Posted by: ollobrains
« on: June 12, 2012, 01:08:31 AM »5 day is the construction-fiancial bonus and yeah its fairly substantial
Posted by: Nathan_
« on: June 11, 2012, 11:49:20 PM »That is good to hear, I was running 5 day increments to test the extra wealth from shipping vs 30 days, but since I got nuts with financial centers that is hard to ferret out from the raw numbers(lots of civ ships running around though). Ultimately though my computer is too old for running like that so I'll be happy to return to 30day increments.
Posted by: xeryon
« on: June 11, 2012, 05:22:19 PM »So, what you are saying is that we were sort of correct on the leader advancement being stunted with 30 day increments? 
Posted by: Steve Walmsley
« on: June 11, 2012, 01:50:51 PM »I've checked the code. The chance of illness or death was based on exact time passed. The chance of bonus increase was a set amount per 5-day increment 
. I've corrected that for v5.70 so that everything is based on exact time passed.
Steve
. I've corrected that for v5.70 so that everything is based on exact time passed.Steve
Posted by: ollobrains
« on: June 07, 2012, 05:14:29 AM »yeah i read that thread about the coming leadership changes, steve hasnt logged in since may 27th so my guess its one of his little breaks, and if and when he returns to aurora development this month we might see some changes if he sees fit, the ideas presented by others are very grounded and sensible i guess its a matter of time and getting them in
Posted by: UnLimiTeD
« on: June 07, 2012, 04:41:23 AM »Within that long explanation of the basis for neat bell curves, I still see the possibility of vastly higher results, they just happen to be extremely unlikely, and it could go the other way around.
Though I've certainly noticed that ground war rages on a lot longer with 30 day increments, so when damage there isn't multiplied, it isn't that far off that Steve missed it with the bonuses themselves.
I suppose we can only be sure by asking him?
Though I've certainly noticed that ground war rages on a lot longer with 30 day increments, so when damage there isn't multiplied, it isn't that far off that Steve missed it with the bonuses themselves.
I suppose we can only be sure by asking him?
Posted by: xeryon
« on: June 07, 2012, 01:07:45 AM »That, is one hell of an explanation.
Some of it is over my head, but I understand enough. My thought, which I was struggling to convey, was that the average ends up being the same in both cases, but the possibility for extreme examples at either end would go up with more iterations. You tell me that is not the case and you appear to know vastly more then I do on statistics so I shall let that be. You have given me a few key terms I will take some time to study and familiarize myself with.
Some of it is over my head, but I understand enough. My thought, which I was struggling to convey, was that the average ends up being the same in both cases, but the possibility for extreme examples at either end would go up with more iterations. You tell me that is not the case and you appear to know vastly more then I do on statistics so I shall let that be. You have given me a few key terms I will take some time to study and familiarize myself with.
Posted by: sloanjh
« on: June 06, 2012, 11:31:55 PM »I know this is a studied and well known area, I just don't know what it is called.The general area is statistics, but I assume you knew that
. Maybe "Gaussian distributions" or "Poisson statistics" is what you're looking for. The important effect (for Gaussian distributions) is (roughly) the following:Let's say you have a bunch (a large number) of buckets, and a N times as many balls as you have buckets, and you randomly drop balls into buckets until all balls are in a bucket.
On average, each bucket will have N balls in it (because of the way you set things up). The statistical effect is that, if both N and the number of buckets are very large, then probability of finding a particular number of balls in a particular bucket will have a "Bell Curve" (Gaussian) distribution centered on N and of width proportional to sqrt(N). In practical terms, this means that most of the time, the number of balls "n" in a particular bucket will be between N-sqrt(N) and N+sqrt(N). I can factor out an N to write this a different way: between N*(1-sqrt(1/N)) and N*(1+sqrt(1/N)). The reason I wrote it the second was is because the +/- bit is the relative size of the fluctuations with respect to the average value. So the bigger N is, the smaller the relative fluctuations are (even though the absolute fluctuations are getting bigger).
