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1000 tributes collected. Here are the results. Worrying

I noted what amount of tributes I received for 1000 times.

Before I start, an important precision: All my expected probabilities are for 30 kingdoms at 26% chance BUT all my 1000 tributes collected had better probabilities! The first 837 tributes I had 29 kingdoms at 26% and 1 at 36% (Ghulvania) and the last 163 tributes I had 28 kingdoms at 26% and 2 at 36% (Ghulvania and Khaziel).

The probability to receive a tribute in the 0 to 6 tributes group is 30,3%.
The probability to receive a tribute in the 7 to 30 tributes group is 69,7%.

That means its expected to receive for 1000 tributes: 303 tributes in the group 0 to 6 and 697 tributes in the group 7 to 30.

I received 356 tributes in the 0 to 6 group and 644 tributes in the 7 to 30 group.

After 300 tributes, I was already with 24 more tributes received in the 0 to 6 group.
After 400 it was +29. After 500 it was +40. After 600 it was +43. After 700 it was +52. After 800 it was +54. After 900 it was +52 and After 1000 it was +54.

What does that mean? Despite the fact that my probabilities were better than 30 kingdoms at 26% as I had also 1 and then 2 kingdoms at 36%. Every blocks of 100 tributes gave me more than expected tributes in the 0 to 6 group!! Only 1 block (the 800 to 900) gave me +2 more tributes than expected in the 7 to 30 group! But for that I had to have 2 kingdoms at 36% (for the 63 last tributes of this block) and the final block from 900 to 1000 again gave me 2 more tributes in the 0 to 6 group despite the fact I had this time 2 kingdoms at 36% for the whole 100 tributes in this last block!! :thinking:

Here are the details for each tribute:
0 tribute: 0 (0)
1 tribute: 3 (1) +2 (Expected to receive 1 in 1000 tributes but I received 3)
2 tributes: 11 (6) +5 (Expected to receive 6 in 1000 tributes but I received 11)
3 tributes: 29 (21) +8
4 tributes: 52 (50) +2
5 tributes: 106 (91) +15!
6 tributes: 155 (133) +22!
That is 54 more than expected for this group 0 to 6.

7 tributes: 140 (161) -21! (Expected to receive 161 but I received only 140)
8 tributes: 152 (162) -10!
9 tributes: 141 (139) +2
10 tributes: 95 (103) -8
11 tributes: 45 (66) -21!
12 tributes: 40 (37) +3
13 tributes: 22 (18) +4
14 tributes: 7 (8) -1
15 tributes: 2 (3) -1
16 to 30 tributes: 0 (1) -1
That is 54 less than expected for this group 7 to 30.

Now if a math specialist could indicates me the probabilities to receive tributes in the 0 to 6 group and in the 7 to 30 group for 29 kingdoms at 26% and 1 kingdom at 36% and also for 28 kingdoms at 26% and 2 kingdoms at 36%. Would be cool.
For 30 kingdoms at 26%, its 30,3% for 0 to 6 group and 69,7% for 7 to 30 group. Obviously with 1 or 2 kingdoms at 36%, the chances will lower in the 0 to 6 group and raise in the 7 to 30 group, which should indicates even more that there is a problem here.

13 Likes

Have we received any info on how that 6% guild statue chance actually factors in? Three possibilities:

1.) Strict addition, 20% + 6% = 26%
2.) Multipilcation, 1 - (1 - 0.2) * (1 - 0.06) = 24,8%
3.) Fraction of base amount, 20% + (6% of 20%) = 21.2%

Which of those three cases match your measurements better?

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Not enough statistical information is present to draw a firm conclusion about the sample. Without any analysis work performed on in the sample presented, drawing a meaningful conclusion about the sample is not possible.

For example, just because your result for 6-tributes is 22 away from your expected value, doesn’t necessarily make that deviation statistically significant. More information about the sample is needed.

What’s the standard deviation of the sample? What’s the confidence interval used in your analysis?

Also, the fact that you note that 12 and 13-tributes have a positive variation against expected values is contradictory evidence against the negative bias you are claiming that your sample is exhibiting.

Although, at first glance, the data might suggest negative bias in your sample, it doesn’t fit the mold of a negatively-shifted bell curve towards lower tribute quantities well.

Therefore, IMO, the evidence presented is inconclusive and thus unconvincing of the OP’s claim, as it currently is presented, without some statistical number crunching first.

3 Likes

Very interesting! My results correspond to 30 kingdoms at 24,83%.

But honestly, I can bet on 100 players, 100 will understand that these 6% bonus means that we have 26% chance! (or 36%) if its truly option 2 of what you say, then devs must say it because it cant be more misleading.

edit: well I still had 1 kingdom 9 stars for the 1st 837 tributes and 2 kingdoms 9 stars for the 163 last tributes so even if your option 2 is what is in action, it still feel unlikely. (but less unlikely than before I can admit)

1000 tributes collected are enough imo. Especially if you consider that my expected numbers are for 30 kingdoms at 26% chance but ALL MY 1000 tributes collected were with 1 kingdoms at 36% for the first 837 tributes and even 2 kingdoms at 36% for the last 163 tributes collected.
And despite of that, every new 100 blocks of tributes were all giving more tributes in the 0 to 6 tributes group.

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1, 2, 3, 4, 5 and 6 tributes are all above expected value! And that was the case for every new block of 100 tributes! Excepted the 800 to 900 block, but at that time I had 2 kingdoms at 9 stars. But then the last block 900 to 1000 still gave me 2 more tributes in the 0 to 6 group.

Its not contradictory! If you take in count the whole group of 7 to 30 tributes, thats 54 less received than expected.

9 tributes also had a positive number but thats too few to counter the deficit of 7,8,10,11,14,15,… (54!)

1000 tributes from one player doesn’t sounds enough…
Now, 1000 tributes out of 1000 players would probably be.

What @Lyrian meant, i believe, is that you could simply have an odd result pending to insatisfactory results and that the expected results are biased by the simple fact that you had expected results to begin with.

But congratulations for your effort anyway.

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if my 1000 tributes were all with 30 kingdoms at 26%, I would say its unlikely but still possible. But not with 1 (for the 1st 837) and then 2 kingdoms at 36% for all the 1000 tributes tracking.
What feels just not possible is that every blocks of 100 tributes were aggravating the problem.

Now remains this option about that the 6% of statues are in fact 4,8% (I dont understand how the guy who posted that arrive to this number but that could explain things)

1000 samples is enough to at least show a trend, especially with pretty much all groupings off expected values in the same direction even within subsets. Just because the data is not conclusive doesn’t mean it should be ignored.

7 Likes

Could a dev clarify how the guild statue bonus about tribute chance is working, please?
with 20% base bonus and 6% bonus from statue, do I have 26%?
How are calculated these 6%? Honestly any normal person will believe that it give 26%, no?

@Cyrup @Ozball

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But in the same sense, we could have 1000 samples showing a trend in the different direction. That’s also possible but just as well not very conclusive…

Keep in mind that my true tribute chances were higher for all my 1000 tributes collected than the expected numbers I wrote (I didnt know how to calculate 29 kingdoms with 26% and 1 kingdom with 36% and also 2 kingdoms with 36%), but its aggravating the problem by a lot.

Yes, i understand. It’s a shame that we don’t have more data collected in the same fashion to have more samples.

All i’m saying is that you could end up with a positive variation instead of a negative one.

I agree with you. But believe me, if you did this 1000 tributes data and saw every new block of 100 tributes everytime going in the same direction, things become crystal clear.
Now we can wait for a dev to clarify how the 6% bonus from statue really work because that could explain things. For me, its clear that from 20%, I go to 26%. If not, thats extremely misleading to say the least.

2 Likes

I agree, but as i said before it feels a little biased from you to expect very solid and conclusive results.

Using the good old “Coin Toss” example you could make 1000 tosses and obtain:

  • 540 Heads
  • 460 Tails

Which is a deviation from the expected 500/500 for each side. Now if you compare the results with other 1000 people then the deviation would be very small and close to an acceptable 50% for each side.

But you certainly know that already, i just think you are disappointed with the results because your work was not easy and surely took a lot time, but until we get some clarification of about the statue bonus that’s it. Again, congrats on your work.

Thank you! :grin: It was indeed quite a long work! :sweat_smile:

Just about you coin example, I totally agree I could have 540 heads and 460 tails with 1000 tries. For 50% chance tail and 50% chance head. But with 2 kingdoms at 36%, its like since begining I had more than 50% chance for tails and less than 50% chance for head and still end up always with same result every new block of 100 tributes. Oh well maybe EXTREME bad luck for me…that can happen but thats clearly not what I believe.

Looking at the data, it seems somewhat likely that the kingdom tribute chance and the statue tribute chance are considered two isolated events. Meaning that for each kingdom you get two rolls, one on the kingdom chance and one on the statue chance, if either one hits you receive tribute.

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There is no “gambling fairy” that makes sure that, by the time you reach some number of trials, you have exactly the “right” number of results for every option.

If you toss a coin 1,000 times, it is very rare you’ll get 500/500.

If you roll a D4 1,000 times, it is very rare you’ll see 250 of each face.

If you roll a D10 1,000 times, it is very rare you’ll see 100 of each face.

What Ivar means is, in all of these cases, if you look how far “off” you are and quantify that “miss” with a number like standard deviation, we expect that as “number of trials” gets bigger, or as more people do 1,000 samples, that deviation will get smaller and smaller.

So while it’s rare to get 500/500 out of 1,000 coin tosses, when you get to 10,000 tosses it’s more likely you are CLOSER to 5000/5000 than you were to 500/500. But if, as you accumulate more and more data, you get further and further away from the expected result, things get concerning.

But probability is a cruel mistress. It is completely within the realm of possibilities that you could get a 9999/1 result out of 1,000 coin tosses. Especially if you aren’t taking video to prove it. How many samples is “enough”? It can be subjective.

Considering how many kingdoms there are and the relatively low probability of any one kingdom giving a tribute, 1,000 seems like a small (but tedious) number of trials. I’d spend more rolls proving a D20 is fair than I’d spend coin tosses.

Ok, thanks! I will still wait for a dev to confirm that but it transform the impossible into just a very very bad luck thing.
Now could I receive 2 times a tribute from the same kingdom? One time with the 20 or 30% and then 1 time with the 6%? :laughing: