2 hours ago, Baaa said:The bits you've quoted are saying exactly what I've been trying to say all along, there is always a variance outside of the mathematical model. So why not factor it into your calculations?
I used 0.5 as it is the median of 0 and 1. It is the figure used by Hopgood in his book to introduce variance. It is neither positive nor negative, it is simply the middle number (or median) with which to start.
Apply it to what ? Let's start simple, a single die roll. Those happen often enough. To what does 0.5 get applied to? 1/8th crits, 3/8th hits, 2/8th eyes, 2/8th blanks? How? Maybe you want to go 1/16th to 3/16th crits, and 3/16th to 9/16th hits, and 2/16th to 6/16th eyes, and 2/16th to 6/16th blanks. But you know what that works out to? 1/8th crits, 3/8th hits, 2/8th eyes, 2/8th blanks.
Because that's how averages work.
OK. Maybe if we're looking at just Hits/Misses on red dice without mods, just to make it simple. We could run the calcs at 0.45 as the probability of a hit, and at 0.55 as the probability of a hit, but all that'll do is give is something almost like a confidence interval. We'd get a wider interval testing with 0.4 and 0.6. But here's the most important thing: the center of that interval, however, is just going to be the results of 50% hits, 50% misses.
Unless you're applying these factors to only one set of results and not the other we'll wind up with the same averages, because that's how it works.
2 hours ago, Baaa said:At the end of the day, in any dice game you either go with the averages and curse the dice when they don't come up (you can always console yourself with the thought that over a thousand dice rolls it would have been came up the way you wanted them to) or you accept that there are factors which the mathematical models don't take into consideration.
I choose the latter.
Honestly feels like this is still just magic.
Part of understanding randomness is understanding that bad rolls just happen sometimes. That's in the model. Any single game, any single afternoon of games, is a small sample size, a small number of rolls, as far as the math is concerned. Trusting the math says you'll have good games and bad games. I personally don't need magic to learn how to handle the swings.
The other thing that's great to understand? When things aren't math. My favorite list for this example is Four Fearless Fangs. These suckers can highroll like no-one's business. The games I play where I'm able to live at Range 1, my dice are on fire. The games where my opponent is keeping me at Range 2? My dice stink. Only, it isn't really about dice. But that's just a trick of the mind. It's about position. What's happening is that I'm either outflying my opponent, or they're outflying me. It looks like dice, but a lot of it is skill.
You want to believe in magic with the dice? Go ahead. Just don't tell us we've got to put magic into our mathematical models, or else we're doing it wrong.