Quote
Because of this distribution if you amplify the opportunities to score a hit by 6 fold. The chance of a given hit probability is very minimal, as you noted it is only a .15% increase or some such, but given the ten year span of 120 rolls verses 720 rolls that 0.15% chance builds and I envision a distribution more like this:I'm not sure what you're trying to say with your table - I think you're saying that you expect the second case to have more promotion "hits" than the first case. But the situation is exactly set up so this is not the case - the average value of hits is exactly the same in each case. For the 6% case, the average number of hits after each roll is increased by 0.06 = 0.06*1hit + 0.94*0hits. So after 120 6% rolls, you will on average have 7.2 hits = (0.06hit/roll)*120rolls. For the 1% case, the average number of hits after each roll is 0.01 = 0.01*1hit + 0.99*0hits. After 720 1% rolls you will on average have 7.2 hits = (0.01hit/roll)*720rolls, i.e. exactly the same. The higher number of hits is exactly balanced by the lower chance of getting a hit for each roll.
Now 7.2 isn't a very big value for N, so we're probably not very far into the large N regime. But the other important thing is to think about the difference between a single 6% roll and 6 1% rolls. For the 6% roll, you've got a 94% chance of no hits and a 6% chance of one hit. For the 6 1% rolls, you've got a 94.148% chance of no hits, a 5.706%chance of 1 hit, a 0.144% chance of 2 hits, a 0.002% chance of 3 hits, and even smaller chances of 4-6 hits. The important take away here is that I can replace a cluster of 6 1% rolls with a single roll that can have 0-6 hits with the probabilities listed above (i.e. an identical distribution) and then use these probability distribution to interprete a sequence of 120 random numbers either using this clustered distribution or using the normal 6% distribution. If I do that experiment, then there's only (roughly) a 1-in-5 (= 0.148*120) chance that I'll see any difference at all in the roughly 7.2 hits that I expect. And Gaussian statistics says that if you increase the number of rolls the relative fluctuations will go down, not up. Does that help you see why it's a small effect?
John
PS - All this assumes that there isn't a bug in the code and that Steve actually is multiplying by the appropriate factor for longer intervals. He certainly intended to do so, but he could have missed a spot.
Posted by: xeryon
« on: June 06, 2012, 01:31:33 PM »I have noticed too where you hit periods of highly active advancements. The streaky nature rather fits the RP style of the program and does not bother me.
Posted by: Erik L
« on: June 06, 2012, 12:46:07 PM »There is also the fact that the random number generator isn't truly random, and is generating streaks on occasion, but the effect I'm noticing is TREMENDOUS. About 1/2 of my leaders are 50%/50 labs or better, and on a 30 day game I usually get only 1 leader into that range. What rng is being used would be interesting to find out.
Given that it is written in VB6, it is most likely the built in random function. I'm not sure if Steve is seeding it or not, but whenever I used it, I seeded it with the number of seconds past midnight.
Posted by: Nathan_
« on: June 06, 2012, 11:34:04 AM »There is also the fact that the random number generator isn't truly random, and is generating streaks on occasion, but the effect I'm noticing is TREMENDOUS. About 1/2 of my leaders are 50%/50 labs or better, and on a 30 day game I usually get only 1 leader into that range. What rng is being used would be interesting to find out.
Posted by: xeryon
« on: June 06, 2012, 09:57:22 AM »Not being a mathematician I am having a hard time describing the effect I am thinking of.
If I have 100, or even 1000, cases I am working with there will be certain individuals which will more frequently score 'hits' then others and some that will score less. This would give a results list that had a few people at the bottom of the list, a wide distribution throughout the average band and then a few at reached exceptional. I know this is a studied and well known area, I just don't know what it is called.
Say you follow 10 leaders over 10 years and each leader has all other attributes being equal you would end up with a hit distribution somewhat like so:
Leader 1 - 0
Leader 2 - 2
Leader 3 - 4
Leader 4 - 4
Leader 5 - 5
Leader 6 - 5
Leader 7 - 6
Leader 8 - 6
Leader 9 - 8
Leader 10 - 10
Because of this distribution if you amplify the opportunities to score a hit by 6 fold. The chance of a given hit probability is very minimal, as you noted it is only a .15% increase or some such, but given the ten year span of 120 rolls verses 720 rolls that 0.15% chance builds and I envision a distribution more like this:
Leader 1 - 1
Leader 2 - 2
Leader 3 - 4
Leader 4 - 5
Leader 5 - 6
Leader 6 - 6
Leader 7 - 7
Leader 8 - 8
Leader 9 - 10
Leader 10 - 12
This is all just my brain giving out what appears to be logical to me.
