December 21, 2010, 05:37  #31 
Prophet
Join Date: Mar 2008
Posts: 2,712

BTW  when I did no selling I had the money drop multiplier scale, x2 on DL1, x3 on DL2, and x4 beyond that to encourage people to go down at least a few levels. Are you doing anything like that?

December 21, 2010, 06:38  #32 
Knight
Join Date: Jul 2009
Posts: 523

This is so deja vu from what I had.
The "infinite variance" formula, which supposedly retains same "mean" (no idea, maybe it does, since a longint amount of gold can drop or whatever), is the main culprit. First there is an average defined per dlvl. Then spread. But the average is destroyed (lowered markedly) by the "infinite variance" part, as it drops to what was it 0.4/1.4 approx on half of the drops. It needs to pass three 50% checks to get back to average. So 87.5% of chosen "averages" are instead at or well below average, 50% being only around 28.5% of the chosen supposed "average". Sure, in theory you could get a gigaziga amount of gold from one single drop. But that is just plain stupid game mechanics in a game design / game balance sense. The equivalent of winning in lottery. I once won a semijackpot. Townperson dropped over 5k with initial noselling changes that still retained this stupid "infinite variance" snippet. I actually first thought I had made a mess. Then I finally actually READ the "infinite variance" code, it boggled my mind ... 
December 21, 2010, 11:15  #33  
Angband Devteam member

Quote:
This is interesting. The infinite variance stuff was put in by Pete Mack, who doesn't usually make elementary mistakes. I think what you're saying is that 87.5% of drops are below average, but the remaining 12.5% are so much higher that they keep the mean unaffected. So indeed it is a bit like wandering around waiting until you "hit the jackpot". It was originally put in to make gold drops more interesting, but perhaps it has had the opposite effect. On the main agenda: Buzzkill 1, Eddie 0. no_selling can never be "simply a different way to play", as the shopping aspect has such fundamental impacts on the game. Given that every player with selling on has a different threshold to which s/he will prioritise stuff to sell over other uses of slots, it is impossible to balance no_selling with that. So a lot of people will find no_selling a challenge game  nowhere near as tough as ironman, but a lot more limited in the amount of buying they can do. That's why it's an option. Now, if DaJ and Eddie both had a x4 mult (from dl3 onwards) of 3.0.9 gold drops, then the only datum I need is: by what factor were 3.0.9's gold drops reduced in 3.1.0? Can anyone tell me this to save me an hour's faffing about with git? 

December 21, 2010, 12:30  #34  
Knight
Join Date: Jul 2009
Posts: 523

Gah yeah mixed with median in my mind, sorry, as said elsewhere talking mathglish gets funky sometimes for me. =P
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December 21, 2010, 15:30  #35 
Prophet
Join Date: Dec 2009
Posts: 7,684

I don't have hard numbers for you, but I'd guess by a factor of 2.5 or so. Used to be townspeople would drop gold in the 1530 range; now they drop in the 612 range.

December 21, 2010, 15:43  #36 
Angband Devteam member
Join Date: Aug 2008
Location: Philadelphia, PA, USA
Age: 36
Posts: 1,516

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. EDIT: Doing a bit of research, some distributions don't have a variance, so maybe that is what infinite variance means. I haven't looked at the actual method used yet, but I do know of distributions which have infinite range but have a mean and a variance (the exponential distribution, for instance). I am not some kind of statistics expert though so people should feel free to correct me if I'm wrong. Last edited by d_m; December 21, 2010 at 16:03. 
December 21, 2010, 15:54  #37  
Knight
Join Date: Jul 2009
Posts: 523

Quote:
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. 

December 21, 2010, 16:02  #38  
Angband Devteam member

Quote:
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. 

December 21, 2010, 16:12  #39 
Prophet
Join Date: Dec 2009
Posts: 7,684

How about just rolling Nd6, where N is determined by the treasure type? Copper = 5, adamantite = 200, everything else is inbetween. Nice and simple, known distribution, easy to balance. I'm not really seeing the valueadd in making this particular formula supercomplicated.

December 21, 2010, 16:47  #40  
Angband Devteam member

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