If you toss 10x 100 times a coin, its also very rare you will always get much more heads every 100 tries. and never one time more tails. Especially considering you have more chance to receive tails (read 2 kingdoms at 36% and not just all 30 kingdoms at 26%)
Sirrian would probably respond with at least half an essay, too bad he doesnāt frequent the boards any longer. Anyway, 1000 samples gives a very high confidence rating that the two probabilities arenāt just added up.
Iām afraid not, your tribute counters would be much higher. 
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See also:
(in which the total sample between all of them was much smaller, showed a trend, was investigated, was determined to not be working correctly, and subsequently āfixedā but the fix was not specified)
There is also a precedent of them accidentally leaving an entire kingdom off the tribute table for several months (it was impossible to tribute from that kingdom, skewing the values).
We could see a trend away from expectation with any given data set, no matter how big, it just becomes increasingly unlikely and eventually enough to be called āstatistically impossibleā. So the while the sample isnāt conclusive, there is no way weād be able to get that kind of data from our end either way. At the same time, this isnāt the 415th post of someone complaining about AI resurrects, devours, explodes, cascades, or anything else supplying anecdotal evidence and not actually recording anything. We have 1000 samples here. Not 1000 coin flips. 30,000 independent trials grouped into 1000 sets of 30 consecutive trials each, grouped into smaller sets of 100 that show a trend. I think this deserves a bit more scrutiny than āyeah, but it could still happen because random is random so everything is working fine as is, but if you showed me a million samples, then weāll talkā.
This isnāt the same as the 415 other threads complaining about RNG or AI bias because they have a āfeelingā or they saw that one time that one extremely improbable event happening or a bunch of ābadā events happening more than they think they should but without recording any hard data, or with them starting with skewed data by recording the edge case first and ending on another arbitrary number where they got a result confirming their assertion. If it was, Iād be right there siding with the skeptics. I think this warrants investigation, or at very least a response. That way, when the next person comes up claiming they āfeelā their tributes are slightly lower than the expected 26%, I can just say āyeah, but its actually 24.8% because they are rolled independently but you canāt double tribute the same kingdom. Here is the dev response. Assuming that, these numbers are now much closer to the expected valuesā, and save them from either thinking the game is somehow ācheatingā them or gathering 1000 tribute samples (months of data gathering, mind you) and have it just brushed aside by āyeah, RNG is RNG, what can you do?ā.
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Thanks for this post! About the little quote of the kingdom skipped and never giving tributes: I am asking since now 2 years to have the option to see the kingdom names who awarded tributes with detailed explanation. But without success. 
I would love to see when I receive 10 tributes, the name of the 10 kingdoms who awarded the tributes with detailed explanation of glory, gold and souls gained from all of them. I still hope to see this feature one day.
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Yes we ācouldā, and its very possible. but I doubt it. For being close to max on the same system as @anon43026234 my tributes are not quite where they were ~4 months ago. Even adding a new Kingdoms has not pulled things up.
Unfortunately I have no recorded data, but frequently fire the game up just to collect so I keep an eye on it, for over two years now Iāve been watching Tributes totals.
I would not be surprised to learn that a small bug was accidently introduced a few months ago.
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Out of 1000 tributes what was your highest tribute?
I tracked my own data for a while some months ago. Probably close to 1000 tributes. I spent two or three months well below my expectation value. At one point I was more than 99% confident that I wasnāt getting the correct tributes. Made a thread and everything.
Then, the next month, I was so far above the expected values that things rapidly approached the mean again. I was pulling 12, 13 and 14-kingdom tributes like crazy.
I suspect, but obviously canāt prove, that Truxton is in a similar place to where I was. People who track tribute chances and get normal/high results donāt make threads about it.
In response to someone elseās question, I have seen 15-kingdom tributes multiple times. I donāt remember seeing anything 16 or higher, but those are so rare itās entirely possible that I wouldnāt have seen one anyway, even across months of tracking.
Edit: hereās my thread.
I was wrong about how many tributes I tracked. It was less than 1000, but easily thousands of individual chances for kingdoms to give tribute. Which, if they are all independent, is just as good as tracking tribute totals.
