Following patch 1.08, I’ve done a binomial distribution check on how the new equates to the old…
Prior to 1.08, if you had all 20 Kingdoms at Level 10:
Chance of 0 Tribute: 12.2 %
Chance of 1 Tribute: 27 %
Chance of 2 Tributes: 28.5 % (+ 2 gems)
Chance of 3 Tributes: 19 % (+ 10 gems)
Chance of 4 Tributes: 9 % (+ 15 gems)
Chance of 5 Tributes: 3 % (+ 20 gems)
Chance of 6 Tributes: 1 % (+ 20 gems)
Chance of 7 Tributes: 0.2 % (+ 20 gems)
The end result was that, on average, you could expect 4.66 gems on average per cash collect.
Since patch 1.08, if you had all 20 Kingdoms at Level 10 and below Kingdom Power Level 3:
Chance of 0 Tribute: 12.2 %
Chance of 1 Tribute: 27 %
Chance of 2 Tributes: 28.5 % (+ 1 gems)
Chance of 3 Tributes: 19 % (+ 2 gems)
Chance of 4 Tributes: 9 % (+ 3 gems)
Chance of 5 Tributes: 3 % (+ 4 gems)
Chance of 6 Tributes: 1 % (+ 5 gems)
Chance of 7 Tributes: 0.2 % (+ 6 gems)
The end result was that on average you would expect 1.12 gems on average per collect (that’s about a quarter the amount beforehand).
Then I was wondering if it would re-balance when uncapped if I got all 20 Kingdoms to Power Level 3 (double tribute chance)…
Chance of 0 Tribute: 1.2 %
Chance of 1 Tribute: 5.7 %
Chance of 2 Tributes: 14 % (+ 1 gems)
Chance of 3 Tributes: 21 % (+ 2 gems)
Chance of 4 Tributes: 22 % (+ 3 gems)
Chance of 5 Tributes: 17 % (+ 4 gems)
Chance of 6 Tributes: 11 % (+ 5 gems)
Chance of 7 Tributes: 5.5 % (+ 6 gems)
Chance of 8 Tributes: 2.2 % (+ 7 gems)
Chance of 9 Tributes: 0.7% (+ 8 gems)
You would expect 2.99 gems per cash collect. So even after that miraculous effort of leveling troops and adding traits…one can expect to earn 36% less gems via the Tribute route than at the end of 1.07.