If you don't know how much time is left for both players, it's better to play fast and hope for the best.
New chess rules
There was an interesting variant on this forum a few years back, called Chess 2. Boiled down, you could choose between 8 different starting sets with variant and ordinary pieces, and if your king crossed the 4th rank, you won. I suggest you look into that.

Omg u compared with that game XD, the critical point in that sport is where an opponent arms can do a blood choke lol. Its hard to compare man. Actually, chess is now really need a nee variations and rule.. Its ridiculous that nowadays we have computer AI, and it shows who turn 1st is the winner. Its really hard a turn based game such as chess compared to Shoter/MOBA competition or like a UFC that Real Time happening.. Yrah man, chess is now just a game. Cant call as a sport
While playing one minute bullet chess I regularly watch opponent players who desperately want do achieve something running with a single king vs. for instance two queens plus rook in a situation with no chance for a stalemate or getting a draw on time. But still, they run as fast as a jaguar (Usian Bolt would be ashamed) . How they feel in those moments I can only fantasize: probably they feel an enormous thrill maybe equal to a rush of adrenaline or something similar. So as they efforts should not be in vain, I would like to suggest changing the chess rules: the absolute winner of the chess game should be the player who gets his own king in the opponent's first row - and as a special reward - double points for each win like that. What do you think? If I get positive opinions I shall officially send that proposition to FIDE. Thank you in advance.