Porcellio Card ??

[mahawirasd]

don't sweat it, i've levelled my bard quite a bit on exclusively porcellios until i finally got the card... It's gonna drop one of these days, just pray it's sooner rather than later...


-w-

[Former-GM-Vanadis]

Whispers, your math is wrong.

The probability of getting atleast 1 card is the compliment of the probability of getting no card, thus the formula is

1-(0.9997)^x

where x is the amount of kills.

So for 5000 monsters, it's ~77.7% probability to get atleast one card.

But even so, the next monster will still only have 0.03% probability of dropping the card. And killing 5000 more monster will give you a 77.7% probability of getting atleast one card.

[Whispers]

Explain that.??It makes sense to me that if you kill x amount of monsters then you could assume your chances increased x amount of times.??I don't follow that line of logic as each monster retains its 0.03% likelihood of dropping a card; but I'm intrigued as to how someone came up with the formula which tells us how often something might happen.??

I'm not a gambling man, so such studies have never interested me.??xp

I'm going to get my high school diploma starting next week, though (dad's death seven years ago kinda forced me out of high school >_> ).??So, hopefully I'll learn all of this advanced mathematical forumulae.??I technically only have an eighth-grade education.??-_-??Though my own personal studies have - hopefully - raised my intelligence beyond that of a 13-year-old.??<_<
I do have my GED and I got *checks* 59 in the 20-80 "standard score" range and an 82 in the "percentile ranks"!??That means I did better than 82% of high school seniors according to the "Interpreting GED Test Results" info on the back of my GED.??Is it bad that a guy who didn't even finish the ninth grade did better than so many seniors???0.o

Math is my second-to-lowest score on here.??
And I always thought I was so good at math because I can do calculations really quickly in my head.??I guess computation is meaningless without proper input.??=/

[EDIT]

I get the favorable chances being complimentary to the unfavorable which would make for the 1 minus 0.9997; but what is the ^ for???I always figured it was a way of implying a number was an exponent.??If so, then how does the chance of not getting a card multiplied by itself the number of times attempted subtracted from one bring you to the probability???It sorta makes sense to me, but not completely.
Does the formula make sense to you???If so, could you explain it???It's so much easier to teach something if it makes absolute sense to you.??=3

It'll probably make sense to me by the time I wake up. Math works like that for me. I don't study it because when I sit down and think of it it makes sense. In the seventh grade I had a number of systems and formulas I made myself... Which I've now forgotten, but I had them nonetheless!
The Chance * Attempts = Probability made sense to me as you can't really test or prove it anyway. At least not in my line of belief.

[mahawirasd]

perhaps we could start here:
http://en.wikipedia.org/wiki/Binomial_distribution

well basically the way Aki and the others calculated it, they are assuming normal distribution...

the gaussian bell curve itself is genius imho, but perhaps it's not the best idea to use it in a system such as RO as some ppl really are just born luckier than others...


-w-

[Neuneck]

A little excursion into probabilities:

A probability is the rate at which an Event will occur. It is a number between 0 and 1. (Yes 1% is just another way to write 1/100 or 0.01)
For every event there is the contrary event, that will take place every time the Event hasn't taken place. Let's call the Event E and the contrary event C.
Of course the probablities of all things that can happen add up to 1. This comes from "nothing happening" being the contrary event to "anything happening". Now the chance for an event to occur is p(E), the chance of the contrary is 1-p(E) = p©.
If you repeat the experiment, the chance an event occurs multiple times is p(E) ^ x where x is the number of times you repeated the experiment. If you have 50% chance of hitting and you strike twice your chance to hit BOTH TIMES is 0.5 ^2 = 0.25 = 1/4. Now let's assume you have a 20% chance to score a crit. Critting every strike in a row of 5 would be 0.2 ^5 = 0.00032 = 0,032%. The chance to crit AT LEAST ONCE in those 5 strikes is the contrary to not critting a single time. Not to crit has 80% chance of happening. So the cance not to crit in 5 strikes is 32.768% (it's 0.8 ^5, because 1-0.2 = 0.8 is the chance not to crit and you repeated the experiment five times). The chance to crit at least once is 1-32.768% = 67.232 %.
For cards it's 0.03% = 0,0003. So the chance not to find a card in a monster you kill is 99.97%. If you kill X monsters the chance not to find any cards is 0.9997 ^X. The chance to find at least one card is the contrary of that so it's 1-0.9997^X. Or 1- (1-0.0003)^X.
Of course the chance to find the card in this specific monster still is 0.03%, but killing lots of them will increase your chance of finding one. If this weren't so, farming cards would become about impossible...

I hope this was understandable...


Btw. A ^B is "A to the power of B" it's A multiplied B times with itself. 2^3 is 2*2*2 = 8.

[GM-Ayu]

A little excursion into probabilities:

A probability is the rate at which an Event will occur. It is a number between 0 and 1. (Yes 1% is just another way to write 1/100 or 0.01)
For every event there is the contrary event, that will take place every time the Event hasn't taken place. Let's call the Event E and the contrary event C.
Of course the probablities of all things that can happen add up to 1. This comes from "nothing happening" being the contrary event to "anything happening". Now the chance for an event to occur is p(E), the chance of the contrary is 1-p(E) = p©.
If you repeat the experiment, the chance an event occurs multiple times is p(E) ^ x where x is the number of times you repeated the experiment. If you have 50% chance of hitting and you strike twice your chance to hit BOTH TIMES is 0.5 ^2 = 0.25 = 1/4. Now let's assume you have a 20% chance to score a crit. Critting every strike in a row of 5 would be 0.2 ^5 = 0.00032 = 0,032%. The chance to crit AT LEAST ONCE in those 5 strikes is the contrary to not critting a single time. Not to crit has 80% chance of happening. So the cance not to crit in 5 strikes is 32.768% (it's 0.8 ^5, because 1-0.2 = 0.8 is the chance not to crit and you repeated the experiment five times). The chance to crit at least once is 1-32.768% = 67.232 %.
For cards it's 0.03% = 0,0003. So the chance not to find a card in a monster you kill is 99.97%. If you kill X monsters the chance not to find any cards is 0.9997 ^X. The chance to find at least one card is the contrary of that so it's 1-0.9997^X. Or 1- (1-0.0003)^X.
Of course the chance to find the card in this specific monster still is 0.03%, but killing lots of them will increase your chance of finding one. If this weren't so, farming cards would become about impossible...

