The End Turn button remains grayed out and does not update to the next turn number (Almost always says "End Turn 5" since Poker is a 5 cost card). I can still undo the cards played on my previous turn, play cards, and undo the cards played on my current turn.
I've seen this happen on 2 runs, and on both runs I reloaded the page and continued the run. Still, once the opponent played Poker (since the game doesn't change the RNG on reload) the game will freeze and I can't proceed.
Here's an example game turn log where it froze:
Turn 5 of 7
You draw Red Guardian
Cartoon Villains draw a card
Cartoon Villains play a card to Left Location
You play Red Guardian to Left Location
You play Red Guardian to Middle Location
Cartoon Villains reveal Poker in Left Location
… Poker repeats DojoBojo's ability
You play Red Guardian to Middle Location
You play Red Guardian to Left Location