Isn't this 15% the ratio of upgraded cards in their decks? Winning any
one of these cards (from 1 spin) then has a probability around:
p = Sumi((n(i)/60)3),
where
i goes from 1..9 (i.e. 15% of 60) and
n(
i) is the number of copies of the
ith upgraded card in the deck. For winning exactly
k upgraded cards in 3 spins is:
q = Binomial(3, k) * pk * (1 - p)3-k,
where Binomial is the binomial coefficient.
We can assume that
n(
i) = 1 for any card
i in the deck, as upgraded cards (if I understand it correctly) are assigned randomly during dynamic deck building, before each game. Therefore there's no bias for two cards of the same type to be upgraded. Of course the value of
n(
i) depends heavily on the redundacy of the actual deck, but to analytically calculate this would be quite hard. Thus - with our fair assumption -
q gives a chance of:
0.012499% for winning exactly 1 upgraded card
5.20812*10
-7% for winning exactly 2 upgraded cards
7.2338*10
-12% for winning exactly 3 upgraded cards
("at least k" wins can be easily calculated by adding appropriate probabilities)
These are obviously lower than 15%. I can confirm on this. I've played around 100 games against AI5 winning around 80%, and got only one upgraded card at all. Values of course may be further modified by specific card checking algorithms of the spinner (i.e. pillar exclusion, etc.), which about I don't know much.
Please correct me if I'm wrong.
