In poker, players used a Buck knife to determine who’s turn it was to deal.
If the Buck Knife was in front of you it was your turn to deal and you would say “The buck stops here”. If you didn’t want to deal you “passed the buck”.
“The buck stops here” is a phrase that was popularized by U.S. President Harry S. Truman, who kept a sign with that phrase on his desk in the Oval Office. Truman was an avid poker player.