The chance that the cards appear in one of the categories is very low, even lower is the chance IF the card is in the categories to get one of the cards. In addition to this, you have to get the right one to complete the collection.
On my DE World 1 I have since the introduction of the collector cards 1 Tarot Card and 2 of the other cards. In the sum of all my worlds 12 Cards (8 worlds including the Beta, not counting the worlds where I sporadically log in - additional 8 worlds).
These achievements / collections should be achievealble in a normal manner of time.
Because of the amount of other events, the travelling fair does not appear much often, then the collection cards have to appear, then spinning the wheels (or whatever game you make) gives you a small chance.
Just a rough calculation:
The appearance of the travelling fair is due to the amount of events (lets calculate in dubio pro reo) 6 times a year
To get a certain item from the 5 choices in the small games:
20%
The probability of getting a green item ca.
15% (of getting a blue item
1%)
from the link above
https://tw-calc.net/tombola/1 for both collections around
0.25%
I don't know if the probability in the collection itself is different, but again to get the right card is 1 out of 5 or
20%
By calculating only the values of if there is a green item (15%) getting it (20%) and getting a card (0.25%) and getting the right card (20%) I will get on numbers even my computer cannot calculate anymore because they are to small...
Just calculating the probability from tw-calc with the probability of getting the right card is tremendously low with 0,25% x 20% (if the distribution for all cards is the same):
0.05%. This means you get in one out of 10.000 spins the right card. If you calculate with the numbers above (6 times a year travelling fair) with two spins a day and a full time of travelling fair (14 days) means 84 spins a year. To get the cards you have to play around
119 years....