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As noted in the thread you linked, they specifically said they didnāt change any tribute values as of 3.1, but all the numbers posted in your thread would fit better if you assume tribute chance was 24.8% rather than 26. Pre April 2017, the 6% was being applied multiplicatively (so we were getting 21.2% per kingdom) and was supposedly fixed to be additive at that time (posted the link above), which should be 26% for three star and above kingdoms (before 9 star). Your thread was dated September 2017 and specified post 3.1, so all your data should have come from after that fix.
It looks like you didnāt post the numbers when you started trending back toward 26%, which I really think would be useful here. As of now, all data sets posted on the forums, including the ones you collected and were sent to you, are showing below the expected 26%.
Either way, if it does turn out they purposely implemented it in a different way that causes slightly lower numbers than expected but still a mathematically sound 6% (eg., independently rolled checks for the 6% statue and the 20% kingdom chance, as has been postulated, giving an effective 24.8%), Iād be fine with that (others might not be, but really, what could we do either way), it would just be nice to know. But if it is an actual mistake, it can be corrected.
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Good post. You may be on to something here, although Iād like a larger sample size. I suspect there may be an issue with the formula as you propose.
15 was my highest tribute. I received it 2 times (its expected to receive 3x a 15 tributes over 1000 tributes collected).
I havenāt cleared my recycle bin in months, which means I still have the spreadsheet. How convenient!
The last time I posted a table in my old thread, hereās what I saw:
| Kingdoms | # Times | Expected # | Difference |
|---|---|---|---|
| 0 | 0 | 0.04 | 0 |
| 1 | 0 | 0.42 | 0 |
| 2 | 3 | 2.05 | 1 |
| 3 | 9 | 6.47 | 3 |
| 4 | 15 | 14.8 | 0 |
| 5 | 29 | 26.0 | 3 |
| 6 | 44 | 36.5 | 8 |
| 7 | 56 | 42.1 | 14 |
| 8 | 30 | 40.7 | -11 |
| 9 | 29 | 33.4 | -4 |
| 10 | 19 | 23.4 | -4 |
| 11 | 8 | 14.2 | -6 |
| 12 | 8 | 7.50 | 1 |
| 13 | 2 | 3.44 | -1 |
| 14 | 1 | 1.38 | 0 |
| 15 | 0 | 0.49 | 0 |
The next many tributes came and went, and hereās what I ended up with:
| Kingdoms | # Times | Expected # | Difference |
|---|---|---|---|
| 0 | 0 | 0.10 | 0 |
| 1 | 1 | 1.00 | 0 |
| 2 | 4 | 4.94 | -1 |
| 3 | 16 | 15.6 | 0 |
| 4 | 42 | 35.7 | +6 |
| 5 | 72 | 62.7 | +9 |
| 6 | 93 | 88.1 | +5 |
| 7 | 115 | 102 | +13 |
| 8 | 81 | 98.3 | -17 |
| 9 | 63 | 80.6 | -18 |
| 10 | 61 | 56.6 | +4 |
| 11 | 29 | 34.4 | -5 |
| 12 | 18 | 18.1 | 0 |
| 13 | 10 | 8.32 | +2 |
| 14 | 4 | 3.34 | +1 |
| 15 | 2 | 1.17 | +1 |
| 16 | 0 | 0.36 | 0 |
These numbers are a good mix of above/below average. Earlier versions of this table, as shown above, were always below expectation above my average value, and always above expectation below the average. Itās still not quite at average, but itās better. The net success rate is about 25.5%, with a 95% confidence interval that includes both 24.8% and 26%.
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I understand what you mean, but thats not what I experienced. I even received 3 more 12 tributes and 4 more 13 tributes than expected.
My problem was to see every new blocks of 100 tributes going always more than expected in the 0 to 6 tributes group. You can see in my opening post that, excepted the 0 tribute that I never received, all other tributes in the 0 to 6 group were collected more than expected. Especially more strange when you consider my expected numbers are for 30 kingdoms at 26% but I had in reality 1 and then 2 kingdoms at 36% for the whole 1000 tributes collected! (I just had no idea how to calculate the probabilities when not all kingdoms are at same chances. Thats why I used the probabilities for 30 kingdoms at 26%).
