This Is How We Roll: Decision-Making While Rolling

#14

Two problems with the analysis:

  1. Rather than “XP(20)-XP(n)” it should be the effort to go from level n to level n, which is related but not identical to the XP needed, because of 10% XP cap.

For most people the best way to level after level 10 would be in gland (reaching the 10% cap until level 17 or 18) the effort needed is closer to linear than quadratic (in terms of 20-n).

  1. I need to think more but I believe you missed an important consideration here. This formula assumes that you either level from n to 20, or start over entirely. But you can also e.g. level from n to n+1 and restart if the roll at level n+1 is too bad.

To do it correctly I think you have to set up a recurrence for all possible percentiles at different levels. Assuming the effort needed is modeled as a linear or quadratic function, I suspect there is still a “simple” formula because it’s just a linear or quadratic combination of binomial coefficients. But I’m not too sure off the top of my head.

#15

This seems to be a rather bad assumption since this is the exp cost of the “normal” rolling process and you should be able to safe yourself a bit of exp for the new rolling attempts by using your method.

#16

A few bits of feedback so far (thanks!):

True, it is. A +10HP roll might still be garbage if it’s -35MP.

I’m thinking of ways of extending this work to account for a fixed mana:life ratio and then reformulating the tables to account for an “effective roll” of HP+(MP/ratio). However, I’d need to treat spellcasters and non-spellcasters differently since their MP gain rates are different.

Always more to think about.

 

XP(n+1)-XP(n) (i.e., how much XP you must earn before your next level-up) is easily measurable. “Effort” is not, and would vary from player to player. And again, I’m not addressing the easiest ways to earn 18,050 XP quickly, I’m just addressing some decisions you might wish to make along the way.

 

You’re welcome to stop and check your roll at every point. It might get tedious, but that can be useful at times.

 

Ahh, you caught that. You have no idea how much that kept me up at night.

My first attempt at approaching this problem lumped everything together into a single formula (“how much XP does it take to roll an acceptable character?”) and attempted to use minimization techniques. However, that was a self-referential function and simplification efforts didn’t help much and eventually I just had to focus on decision-making for this one paticular roll in a vacuum, which led to what I presented above.

I might try to go back and address that, simply to see how big a difference it would actually make.

 

-facepalm-

I broke it up so people could easily refer to particular sections. In retrospect, I wish I did a better job of that in my other math posts.

 

I appreciate the feedback so far, feel free to keep it coming!

 

Edit: Oh, and:

Heh. I’m actually a mod on r/RotMG, but the site is blocked by my workplace firewall so I’m hardly ever there. Feel free to link to it if you’d like (and give credit to u/otherbill, of course).

#17

Totally forgot you were a mod there. Linked and credited.

#18

Reading this took me back to the days of the old forums where your pet ability analysis was pinned for all eternity. Very well done.

Don’t worry, you’re still more active than Walorus.

#19

And that zxcv_rotmg guy…

Great post OB!

#20

does this mean I was hecca lucky with my +40 first samurai roll?
also cool
This has so many other variables depending on the player reeeeeeee
sounds fun
I only care about hp

#21

#22

XD who else skipped the whole thing just to see how long it was.

#23

fuck the horrors of prob and stat class are flooding back now

#24

image

y’all hear sumn?

#25

Okay, that warrants a :laughing:…and a trip straight to the Level 20 probability tables. :slight_smile:

#26

I see that they just released an 8 pack of these in the store (packages tab). With XP boosters helping to fasten the pace of leveling it barely seems worth even the discounted cost.

Historically, I have used the image three times and have always received a 0 or positive hp/no roll, but that is not statistically sound. Has anyone used them and recieved a negative roll?

#27

Sorry I missed the assumption that you only check the roll once.

#28

I think I used two of them and once rolled 0 and the other time -8 iirc.

#29

From my Sorc, that I used it on:
image
I could probably put the other one I got (from the Oryxmas Mystery Gift) on my Samurai and see what I get.

#30

i have an idea!
if the roll was above average, the stats would be in a green color, like this:+30 HP
if the roll was below average, the stats would be in a red color, like this:+20 HP
this could only be applicable to the hp and mp stats, or it could be added to every stat.

#31

Or just have something track the roll progress and give you the equivalent of /tell MrEyeball stats.

Honestly I’m so bad at remembering stuff, keeping track of 9 lvl ups and their respective changes to the roll is too challenging ;-;. Especially when I use my extraordinarily big brain to compute 2 + 2 = 5

#32

So, something along the lines of…

Options -> General -> Show stat incr. on level up

As well as

Command: /stats - Shows the difference in stats compared to average stats at that level

Well, that’s just your thoughts translated into my thoughts, translated into my words. Sort of.

#33

Wait… this is not necessarily true if you stop early

Edit: Also how did you create the cumulative Q probabilities table? I’m guessing a Mathematica program to do all the generating functions for you? Or did you manually sum them all up lol

Edit 2: Oh oops sniped by Mynamerr