There are 21 cards and each player chooses two cards, since there are four players, at least 8 cards are flipped at each game. 8/21=0.38 That means we have more than 38% chance of one player choosing a certain card such as boomerang or even just a level 4 pearl.
This is a screenshot of the cards for completing DZH.
In the screenshot there are 1 undead axe and 3 S-lv4 pearls. 4/21=.19=19% So theoretically the prizes are there and for around every 5 DZH a player will get a rare item right? Well as many people have noticed already, that is not the case. The chances ddtank shows us and the chances in reality are very different. I personally think the chances get worse after each revision. In DDTANK 3.4 I get 2 level4 syn stones for every GD run and at least 1 tribe card and often for TD runs. Guess what I get now?? S-LEVEL 2 PEARLS. While not as noticable, they applied this to synthesis and probably fortification as well. The % is likely 2 or 3% lower than what is actually shown. Before DDTANK 3.6 I can syn +50(lv10 league boost) in 5-8 tries average with 10% success. But now when I try syn with the lv5 stones from ares I fail 20+ before success!!
tl;dr Don't believe what ddtank tells u