Update on my wishful thinking and believing that Nordeus might not be that greedy after all:
I just reached level 16 (after 2 red cards), and looks like one of the possible rewards in “lucky round” 20 is a ticket. So, I’m pretty sure these will be the only “free” tickets we can get after playing just once. In other words, Nordeus tries to kill two birds with 1 stone: reduce the possible rewards we can win (a free ticket might be made useless by a round 2 red card), and make players who want to gamble on draw frenzy pay much more than before (it was 20T to play an additional game in earlier versions).