Did anyone else notice that the random determintation of income development with a stress die seems to result in a downward spiral?
I have no math degree, but judging with my basic math the distribution looks like this:* Botch: 1%
0: 9%
2: 10%
3-8: 63.1%
9: 10%
10-19: 5.21%
20+: 1.69%
Add to that the fact that equivalent increases and decreases don't cancel each other out, but result in a net loss (50% x 150% = 75%).
I'm thinking about shifting the number to 3-7 (x1), 8 (x1.05) and 9-19 (x1.2). As an alternative, I might also adjust the decrease rates to cancel out the appropriate increase (Botch: x2/3, 0: x5/6, 2: x20/21). Any other ideas how to handle this?
Basically I didn't write those rules, but I kind of hate the gamerist assumption that, like in a computer game, if you just leave your empire to do stuff it will accumulate profit. Actually, in the real world this doesn't happen: every business in history eventually failed because of story events. Those that succeed are propelled forward by what in gaming terms would be story events.
This is true, although the effect is extremely slight. The weighted geometric mean (according to my hasty calculation) is 0.989; meaning that if you rolled 100 times (i.e. after 100 years of random outcomes), on average you'd get a third (0.336) of what you started with.
This is a slight overcorrection, yielding a mean of 1.007, roughly corresponding to an average doubling after 100 years. Unless of course you want to model slight growth on average...
By my calculations, if you tone your suggestion down slightly so that a 9 results in x 1.115 instead of x 1.2, then the geometric mean becomes almost exactly 1, if you want a truly "fair" table.