The random rule is not okay

[Nyalia]

There is currently 80 cards in the game

20 1*
17 2*
13 3*
10 4*
20 5*

Lets assume you have every card for maximum chance of winning a random battle, you have a 0.375 chance of drawing a 4 or 5 star card per card so a fair assumption should be made that 0.375 x 5 > 1 therefore you should get one. After getting that one card be it 4 (33%) or 5 (66%) star you will then be only allowed 3 or below cards to be randomed in.

Five of the 5* cards are completely unobtainable (three are not in game yet at all, one is only obtainable by being in the top 3 of the current tournament when it ends, and one is not obtainable until at least the next tournament since it requires 30 tournament wins and you can't have more than 15 yet), so you should use 15 as the number, not 20. That means you actually have a 40% chance of a 4* and a 60% chance of a 5*.