But as some players mentionned above, the problem could come from how the guild statue give the 6% bonus. (26%, 24,8% or 21,2%) I hope a dev will explain us how its calculated.
Focussing only on the opening post - I donāt think those results are skewed far south enough of the expected values to draw anything other than a minor sense of unease. 35% in the low band instead of 30% is hardly disastrous.
I am not rubbishing the post @anon43026234 or the effort behind it, but I donāt think anyone needs to be too alarmist just on this data.
I do sense myself that tributes feel lowā¦ but thatās an emotional response, I have no evidence reallyā¦
Thanks for posting these 2 stats.
You can see you have same prob as me the 2 times.
on 1st page you received 15 more tributes in the 0 to 6 tributes group and 11 less than expected in the 7 to 30 group.
On the 2nd page, you received 19 more tributes than expected in the 0 to 6 group and 19 less in the 7 to 30 group.
You might be right but keep in mind I had 1 kingdom at 36% chance (for the 1st 837 tributes collected) and then 2 kingdoms at 36% chance (for the last 163 tributes collected) so I had in reality for the whole 1000 tributes LESS than 30,3% chance to receive a tribute in the 0 to 6 group.
My math have limits and I cant tell you exactly the exact probability, but obviously lower than this 30,3%.
I bet the whole game (including tributes) runs from the same questionable & streaky RNG algorithm.
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As we discussed with Grundulum previously about his data, to actually reliably do any statistical test, the data has to be recorded in the order it was generated. Then, it is possible to determine whether t is random and what is the expected 95% or 99% confidence interval. If this is the case, please let me know and upload your spreadsheet somewhere. I can run the tests or tell you how to do it.
The rolls for tribute are apparently run on the server. So, that means most likely pRNG seed based on server clock for a particular session sequence. To put it bluntly, it might be not very random but it might as well be. This can be only determined with exact sequence from tribute 1 to tribute 1000.
it is also possible to compare the results with a simulation which can be created in Excel (any version after MS Office 2010 will suffice).
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In either case, I had some spare 20 minutes and decided to run a simulation and compare it to your data.
Here is the results in the form of a frequency plot:
Descriptive statistics tests show that distribution is not normal according to both Shapiro-Wilk or Grubbās tests and so the samples cannot be compared by regular Studentās t-test. Hence, I used a non-parametric test for comparison, Mann-Whitney test for two independent variables. The P values were: 0.47 for one-tail and 0.94 for two-tail distributions. It is obvious from the graph that we have a two-tailed distributions in both samples, so the correct value is 0.94. Since it is larger than significance value for the test (0.05), it is very safe to conclude that two sets of samples come from the same distribution and are not different.
Because I used same pRNG to generate the simulation (Mersenne-Twister) that the server is apprently using, it is obvious that your data fall into at least 95% confidence limit of the expected values. So, there is nothing wrong with your tribute, all numbers are OK, server is working just fine. Everyone can relax and take a deep breath. 
Whether individual runs are random and independent, is another story however. But as I said previously, exact sequence of data is required to estimate that. Here we just see an example of Law of large numbers.
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Hi, I unfortunately dont have the exact sequence of my 1000 tributes collected. But they came randomly in a normal way for all the process. I only have infos for each new block of 100 tributes (started only that after 300 tributes collected where the problem of having too much tributes in the 0 to 6 group was already at +24). Every new block of 100, this problem was getting bigger.
Also did you take in count that I wrote expected probabilities for 30 kingdoms at 26% but in reality I had better probabilities for all my 1000 tributes! (1 kingdom at 36% for the 1st 837 tributes collected and 2 kingdoms at 36% for the last 163 tributes). I used probabilities for 30 kingddms at 26% because I had no idea how to calculate probabilities if 1 or 2 kingdoms are at 36%.
So in conclusion, if the 6% bonus from statue is adding (20+6=26%), then there is definately a problem here. But if its cumulative (24,8%), then that could just be bad luck.
Im still waiting for an answer from a dev on how the 6% of the statue is working.
Yes, of course. 
It is easier if you make a spreadsheet in Excel for these calculations. Assuming the events are independent, just replace one or two numbers (0.26) with 0.36. However, this independent assumption might not be true and might need to be checked. Unfortunately, the data you collected might not be in suitable format to make this happen.
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