TL;DR - Data I collected shows guild tribute bonus NOT being added to city tribute chances.
Results
I’ll start with result - I’ve documented below how I did the calculations as well as shared the spreadsheet with the data & calculations. To clarify - the below chart show odds of X number of cities sending tribute - NOT how much tribute you get.
For the chart below & for duration of my data collection -
- All 25 cities at lvl 10, all cities below 3 stars [every city has 10% tribute chance]
- Guild bonus = 2% [Red statue @ lvl 38]
Measured data was taken over the course of 7 days where I collected tribute ~70 times.
As is evident - Measured rates differ pretty substantially to what the statistical calculations says they should be.
BUT - if I set guild bonus = 0% & repeat the calculation - look how much closer measured is to calculated.
My question - is there a bug in the code not factoring guild bonus into tribute calculations?
Assumptions
When tribute is collected, each city independently checks to see if it should send tribute. i.e. 25 independent trials, each with their own chance of success.
The guild tribute bonus (Red & Yellow statues) applies to ALL cities. i.e. if guild tribute bonus is 5%, every city gets a 5% increase in tribute chance.
How to Calculate Tribute Chances
Two cases to consider here.
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All cities are the same lvl - represented by “Bernoulli Trials” - every experiment has the same chances of success. The odds are trivial to calculate and follow the binomial distribution.
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NOT all cities are the same lvl - represented by “Poisson Trials” - not every experiment has the same chances of success. Odds are much more complicated to calculate, typically solved by a mathematical technique referred to as convolution.
After a lot of research, trial & error, & dabbling in the R statistical tool, I made a google spreadsheet that will allow you to enter the tribute chance for each city and guild bonus. Found here.