Board Game Arena

I want to report a bug in game. But the game will still be running a few days or weeks (Ark nova). Is it possible / helpful to report a bug before the game terminates? If yes, how can i find out the number of the game that is needed to report the bug?

You can find the table number at the end of the url, in your case https://boardgamearena.com/10/arknova?table=399588301, the table number is 399588301.

As for Ark Nova, a bug is highly unlikely after so many games played. Please check the hints given here https://boardgamearena.com/bug?id=86536 first.