates, you should store a variable for how many times you have already done something (call it x) and if you can only do y things in a period then you use the function:

f(x) = (y-x) if y-x > 0 or 0 if y-x < 0. This way if you "use" up your abilities in a period then you don't get the extra advantage.

Once you go into a new period you can update the value of x to increase in whatever way you need.

Re: Crit chance word problem

Quote:

Originally Posted by

**chiro** You said you can jump 2% higher for every DEX point but this means if DEX = 100 then you should jump 200% higher not 100% higher (i.e. 3x not 2x) as you claimed.

The inability to edit after a short period is very frustrating :/ You are correct in that I misstated, but I meant it the way I worked it out: Cjump = (DEX/50)Rjump. So that's 2%, not +2% - the word "higher" was poorly used - should have said "as high." So at DEX = 50, then, my critical jump is the same height as my regular jump.

I simply want to know what % of the time, as a function of AGI, I must critically jump such that if AGI = DEX and AGI+DEX > 200, and my cricial jump height is (DEX/50)x my regular jump height, my average jump height is ((AGI+DEX) - 200 ) * 2% -- or [((2AGI)/100)-1]x -- higher than my regular jump height.

Re: Crit chance word problem

The probability your jump will be critical is $\displaystyle \dfrac{\text{AGI}}{100}-1$. The probability your jump will not be critical is $\displaystyle 1-\left(\dfrac{\text{AGI}}{100}-1\right) = 2-\dfrac{\text{AGI}}{100}$. The height of your critical jump is $\displaystyle \dfrac{\text{DEX}}{50}\text{DEX} = \dfrac{\text{DEX}^2}{50}$ where $\displaystyle \text{DEX}$ is the height of your regular jump. So, the expected value (or average value) of your jump is:

Pr(reg jump)*Height(reg jump) + Pr(crit jump)*Height(crit jump):

$\displaystyle \begin{align*}& \left(2-\dfrac{\text{AGI}}{100}\right)\text{DEX} + \left(\dfrac{\text{AGI}}{100}-1\right)\dfrac{\text{DEX}^2}{50} \\ = & 2\text{DEX} - \dfrac{\text{AGI}\cdot \text{DEX}}{100} + \dfrac{\text{AGI}\cdot \text{DEX}^2}{5,000} - \dfrac{\text{DEX}^2}{50}\end{align*}$

And you want that to equal $\displaystyle \left(\dfrac{\text{AGI}}{50} - 1\right)\text{DEX} = \dfrac{\text{AGI}\cdot \text{DEX}}{50} - \text{DEX}$.

Setting the two expressions equal:

$\displaystyle \begin{align*}2\text{DEX} - \dfrac{\text{AGI}\cdot \text{DEX}}{100} + \dfrac{\text{AGI}\cdot \text{DEX}^2}{5,000} - \dfrac{\text{DEX}^2}{50} & = \dfrac{\text{AGI}\cdot \text{DEX}}{50} - \text{DEX} \\ \text{AGI}\left(\dfrac{\text{DEX}^2}{5,000} - \dfrac{3\text{DEX}}{100}\right) & = \dfrac{\text{DEX}^2}{50} - 3\text{DEX} \\ \text{AGI} & = \dfrac{\dfrac{\text{DEX}^2}{50} - 3\text{DEX}}{\dfrac{\text{DEX}^2}{5,000} - \dfrac{3\text{DEX}}{100}} \\ \text{AGI} & = 100\end{align*}$

So, that only occurs when $\displaystyle \text{AGI} = \text{DEX} = 100$. You said there is a 0% chance of critically jumping when $\displaystyle \text{AGI} = 100$, so the answer is $\displaystyle 0%$. I have a feeling that is not the answer you were looking for, so perhaps something was still misstated?

Now, if you are just looking for the average height of your jump when $\displaystyle \text{DEX} = \text{AGI}$ as a function of $\displaystyle \text{AGI}$, that is much simpler:

$\displaystyle 2\text{AGI} - \dfrac{\text{AGI}^2}{100} + \dfrac{\text{AGI}^3}{5,000} - \dfrac{\text{AGI}^2}{50} = \dfrac{\text{AGI}^3}{5000} - \dfrac{3\text{AGI}^2}{100} + 2\text{AGI}$