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Old December 21, 2010, 16:54   #37
Join Date: Jul 2009
Posts: 525
ewert is on a distinguished road
Originally Posted by d_m View Post
Just to clarify, there are three things we can talk about with the probability distribution of gold drops:

range: the range of possible gold drops (currently 1 - MAX_INT)

mean: the average gold drop (currently considered too low)

variance or standard deviation: relates to the expected deviation from the mean

So what I think we're arguing about is "infinite range" not "infinite variance" (I'm not sure what infinite variance would mean). I think the correct solution is actually to alter the mean (and optionally the variance) to get things to a level we want.

I don't see anything wrong with an algorithm with infinite range as long as it works.
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.
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