Value of Studying from Vis

In light of this evidence, will you study from vis more?

  • Yes
  • No

0 voters

Inspired by getting 3500 xp or so from studying from vis, I have calculated the statistical average of studying from vis:

0.1*(2+..+9)+ Sum( 0.1/(10^i) (2^i)(2+..10)) i =1 to infinity
= 4.4 +1.35 =5.75

So the expected value (the total unconditional expectation) is 5.75+1.09*Aura. Kinda crappy.

The next problem is with the second moment: (used to get variance)

0.1*(2^2+..+9^2)+ Sum( 0.1/(10^i)(2^2i)(2^2+..10^2)) for i =1 to infinity
= 28.4 + 38.4*2/3=54

Variance is 54-5.75^2 =21

So the standard deviation is roughly 4.55

I think. Dang, this still bothers me as I'm now totally unsure of being correct.

Original work:

So... 92.5-11.15^2<0

0.1*(2+..+9)+ Sum( .1/(10^i) (2^i)(2+..10)) for i =1 to infinity = 71.9 +Aura.

Sounds like a winner.

Variance to follow.

Note, following expected values should add the aura automatically to whatever expected value given.

Last but not least... PLEASE VOTE!

I am not a mathametician, so I have no idea what your Arcane calculation means. Smacks of Numerology.

But anyways, I often choose "Unimaginative Learner" as one of my flaws, and I like to save my vis for other uses (enchantments, penetration, rituals, currency, etceteras)

This means, on average, the amount of xp you can expect to get when studying vis for a single season.

Of course, conditional on not rolling a 0 or 1, the average xp you can expect is 5.5.

How in the world does that equation equal 5.5? i do not understand. But still, 5.5 is pale in comparison to a decent summa that can be studied multiple times, or even a Tractatus or a Teacher. The yeild is too low on average. The vis is better spent purchasing books. IMHO.

If you study for the first actuarial science exam, these calculations are easy. Except for finding the expected value of the vis squared. I keep getting a number that's too damn small, so I can't figure out the variance.

You are missing the point :laughing:
I haven't the foggiest idea of what "actuarial science " is. Last math class I ever took was Introduction to Algebra back in sophomore year of high school. I passed with a D and never touched another math class since then. I learned all my math counting money and playing RPGs. I took a pretest in college (community college was all I could afford for myself). I placed really high on their scale, which confused me. But I never took the class. I studied History, Literature, and Philosophy (things that are of no use in the job market). One year of Astronomy, the math was simple.

I do know that it was John Dee that first introduced mathematical symbols to England, such as the dividion sign. People thought that this was his black magic, nevermind his true esoteric ramblings.

Math scares me and I think you are a witch.

(JK! :smiley: )

Actuaries (Actuary for short) largely calculate how much insurance should cost, or how much money the insurance company needs to meet all of their obligations. Very lucrative you can hack writing exams for 5 to 10 years.

Anyways. Too truly powergame in any RPG, use of math/statistics is definately required. I saw a calculus treatise on D&D to figure out the optimal amount of power attack to be used given the your to hit bonus and the enemies AC. Cool question. I went in, fixed it and use MAPLE to solve some of the algebra problems numerically, since the by hand stuff was too complicated.

I do have a math/stats major, so these things come easy to me. To go even more off topic, what I find so terrifying, is how complacent people are having a poor understanding of math, which is the foundation of pretty much all science.

Can you explain the equation to me? Why isn't it 0.9*(2+..+9)+ Sum(0.1/(10^i) (2^i)(2+..10)) for i =1 to infinity = ????

Bold and italics mine.

The italics part is because: Recall that The expectated value of a function X:

E(X) = Sum( P(X=x)*x) for all x element of X

P(X=x) is the same for x element (2,..,9) ... As for the bold part, I think you're correct there. Dang. need to recalculate.

Please note that taking into account the various average and such it is mostl ikely 5.7 + aura or 10-11 if you have a good aura, 8-9 if you are in average aura. (This ignores the 1% chance of botch in 100 rolls on average and takes an average 5.5 as the * for 1,1,* that happens 1% of the time)

A quality of 10-11 is very good when you have exceeded the level of the covenant's books

You beat me to the punch. If you want a real average, you should calculate in an aura bonus (5 or so) and reflect the fact that 9% of the time you'll only get the aura bonus and 1% of the time bad things will happen to you.

