It's a tough formula to crack. I certainly didn't set my standards low, this time. And it's not like I can just Wolfram Alpha it. I can prove it though, and that proof is enough to reverse engineer it. There are a couple repeated partial functions or formulas that are used, and they're... screaming at me but I keep missing the picture. In the original Visual Basic for Applications:
It isn't the best paste in the world and it leaves out context, I'm sorry. The general idea here though is this: there is a loop through about 5 control variable sets for a calculation called SumZwi (yet another thing I have no bloody idea about... [but that's for later]), in which this variable is calculated. It's used in two of the four forks of the formula and it's making me wonder if I'm missing something obvious? I probably am. However, I'm still researching on it. (Any idea, or understanding on a better way to ask, is welcome as well.)
I've never felt so terrifed and intensified in my life.
What I've done thus far, though, is distill the ErgHen formula into about... five functions? I need to recount. I'm not sure if I should put those formulas up on the blog or not, however I think the formulas in their non-distilled state are available online anyway, so I think it's okay.
Because I'm not actually positive why they're referred to as Gauss, I'm going to explain that these functions return the integral of the normal distribution over
(-Inf, v]. It took me a little bit to figure out that was exactly what was needed here.
And to embarrass myself some more, I'm going to show off the functions to which I have no good names for, the parts of the formula I'm most captivated by at the moment and testing on the most at the moment.
It took me a while to really understand most of what was going on, enough to be dangerous, really. But I think, or perhaps I merely hope, that that's one of the traits you all looked fondly upon, in me.
... But as I was saying. These formulas power the multiplayer, single-product engine that is the training rounds that I have described, and from that is where I find myself now. Maybe I need to work backwards? Start from a mocked up end-result in order to attain all the mechanics beneath, and then replace the mockup with a real frontend. I have a lot of decisions like this to make, which brings me to one final conclusion: I need to write an outline. How? I have no idea. But I'll write it to you soon.