I hate smithing

[Taushar]

Slowly trying to work my way up smithing. Skill at 283. Tried on 3 occasions working on sickles with strength at 435. No skill ups on 3 stacks of combines. Arghhh. That's 60 combines without a skill up. What are the odds? I hate this.....

Taushar

[Qaladar Bragollach]

Sickles suck... farm yttrium hehe.

[Itek]

Hmm...

Since I'm studying for my probability and statistics class...

"What are the odds of doing 60 combines without a skill up?"

Presuming that you should average one skill up for 20 combines...

(19/20)^60 = roughly 5 percent.

That means that 1 person in 20 that does 60 combines gets no skill up.

If you decrease the average skill up rate to 1 in 30 you get a lot closer to 1 person in 6 who does 60 combines gets no skill up.

On the bright side that means that roughly one in 20 people doing 60 combines actually gets 6 skill ups. So the next 60 you do might get you 6 skill ups, and bring you back to the 1 in 20 average.

NOTE: I've not attempted high skill smithing combines, I have no actual evidence that the 1/20 number is anything other than a guess. I put the 1/30 number up because that seems more in line with what I remember from the "fix" that "smoothed out" the average number of combines to 300.

Best of luck on your combines.

[Ngreth Thergn]

what is that formula? the ^ is raised to the 60th power?

I would not be adverse to adding a "chance to get a skillup in 20 combines" to the calculator, but need the formula in a way I could convince the computer to do

[KyrosKrane]

Actually, if you want to do it right, it gets decidedly more complicated than that.

Do you want "the chance to get one skillup in 20 combines" or "the chance to get at least one skillup in 20 combines"? Those give you vastly different results, and I would doubt either is what you would expect.

Perhaps for the calculator, a better measure would be "average combines to gain one skillup" which is simply (1 / chance to get a skill up).

[Curufea]

x^60 is indeed x to the 60th power

If you want to calculate your chances at getting (or not getting) skill up,
here is a quick drawing:

For the things you may want the calculators to do, here are the formulae (below you'll find a quick justification of them):

as a base : "p" shall be the probability to get a skill up for any combine

* The probability of NOT getting any skill up in "n" combines is
(1-p)^n

* The probability of getting ONE skill up only in "n" combines is:
p*(1-p)^(n-1)

* The probability of getting AT LEAST one skill up in "n" combines is:
1-(1-p)^n


>>>>>>>>>>>>><<<<<<<<<<<<<<<<<<

as a little probability base : the probability of something NOT happening is equal to 1 minus the probability of the said thing happening. Always.
Now to the calculations:


Since "p" is be the probability to get a skill up for any combine, thus the probability of not getting a skill up (again for any combine) shall be "1-p"

The probability of NOT getting any skill up in "n" combines is
(1-p)^n
it's (1-p) for one combine and you multiply that (1-p) for each combine... thus n times.

The probability of getting ONE skill up only in "n" combines is:
p*(1-p)^(n-1)
then again, it's p for one combine (whichever it is!!!) which you multiply by (1-p) for each other combine (there are (n-1), since you did n total, one of them being a skill up and all others without skill up).

The probability of getting AT LEAST one skill up in "n" combines is:
equal to the probability of NOT getting no skill up:
The probability of getting NO skill is known : (1-p)^n
Thus the probability of getting at least one skill up is : 1-(1-p)^n

[Itek]

Aye Ngreth, ^ indicates "raise x to the y-th power" when used x^y

They syntax in C/C++ is -exactly- that.

However Java (and therefore quite a bit of web programming) has NO "raise to the power of" math operator. Sorry, we here in Java-land have decided to forego such a USEFUL construct as "raised to the power of" as a single operator.

No no no...
#import java.lang.math (or some such)

and use the pow(x,y) operation...

but...

don't forget....

pow returns a DOUBLE (large FLOAT) and requires (double x, double y) as it's parameters...


THAT'S RIGHT folks... to do

3^3 (returns the number 27 in C/C++) you must

(Integer) pow(Double.valueOf(x), Double.valueOf(y)) in Java

The problems with making a "calculator" to accurately display the "odds" of a probability statement of any complexity frighten me.

The most straightforward assignment (in school mode for another week, then I get a 4 week break) would be thus

Given a probability function (x,y) where something occurs X times in Y trials, calculate and display the probability of receiving between 0 and Z successes in Z actual trials. Format your display in order by decreasing successes.

