# Can you please verify that Kingdom Tribute chance (w/Guild bonus) is working as intended?

26 Kingdoms* at 3-stars or better (double tribute chance = 20%).
Guild bonus +6% = 26% total chance of Tribute

The expected distribution at 26% has a roughly 50/50 breakpoint at 7:
6 or fewer Kingdoms provide tribute: 46%
7 or greater: 53%

8 or greater: 35% [1 in 3]
9+: 21% [1 in 5]
10+: 11% [1 in 9] We should observe 10+ around once per day on average, sometimes 0, sometimes twice.
11+ 5% [1 in 20]

But the Tributes I’m seeing (smallish sample size) don’t match that. Possibly the Guild bonus isn’t working, or some of the Kingdoms–perhaps the newer ones–aren’t.

Here’s the calculator I used. Maybe my numbers are wrong, maybe it’s my sample size, or maybe it’s just my perception. Any of those are likely.
http://stattrek.com/m/online-calculator/binomial.aspx

I’m not saying that it’s wrong, I’m just asking for someone to verify. Run 10,000 iterations and observe the rates.

*_ I don’t level Silver Drakon (to preserve low Magic) so I haven’t finished Silverglade yet.

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My guess is the 6% from guild is not +6% but rather *1.06.

So the 20% chance becomes 21.2% and not 26%

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Decided to start tracking mine. 27 kingdoms. All at 3*+ so 20% base chance. Guild bonus on.

16 collects so far. Since there is no distinction between kingdoms (as I’m not looking at gold/glory), we can treat that as 16*27 = 432 individual trials. On those collects I totaled 91 kingdoms sending tribute.

91/432 = 21.06%

Margin of error (95% confidence interval) is 1.95Sqrt(p(1-p)/n) where p = 0.2106 and n = 432. Pplugging is gives us 0.03825, or 3.825%

As such, I can say with 95% confidence that the actual chance of a kingdom sending tribute is between 17.24% and 24.89%, which includes the expected value 21.2% but does NOT include 26%.

So I’m pretty sure the real value is 21.2%. I’ll keep tracking for a few days to build a larger sample size though.

edit: 20 collects now. 95% confidence interval is 16.8 to 23.6
edit: 25 collects. 95% confidence interval is 17.14 to 23.16
edit: 35 collects. 95% confidence interval is 16.66 to 21.65 (run of bad luck)
edit: 40 collects. 95% confidence interval is 16.92 to 21.60 (gap is closing)
edit: 45 collects. 95% confidence interval is 16.82 to 21.21 (another single kingdom tribute, yuck)

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What spurred this was one day receiving 10 Kingdoms in Tribute, and being surprised.

Then I blinked and thought “Wait, 10 shouldn’t be that rare [at 26%].”

I like your theory, although I wonder why they are so stingy with the Tribute bonus if it’s so relatively insignificant.

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Multiplicative makes more sense though. If you have a level 1 kingdom with 0 stars, it has a 1% chance. You wouldn’t expect that to jump to 7%.

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In that sense yes (or “perhaps” at least ;)), but if it is really so it’s the only place in this game where percentages are calculated in such way. Everywhere else it simply adds up. So a bit more thorough explanation would be welcome…

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We now have a ton of evidence across multiple threads (Kingdom Tribute - Is Guild Tribute Chance Bonus being accounted for? Bug?, plus my own data that I’ve been collecting but hadn’t published yet) that the bonus is multiplicative. I agree that it’s incredibly misleading. It’s also kind of pitiful compared to the yellow statue bonus.

[Math follows, assuming 27 level-10 kingdoms at 3+ stars, and both red and yellow statues maxed]

I am not sure one additional gem every three collections (and 3.2 tribute points in bonus tribute each time) is equal to 5.4 tribute points every time you collect. It does provide another way to compare how much the devs think a single gem is worth: 6.6 tribute points (165 gold, 27 souls, or 6.6 glory).

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Maybe I should amend my request to “Please label the bonus accurately.”

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could this be a bug with intended to be a +6% but turned out calculated wrong on development side?

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It is possible. We’d need to ask @Sirrian or @Nimhain or @Saltypatra for clarification though.

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Might be a separate issue, but are we sure tributes are calculating correctly? This seems to have changed dramatically in the past week or so.

I have all kingdoms at level 9 or 10 and 3* or better, so at least 18% there, plus whatever the guild bonus is. Even if I use a flat 18% in a binomial model, I should be getting 4+ tributes 74% of the time, 5+ 55% of the time, etc. However, I am getting 1-3 kingdoms about 75% of the time, which seems highly unlikely.

Anyone else having similar experiences?

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Looking normal to me. I started recording all my tributes when I saw this thread.

All 27 kingdoms at level 10 and at least 3-stars, in a guild with 5% tribute chance bonus.

So far, I’m at 21 collects: with 137 tributes for 567 samples. (~24.16% rate of success)

says my 95% confidence interval is: 0.2064 to 0.2769

Compared with Rasper’s data, I appear to be on a lucky streak.

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Today has been abysmal, last 10 collects I have a total of 44 kingdoms.

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My lucky streak is over too. With 1242 samples, I’m down to 22.14% rate of success.

95% confidence interval: 0.1983 to 0.2445

I have a feeling this isn’t working as expected as well, my tracking does not fit within the % range, also low 20% for this.

What I’m expecting…
Tribute Chance % + Guild Bonus Tribute Chance % (20%+5% = 25%)

What I think they are doing…
Tribute Chance % * Guild Bonus Tribute Chance % (20%*5% = 21%)

Random is random. I know I’m in an unlucky run atm (of the last 50 I have 5 that were just 1 kingdom, and another 5 that were just 2). I remember getting a few 13s and even a 17 so things can turn around.

Here is my dataset

Updated my dataset, 150 tributes

My average has climbed to 19.7%, still shy of the targeted 21.2% but at least I’ve had a good run recently. If it were capped at 25 kingdoms my chances would be 21.16% which is pretty spot on.

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Just a reminder that my guild’s statue is at 5%, not 6% like yours.

But yeah, I think we’re pretty confident now that it’s a multiplicative and not additive bonus.

the difference between my estimated 21.2% and your 21.0% should be minimal. Amusing however that you got 23 more kingdoms, in 4 less attempts, with a lower % chance

Clearly, the RNG deity is just making up for your 17 kingdom tribute, which is all the more lucky at 21.2% instead of 26%!

1 in 310,749 of getting at least 17.
1 in 2,130,379 of getting at least 18.

(at least until the next kingdom comes out).

yeah, that was a Once in a lifetime event. I’m going to track my tributes till I have 100, hoping the rng evens out, should bring the margin of error down to +/- 1.5%