I'm trying to work out what a magus can 'averagely' spont, using fatiguing casting.

I know it's the total of "(Technique + Form + Aura + Stamina + Stress Die)/2"
Thus, I want to know what the 'average' of a stress die is, so I can work out what to add to the T+F+A+S to make a magus able to cast a spont at least half the time with no issues.

I think I could figure this out, but I never really want to do it. It's been too long since my Probability and Statistics class. I honestly discount the chance it will explode, and just go with the average of 5.5. There is probability that it can go much higher, but there is also a 1 in 100 chance if botching. That chance of botching isn't insignificant, and invariably it comes at some really bad times, and then there's the warping point Or you're in a faerie aura and you add a bunch of faerie (think of a different word starting with 'f') botch dice. And if you're designing a magus with the idea that you can reliably cast a spontaneous spell, you're much better served by learning a formulaic to do the job sooner than later.

Disregarding the chance of a botch its 5.5 (well a little over). 0,2,3,4,5,6,7,8,9 without explosion and then if you assume no double explosions rolling a 1 yields an average of 11. But since you can double explode the average is just a little higher.

Thanks guys. So my calculation for what can be 'reliably' (for a given value of reliably ) is T+F+S+A+5.5 (Call it 5?)

I'm writing up a list of example things that our new players in my current saga could reliably spont in a 0 aura so they can take a look at go "hmmm, so can I do ?"

I'd go with 5...
But don't forget Confidence, and new players often do. While that +3 becomes +1.5, it might be enough. And of course Self-Confident people can add +3 by spending two Confidence points.

Well, I wouldn't go that far. Heroic Personality is also relatively restricted to a specific kind of character. But adding both together, would still leave the score of 2, with 7 confidence points. I started a thread a while back about buying an increased confidence score... I would say that someone with a score of 3 could spend 3, but getting to a score of 3 would take a long time.

Assuming no botch, it's [2+3+...+9]/10 before 1's and then add for 1's: 2x[2+3+...+10]/100 + 4x[2+3+...+10]/1000 + ...
The first part is 4.4
For the 1's that's 5.4x sum of (1/5)^i, where i goes from 1 to infinity.
That sum is 1/4.
So we have 4.4+5.4/4=5.75.

So the average is 5.75 leaving out botches. Botches make it impossible to figure since the total becomes 0, which means the roll's value is negative of the bonus everything else provided. Plus we have to figure out the number of botch dice.

Well, I've never had a character with those combination of virtues, I've never thought about it. MetaCreator does some things that are certainly not RAW[1], and I can generally agree with, this wouldn't be one of them, and it is tough to tell if it is the intent that one can double up on Heroic Personality and Self Confident and get to 3 (7). It's a pretty big jump to make.

[1] The way they handle affinities, for example, by dividing the XP level by 3 to achieve the new level where a higher score is achieved. It fixes the rounding problem of partial experience points, but it is certainly outside RAW.