Sample input:
Enter Expected Successes: 1
Enter Expected Trials: 20
Enter Actual Trials: 60

Sample output:
Probability of 60 successes:
Probability of 59 successes:

....

Probability of 1 success:
Probability of 0 successes:

(Note: You -are- expected to properly handle the display syntax for multiple/single/zero successes.)

Extra Credit: Add a fourth parameter to limit the display to the maximum quantity of successes requested.

The actual formula for prediction of success (gosh, my ECE 380: Probability and Statistics for Engineering Problem-Solving test is in an hour) is

P(x) = [(nCx)* (P(success)^number of successes)*(P(failure)^number of failures)]
where
x = exact number of expected successes
(nCx) is
n = total number of trials
Choose (order doesn't matter) x
and number of successes + number of failures = total number of trials

(Formula for [nCx] is n!/(x!(n-x)!) ... fun huh?)

THEN if you want "what is the probability of getting 0, 1 or 2 successes" you have to calculate it as P(0||1||2) = P(0) + P(1) + P(2)

For REAL fun you can resolve the program in a non-naive way and use dynamic programming/recursive calls/2-dimensional-array-table-building in combination to solve the problem in less then Big-O(n^3) time (the rough naive complexity) and possibly down to Big-Theta(mn log(base 2) n) time with space complexity of approx n^2.

(Yes, Virginia, this semester was a complete nightmare.)

ugly.... or as my Software Engineering Professor likes to say...

"ghoulish"

*Itek runs screaming from the room to avoid another programming assignment*

[Qaladar Bragollach]

ANSI C uses the pow(x,y) function also.... its in <math.h>.

I'm not really a C++ guy, but in C, the ^ operator means bitwise exclusive OR.

Its quite trivial to write an integer power function... its just a for loop (in fact, even if you do, odds are nearly 100% that your compiler unrolls it anyway and the function doesnt actually exist in the compiled executable). Its just not a very common thing to need in programming (unless you happen to be programming a probability calculator... but how often does that happen?)

[Buns]

Bet you guys are fun at parties

[Ngreth Thergn]

Course I use PHP... will ahve to look up PHP's math functions.

[Phantron]

At 283 skill, the odds are well below 5% from non modified combines to skill up. So it is quite likely this happens.

I've been buying 20oz coke bottles that says 1 in 6 wins a free 1L coke. I went through 17 bottles without winning one which is something like 1 in 20 chance of happening, and then got 2 back to back (1 in 36). Given long period enough of time, probability tends to even itself. That doesn't mean you should be expecting to skill up 3 times in 10 combines after a bad run, though. Indeed I'm still doing quite a bit below the expected 1/6 even despite that back to back win!

[Wyora]

Ouch, you math freaks made my head hurt. My bags are full of everything I need to do a run of sickles tonight, I hope the RNG likes me a bit better.

[Gruda]

My worst was 224 sickles without a skill gain.


Ogress of many skills: Baking 200, Brewing 300, Fletching 200, Jewelcraft 240, Pottery 200, Smithing 300, Tailoring 194

[Taushar]

NOTE: I've not attempted high skill smithing combines, I have no actual evidence that the 1/20 number is anything other than a guess. I put the 1/30 number up because that seems more in line with what I remember from the "fix" that "smoothed out" the average number of combines to 300.

Ok, anyone care to guess what the number should be given 435 strength? I mean, I thought that 1/20 number was using something close to 300 stats, I would think 435 would give it a lot better chance than that. If it works out to be like 1/12 or 13 then the whole math you presented goes out the window.

Taushar

[Qaladar Bragollach]

At 400 str/wis/int you achieve max chance of skillup in smithing. More won't help.

There's a perfectly good calculator on the main page. Have a look at it.

The odds of skill up on a sickle at 283 skill with 400+ strength are 3.86%.

While the chance of going 60 combines with no skill up on any GIVEN specific run of 60 is fairly low, you have to look at the bigger picture. On a total run of hundreds and hundreds of combines, the odds of going 60 with no skillup at least once approach 100%. Its almost certain that at some point you will go 100 combines without a skillup. Its fairly likely that you may even at some point gp 200 combines with no skillup.

Random numbers have streaks... thats the way it is. If the numbers were totally evenly distributed such that you got a skillup every 25 combines like clockwork, then they wouldn't be random at all.