Thread: Gold and no_selling View Single Post
December 21, 2010, 17:02   #38
Magnate
Angband Devteam member

Join Date: May 2007
Location: London, UK
Posts: 5,057
Quote:
 Originally Posted by ewert Well the "infinite variance" is from the source code description (increase variance to infinity). With my bad mathglish, I can't really explain properly my objections for this sort of formula, in short it is a lopsided "exponentially growing" (each next step is 50% for 1.414 higher amount), and from my vague recollections of medical statistics, you can't use average values to properly depict the meanings of such a curve. The median being << mean or some such thing, and in this kind of non-gauss-curve-type graph/formula, the median is more proper to look at than mean. Anyways, this makes the formula extremely annoying to balance properly with mental work, leading to mostly just trial and error (too big, too small, change, blabla). This is due to having to calculate probability spread of what 1.414^x/0.414 results in for an average game (that one in a billion chance of a gigazillion fudges the average badly). Make it a normal gaussian curve (which I understand the avg+spread values will give, haven't looked at the underlying code but that is what I assume), so you can design it by mean values to what you want properly ... Apologies for my sucky mathglish.
Interestingly I find myself in agreement with ewert and not with d_m on this issue. I think infinite range is actually a *bad* thing: one exceptionally lucky early drop and the game will be quite severely unbalanced - though I guess this is no different from Maggot dropping a Holy Avenger. Even without infinite range, I think ewert is right that the median drop is a better measure of the game experience than the mean, since games are generally too short for the mean to be reliable.

So I think we have two choices: stick with infinite range and increase the median (which requires also increasing the mean, if my rusty maths is correct) ... or reject infinite range and make the true variance much less so that the median and mean converge.