If I have 100, or even 1000, cases I am working with there will be certain individuals which will more frequently score 'hits' then others and some that will score less. This would give a results list that had a few people at the bottom of the list, a wide distribution throughout the average band and then a few at reached exceptional. I know this is a studied and well known area, I just don't know what it is called.
Say you follow 10 leaders over 10 years and each leader has all other attributes being equal you would end up with a hit distribution somewhat like so:
Leader 1 - 0
Leader 2 - 2
Leader 3 - 4
Leader 4 - 4
Leader 5 - 5
Leader 6 - 5
Leader 7 - 6
Leader 8 - 6
Leader 9 - 8
Leader 10 - 10
Because of this distribution if you amplify the opportunities to score a hit by 6 fold. The chance of a given hit probability is very minimal, as you noted it is only a .15% increase or some such, but given the ten year span of 120 rolls verses 720 rolls that 0.15% chance builds and I envision a distribution more like this:
Leader 1 - 1
Leader 2 - 2
Leader 3 - 4
Leader 4 - 5
Leader 5 - 6
Leader 6 - 6
Leader 7 - 7
Leader 8 - 8
Leader 9 - 10
Leader 10 - 12
This is all just my brain giving out what appears to be logical to me.
Posted by: sloanjh
« on: June 06, 2012, 08:54:43 AM »If you track one individual leader over time his advancement rate over time is realistically the same either way. But when you have 100's of leaders active things really change. Due to randomness certain leaders will score more frequent successful rolls for advancement while others will never advance due to never scoring a hit. Over time you will have completely stagnated leaders and others that seem to rocket to the top out of pure luck.
This effect is small. For the case you cite (1% chance 6 times vs. 6% chance once), the probability of no promotions in the timespan is .99^6= 94.15% vs. 94%. Roughly speaking, this means that less than 0.15% of the time will you get multiple promotions in a single span in the fine-grain case (to make up for the higher probability of nothing happening).
John
Posted by: xeryon
« on: June 06, 2012, 08:16:27 AM »I may be way off base here but I think the issue was one of probability. This is my thought:
A 5 day increment rolls once for each given leader to check for advances while a 30 day increment also rolls once for advancements but the chance for advancement is increased 6 fold. A very simple 5x6 = 30 ratio. The problem with probabilities is that if you have a 1% chance for improvement rolled 6 times compared to a 6% chance to improvement rolled once you will score a hit more frequently on the multiple rolls. Your chance to gain at least one increase in a 30 day period is the same, but with the ability to gain an increase 6 separate times in a 30 day period you have a possibility of the same leader gaining advances multiple times in the same 30 day period.
Over a year you end up rolling 12 times as 30 day and 72 times as a 5 day. If you track one individual leader over time his advancement rate over time is realistically the same either way. But when you have 100's of leaders active things really change. Due to randomness certain leaders will score more frequent successful rolls for advancement while others will never advance due to never scoring a hit. Over time you will have completely stagnated leaders and others that seem to rocket to the top out of pure luck.
A 5 day increment rolls once for each given leader to check for advances while a 30 day increment also rolls once for advancements but the chance for advancement is increased 6 fold. A very simple 5x6 = 30 ratio. The problem with probabilities is that if you have a 1% chance for improvement rolled 6 times compared to a 6% chance to improvement rolled once you will score a hit more frequently on the multiple rolls. Your chance to gain at least one increase in a 30 day period is the same, but with the ability to gain an increase 6 separate times in a 30 day period you have a possibility of the same leader gaining advances multiple times in the same 30 day period.
Over a year you end up rolling 12 times as 30 day and 72 times as a 5 day. If you track one individual leader over time his advancement rate over time is realistically the same either way. But when you have 100's of leaders active things really change. Due to randomness certain leaders will score more frequent successful rolls for advancement while others will never advance due to never scoring a hit. Over time you will have completely stagnated leaders and others that seem to rocket to the top out of pure luck.
Posted by: ollobrains
« on: June 05, 2012, 03:15:50 PM »so run 5 days cycles