I hope this was understandable...


Btw.??A ^B is "A to the power of B" it's A multiplied B times with itself. 2^3 is 2*2*2 = 8.

The only incorrect part is the bolded part. Chance of finding a card is independent event. Just because you killed 15000 monster already, that doesn't push the chance of the 15001st monster to have an extremely high chance of a card. It's still going to be 0.03% of a card. You can't "trick" probability to kill 3000 normal monsters, and then go "oh yeah my chance of finding a card is now up to 30%+, I'll strictly fight mvp now to boost drop rate!"

The formula vanadis provided only helps you summarize the probability of what you have done in the past from happening. It doesn't predict the future of *when* do you get a card. This formula is only effective for theorycrafting, and analyzing the past, and is completely irrelevant to what happens in the future.

[GM-Aki]

Its in the over all amount of kills that your probability goes up. But individually, the drop rate doesn't change thus your probability of getting a card is still 0.03%. But if you kill the same monster 100 times, the drop is the same but since you've killed more than one, you have 100 more times to get it.

[Whispers]

Yeah, I was reading about Binomial Distribution last night.??The formula is solid in my mind now.??It still doesn't make much sense.??How do we know it to be true???How is Attempts * Chance = Probability false?

I don't have a lot of time right now.

LoL - I meant my math score was an 82.??Second worst in the group with social studies at 76... >_>
Best was writing abilities at 99%.??=D
rawr - gtg

[mahawirasd]

as i said dear Whispers, the numbers presented by Neuneck and Aki is based on the assumption of NORMAL DISTRIBUTION.

If you look at that genius of a graph called the Gaussian Curve (the one shaped like a bell), you will see that in the example of 100 ppl looking for a hydra card and killing them at the same pace (just a rough illustration here in the shape of a perfect bell -otherwise that poor bloke in the end might never get the card before ~):
one lucky bastard (sorry for the choice of wording here, but i deem it appropriate) will get a hydra on the FIRST kill while 9 people might get it in < 1000 kills, 15 people will get it in around 1000-2000 kills, and the majority of around 50 people will get it in around 2000-5000 kills, while another 15 people will only get it after 5000-6000 kills, another 9 gets it at 6000-6999 kills while that one poor unlucky bloke gets it only on his 7000th kill...


-w-

[Whispers]

It still makes no sense to me.??Maybe it's because I like to see things with a definite outcome.??What you wrote, Maha, is obvious to anyone (though it takes a keen mind to see the phenomenon graphically), but the logic behind the formula for finding out the probability of obtaining something with a fixed probability after attempting x amount of times alludes me.

Yeah, it's easy to think, "I've killed millions of these things, I can't fail with this next one," but that reasoning doesn't seem correct to me.??It doesn't seem logical.??I now know the 1-(1-probability)^x formula--thank you, Ayu--but it doesn't make sense.

Can anyone explain this to me?

What I mean by "explain" is this:

I have a tome titled "The Dog Owner's Home Veterinary Handbook."??In one of the appendices it has a list of approximate "dog" years compared to human years.??I noticed that in the first year of life a dog ages the equivalent of 15 years.??In the second year of life a dog ages nine years, bringing it's "age" to 24.??Every year after the second a dog ages four years - 28, 32, 36, etc..??After doing a bit of math I created the formula for finding a dogs age past the first year:

• d = 4h + 16,

where d = age in dog years and h = age in human years.??The math checked out, but I was wondering why this specific formula was correct.??The four is obvious - a dog ages four years every year of life past two human years; but why sixteen???Where did that come from?

After a bit of thought and looking at a few more numbers I saw the reason.??We are multiplying by four and adding sixteen for every year past the first.??The progression from the first to second year is nine "dog" years.??Nine is not divisible by four (it is, but we're working with integers).??When we divide nine by four we get 2 with a remainder of one (or 2.25 with 25% of four being one - hooray!).??We then add this remaining 1 to 15 to make 16.??So, what we really have is:

• d = 4h + 15 + 1.

Now it makes sense!??=D


I tried making sense of the probability thing.??I envisioned a bag of 100 marbles.??One of these marbles is black whereas the other 99 are white.??I won't bore you with the math, but I'm still working it out.??Maybe it's exponents I'm having a problem with???I never fully understood their usage.??Why would you raise the unfavorable percentage to the power of the number of attempts as opposed to multiplying the unfavorable percentage by the number attempts instead???It seems to me that If I've killed three monsters I've a three-fold probability not a %^3 probability as I've tried three times.??If I've spent two dollars three times I've spent 2*3 dollars not 2^3 dollars.??If I tie my shoe four times every time I jog and I jog two times a day (I wish xp) then I tie my shoe whilst jogging 4*2 times a day not 4^2 times a day.??I believe I'm making sense here.??The number of tries exponentially raising the probability as opposed to multiplicatively is just...

I hope someone can explain it to me.??I'll hopefully figure it out for myself if no one does, though.??=/

[EDIT]

I'm not saying the formula is incorrect. I'm just saying it doesn't make sense to me. Please don't infer incorrectly.