The Real Significance of Retaining (A Chestrunner Must-Know)

Interesting fact : with 100 lockpicks and a 50% retaining chance, you will open ~200 Chests.

Why is that? Well here's the theory behind it

You have a certain chance to retain, lets call that X (Retain Chance in Decimal Form)
Yes, we're going back to math class everyone.
P=% of Lockpicks you will use (Assume 100%, so 1)
So great, its just 1 + 1X, right? Well no, because you can retain twice in a row...
So 1 + 1X + 1X^2? No, you can retain more than 2 times in a row.
The answer is actually expressed as a Geometric Series...

Limit 1+X+X^2+X^3 ... X^n
n->∞

"Well how can I add up all that"? Well lucky for you the limit turns out much simpler than it looks...
This limit is actually

1/(1-X)

Yup, thats it!
So for 50%, you plug in .5, and get 2. That means if you have 100 Picks, you can open ~200 Chests. (2x100)

You can use this for any retain %

"What's this good for?"
Well numerous things.

1)You can more accurately determine whether or not it is worth Chestrunning in NM vs HM

2) Figure out your expenses for getting Chest/Lucky Titles

3) More accurately determine your profit margin with opening chests

I'm not sure about your math. It confuses me to thing about it, but I think you're missing something. Allow me to try a different approach. With X keys, how many chests will you open?

So with x as number of keys and r as retain rate , it's x+rx...and that's where I think something happens.

xr^2 would indeed be the number left after two runs. Yeah, I guess you're right. That series would be

inf
sum (xr^n)
n=0

Math tells me that if we find m such that mr+1=m, m*x will be the number of chests opened with x keys at r retain rate.

Our rate is 50%, we have 100 keys. .5m+1=m, 1=.5m, m=2. x=100, mx=200. Yeah, you're right. Never mind me, I'm just a blabbering fool.

If I understand this correctly, it's:
100/1+100/2+100/4+100/8+100/16+100/32+100/64+100/128+100/256+...


So if I'd go to just 4096 right there... that makes it 199.975586 chests.

Seems right - it's hard to believe, but statistics say so (disregarding the fact that I may have totally misinterpreted this).

Nicee endless. This'll serve me well indeed.

having fun in precalculus? hehe ...

omg, limit as x approaches 1!!!!! whole world asplodes!!

Wow I'm not good at math. So I compensate by killing stuff In GW

wow congrats on learning some algebra. i can't wait until you learn calculus and real math and contribute knowledge then.

That's an elaborate way of stating the obvious, isn't it? :P

I couldn't believe it myself. I was worried that I had missed something when I noticed that the first three replies had taken it seriously.

What a strange thread...

Well actually its not common knowledge that the whole problem converges.. Not sure how thats obvious, but ok. Definitely wouldn't learn that in precalc, thats for sure
This is a summation problem, not learned until integrating so....
@ guy with creative name (Um yeah): Not this summation

^ ah here I figured it was zero... but I see now its .001


"oh yay a superior wilderness survival rune!"

No, summation is taught in precalc.

depends on what high school you went to =p

No, he must ride the short bus.

i have no clue why you put x and r in math.. -.-

retards

in theory if u flip a coin 30 times ideally it would be

15 heads
15 tails

but in all reality you will get numbers like 14H/16T
etc etc

the more you do the more likely it will be 50/50....ideally

This thread is like saying 1 + 1 = 1^1(1 x 1)/1 + 2/2... window.

*sigh*

The 'real' significance of retaining is that you have a 50% chance that your lockpick wont break, no need to make it complicated when it's already supposed to be understood... 'Simplify, man!'

No im not saying 1+1=.... not anything like that, thanks for bringing the post to the top though (Lol). All these erroneous/inaccurate remarks are making this thread #1, sw33t. The point of this post is to be able to estimate how many chests you will be able to open taking into account your retain %... doing that x + x^2 ... is alot of number crunching, and this simplifies it. If you dont understand how thats not simplified.. well then i dont know what to say

Just wait unti'll you're old enough to go to school.