I guess 5.7 is correct if you say that a roll of 0 does not automatically make a 0 study total for the season.

1% chance of 1,1,...+aura or the jackpot
9% chance of 1 for study total of 2*(2-10) + aura
80% chance of 2-9 + aura
9% chance of a 0 + aura
1% chance of a botch

The important number for me is the mode, which is probably going to be a 6 + aura.

Ok, so the question of what the variance is is stumping me.

What is the variance?

We have:

Roll of "0" = 0 (for simplicity)
Roll of 1 = Reroll and double
When the die is rerolled, treat "0" as a 10.
Otherwise, Roll of "i" = i for i from 2 to 9.

Then, I calculate the 2nd moment as

0.1*(2^2+..+9^2)+ Sum( 0.1/(10^i)(2^2i)(2^2+..10^2)) for i =1 to infinity = 668.4

Which is clearly wrong, as the variance is then negative. I know I must be doing something wrong with the 2nd moment, but I just can't see it. Any help would be awesome.

The average for a stress roll is 5.75
The variance for a stress roll is 33.15625

Wow! Quite a variance there. Never stopped to check it.


This whole thread far surpasses any type of hedge magic and reeks or diabolism...All involved should be marched immediatly and the knowledge they have tried to force on to us destroyed!

There's something that seems to be missing from the discussion. Everyone's looking at the expected rate as experience/season. While this is usually the most important rate, it is one of two important rates (and a third factor). An average of 5.75+Aura gives you about the same average as you'll get from tractatus. Noting we can pull off an extra +1 with commentaries and that getting an extra +1 from resonance is fairly easy, getting to Q10 is the lowest typical quality of anyone with Good Teacher (need Com 0) or with Com +3. So it has been established that using vis gives about the same quality as using tractatus, and a worse quality than using a low-level summa (typical quality >15).

So how about the cost? The low-level summas are relatively inexpensive, and you commonly expect to get to roughly a 6 with them (see ArM5 and Covenants). So, assuming you don't have a good mid-level summa, you'll start making the comparison to tractatus after level 6. If you do have a good mid-level summa, we can probably estimate holding off on the comparison to at least level 11. Since the average quality from a tractatus and from vis are the same, all we really need to do is compare the costs. From levels 6 to 15, it's just two or three pawns, which seems about on par with tractatus costs (again, based of Covenants). The tractatus price for a quality 10-11 won't be based on your Arts, but the vis cost will keep rising. So using tractatus gets better and better.

That leaves us with the third factor: availability. First, I'll address vis. It will get harder and harder to get the necessary quantities of a single type of vis, with the exception of Vim vis (you'll create too great a demand within your covenant as well as simply running into regular supply limits). However, with tractatus, you just need to make a deal, which typically won't have quite this issue. Second, I'll address tractatus. Eventually you'll simply run out of tractatus. Then you're just stuck with that route. You could get some lower quality ones at reduced price and higher at increased price, keeping the averages all about the same. But you'll still run out.

So my overall recommendation would be to use vis from level 6 to level 15 or 20 for your favorite few Arts, but only when you can't get a hold of a good mid-level summa. Once the cost starts getting noticeably higher than the cost of equivalent tractatus, then switch over to tractatus. But if you're considering the rest of your Arts, most of which are unlikely to advance past 20, perhaps not even 10, skip vis entirely.

Edit: Note, all this is for an individual. If the cost of a tractatus can be split among several in a covenant, the argument against using vis except early in Arts you want to push beyond what tractatus can handle only become stronger.


Though your equation is right, I wonder how you're getting 71.9. The same problem could be cropping up in your later calculations, too. Are you doing it by hand or using a computer? Here's a method by hand:

Let S=Sum(1.5^i) for i=1 to infinity

0.1*(2+..+9) = 0.1*44 = 4.4

Sum( .1/(10^i) (2^i)(2+..10)) for i =1 to infinity
= 0.1*(2+3+...+10)Sum(1.5^i) for i=1 to infinity
= 0.1
= 1.35



Hear Hear! Warlocks! Witches! Burn them all!

(cowers and hides behind he tree: