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.
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)
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…
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).
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.
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.
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.
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
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%
