More Histograph attempts
- Thread starter Denniz
- Start date
a space oddity said:Don't worry, I am currently at turn 277 and you caught up with me, scores are about equal at that point.
That's inconceiable!
Are you playing the Mayan? If you are the Mayan, the Ottoman won't stand a chance in the long run (since you have extra food bonus and your population can grow faster). IIRC, my game was in PTW and I saved a military great leader for the Longvity; may be that would help explain why I seem to catch up at the moment.
It is not just a matter being above your curve in the 6th century, but "staying" above your curve til the end. The jury is still out on that.Moonsinger said:It seems that you're all doing very well above my curve.
@space, I'm on my work computer right now so I will have to put up my happiness vs. territory graph later. That one big jump of mine has me curious. I am going to have to figure out what all when on during that time.
a space oddity said:
I don't get it! How do you come up with the formula for the people points? For example, total score = (happy people * 2) + content + territory + future tech. So far, we have the total score, but we don't really know many of them were content or happy.
you dont know how many are happy, content or specialists..Moonsinger said:
but you can eliminate the territory and future techs part.. not far enough along in techs for FT, and the territory values are part of the data viewer gives
It is also unknown how many unhappy and resisting pop you have
the people graph is: 2*happy + content + specialists
if you were trying to balance happy and unhappy people as close as possible to maximize gold, then the graph would give number og pop pretty closely.. however that is unlikely in a milk game... it is more likely most of the pop is happy
meaning as long as your cities are not riotting or you have lots of resistors, and;
A = 2*happy + content + specialists,
then real number of pop lies between:
A / 2 <= pop <= A
Gyathaar said:
Ok, I'm willing to settle for the graph of A, but how do you calculate A? This is what we know from the data that Dianthus provided:
Turn, Year, Culture, Score, Power, Cities, Territory (Tiles), Territory (%)
What is the formula for (2*happy + content + specialists) based on the given data? Basically, how many point do we get for each territory (tiles) or territory (%)?
Moonsinger said:
A(t) is A for turn t (where t is 0 to 540)
score(t) is score at turn t
d is difficulty level (1 is chieftain, 2 is warlord, 3 regent, 4 monarch, 5 emperor , 6 = C3C demigod or vanilla/ptw deity, 7 = C3C Deity, 8 = sid
A(t) = ( (t+1)*score(t+1) - t *score(t) ) / d - territory(t)
Gyathaar said:
Thanks a lot!
That's exactly what I was looking for. You are so smart! How did you figure it out in the first place?
@Gyathaar, please forgive me for follow up with a stupid question, but how do you come up with territory(t)? For example, at turn 540, my territory = 4561 tiles, what is my territory(t) in this case?
it is not that hard..
score(t) = sum(0,t-1)[(2*happy(x) + content(x) + specialist(x) + territory(x))*difficulty] / t
gives:
score(t) * t = sum(0,t-1)[(2*happy(x) + content(x) + specialist(x) + territory(x))*difficulty]
and
score(t+1) = sum(0,t)[(2*happy(x) + content(x) + specialist(x) + territory(x))*difficulty] / (t+1)
gives
score(t+1) * (t+1) = sum(0,t)[(2*happy(x) + content(x) + specialist(x) + territory(x))*difficulty] = sum(0,t-1)[(2*happy(x) + content(x) + specialist(x) + territory(x))*difficulty] + (2*happy(t) + content(t) + specialist(t) + territory(t))*difficulty
set
Y = sum(0,t-1)[(2*happy(x) + content(x) + specialist(x) + territory(x))*difficulty]
so
a) score(t) * t = Y
b) score(t+1) * (t+1) = Y + (2*happy(t) + content(t) + specialist(t) + territory(t))*difficulty
but a into b, and subtract with (score(t) * t) on both sides:
score(t+1)*(t+1) - score(t)*t = (2*happy(t) + content(t) + specialist(t) + territory(t))*difficulty
set A(t) = 2*happy(t) + content(t) + specialist(t)
score(t+1)*(t+1) - score(t)*t = ( A(t) + territory(t))*difficulty
gives:
A(t) = ( score(t+1)*(t+1) - score(t)*t ) / difficulty - territory(t)
(I did it in my head earlier thou
)
I left future tech out of this, since it wil be 0 most of the time.. I figured out where future techs fit in easier at one point by trying different score values from games into formula, and got that score really is the average of :
(2*happy + content + specialists + number_of_known_future_techs + territory)*difficulty for every turn so far in game
score(t) = sum(0,t-1)[(2*happy(x) + content(x) + specialist(x) + territory(x))*difficulty] / t
gives:
score(t) * t = sum(0,t-1)[(2*happy(x) + content(x) + specialist(x) + territory(x))*difficulty]
and
score(t+1) = sum(0,t)[(2*happy(x) + content(x) + specialist(x) + territory(x))*difficulty] / (t+1)
gives
score(t+1) * (t+1) = sum(0,t)[(2*happy(x) + content(x) + specialist(x) + territory(x))*difficulty] = sum(0,t-1)[(2*happy(x) + content(x) + specialist(x) + territory(x))*difficulty] + (2*happy(t) + content(t) + specialist(t) + territory(t))*difficulty
set
Y = sum(0,t-1)[(2*happy(x) + content(x) + specialist(x) + territory(x))*difficulty]
so
a) score(t) * t = Y
b) score(t+1) * (t+1) = Y + (2*happy(t) + content(t) + specialist(t) + territory(t))*difficulty
but a into b, and subtract with (score(t) * t) on both sides:
score(t+1)*(t+1) - score(t)*t = (2*happy(t) + content(t) + specialist(t) + territory(t))*difficulty
set A(t) = 2*happy(t) + content(t) + specialist(t)
score(t+1)*(t+1) - score(t)*t = ( A(t) + territory(t))*difficulty
gives:
A(t) = ( score(t+1)*(t+1) - score(t)*t ) / difficulty - territory(t)
(I did it in my head earlier thou
)I left future tech out of this, since it wil be 0 most of the time.. I figured out where future techs fit in easier at one point by trying different score values from games into formula, and got that score really is the average of :
(2*happy + content + specialists + number_of_known_future_techs + territory)*difficulty for every turn so far in game
Moonsinger said:
territory(540) = 4561
territory(t) = territory at turn t
syntax isnt really correct math syntax.. because ita bit hard to write that on board withou making images and insert into the posts
PS! does your head hurt yet?
I believe that there may be an error within your formula.
A(t) = ( score(t+1)*(t+1) - score(t)*t ) / difficulty - territory(t)
Which can be translated into this (I'm doing this in my head too):
A(t) = (X)/difficulty - territory(t)
Since difficulty in [1..8] there 1= chieftain and 8 = sid, It seems to me that the higher the level, the smaller result you shall get because whatever X divide by difficulty, the end result will get smaller as difficulty get bigger.
Were you just testing my math skill?
A(t) = ( score(t+1)*(t+1) - score(t)*t ) / difficulty - territory(t)
Which can be translated into this (I'm doing this in my head too):
A(t) = (X)/difficulty - territory(t)
Since difficulty in [1..8] there 1= chieftain and 8 = sid, It seems to me that the higher the level, the smaller result you shall get because whatever X divide by difficulty, the end result will get smaller as difficulty get bigger.
Were you just testing my math skill?
no.. its correct.. there is a reason for why the score in your huge sid milk is roughly 8 times higher than the score in the huge chieftain milk maps...
Gyathaar said:territory(540) = 4561
territory(t) = territory at turn t
syntax isnt really correct math syntax.. because ita bit hard to write that on board withou making images and insert into the posts
PS! does your head hurt yet?
Ok, it's time to put your formula to a real test. From my 88K on Sid, this picture shows my score at turn 540:
http://forums.civfanatics.com/attachment.php?attachmentid=89770
Using formula: A(t) = ( score(t+1)*(t+1) - score(t)*t ) / difficulty - territory(t)
A(540) = 47837.6 + 15218.0 = 63055.6
territory(540) = 88553 - 63055.6 = 25497.4 (assuming that future tech = 0)
It seems to me that territory(540) can't be equal to 4561.
formula wont work for turn 540, since you would need the score in turn 541 (2051)
for turn 539 (2049):
checking the save for real values of turn 539 (I assume same number of happy and specialists as in 2050)
A(539) = 2 * 4626 [happy people] + (168+1031+2148)[specialists]
= 12599
calculated using formula:
A(539) = ((88552 * 540) - (88461 * 539)) / 8 - 4561
= 17200.125 - 4561 = 12639
40 points off.. this is due to score numbers stored as integer values in C3C.. if you check with any vanilla or ptw saves, the scores each turn are given as floats, and you will get much more accurate numbers.. in c3c you get integer roundoff errors
Edit: I just realized that you had 31 or 32 future techs in 2049, so the real number was 12630 or 12631.. or just 8 or 9 points off.. which could have been caused by pollution aswell
for turn 539 (2049):
checking the save for real values of turn 539 (I assume same number of happy and specialists as in 2050)
A(539) = 2 * 4626 [happy people] + (168+1031+2148)[specialists]
= 12599
calculated using formula:
A(539) = ((88552 * 540) - (88461 * 539)) / 8 - 4561
= 17200.125 - 4561 = 12639
40 points off.. this is due to score numbers stored as integer values in C3C.. if you check with any vanilla or ptw saves, the scores each turn are given as floats, and you will get much more accurate numbers.. in c3c you get integer roundoff errors
Edit: I just realized that you had 31 or 32 future techs in 2049, so the real number was 12630 or 12631.. or just 8 or 9 points off.. which could have been caused by pollution aswell
here is a plot of the pop and future tech part of scores in the top chieftain,warlord,regent,monarch, emperor and sid huge milk games..
the chieftain game is very zig-zag due to integer roundoffs hurting much worse with lower numbers.
the chieftain game is very zig-zag due to integer roundoffs hurting much worse with lower numbers.
Gyathaar said:PS! does your head hurt yet?
Well mine certainly does.
Here I thought doing this graph would be easy. I "think" I have it right.
Note: The big jump coorresponds to serveral turns after ToA was completed.
Gyathaar said:
Ok, I got it now!
Thank you for being so patient with me!
Bartleby
Remembers laughter
Good luck guys. I'm hoping to start an emperor milkrun in the near future, but I know that I'm not really competing with yous.
