“Ante up and pass the buck” was a popular poker saying in the 1800s. The “buck” was a knife with a buckhorn handle, and it indicated whose turn it was to deal the cards. “As our wit has all been Ann T. C. Pated, we will Ann T. Up and pass the buck.—Weekly Ledger.” was printed in the Mariposa Democrat (Hornitos, CA) on June 11, 1857. “Ante and pass the buck” was printed in the book Roughing It (1872) by Mark Twain.
 
It’s not entirely certain when “pass the buck” meant to avoid responsibility, but it acquired that meaning by at least 1900. “In the popular game of the nation Judge Collins would probably ‘pass the buck’” was printed in the St. Paul (MN) Globe on December 4, 1900.
 
“The buck stops here” (to accept responsibility) is a related saying.
 
     
Wikipedia: Buck passing
Buck passing, or passing the buck, or sometimes (playing) the blame game, is the act of attributing to another person or group one’s own responsibility. It is often used to refer to a strategy in power politics whereby a state tries to get another state to deter or fight an aggressor state while it remains on the sidelines.
 
Etymology
The expression is said to have originated from poker in which a marker or counter (such as a knife with a buckhorn handle during the American Frontier era) was used to indicate the person whose turn it was to deal. If the player did not wish to deal he could pass the responsibility by passing the “buck,” as the counter came to be called, to the next player.
 
(Oxford English Dictionary)
figurative. to pass the buck (to), to make a scapegoat or dupe of (a person); to shift responsibility (to another). colloquial (originally U.S.).
1912   W. Irwin Red Button 341   The Big Commissioner will get roasted by the papers and hand it to the Deputy Comish, and the Deputy will pass the buck down to me, and I’ll have to report how it happened.
 
11 June 1857, Mariposa Democrat (Hornitos, CA), pg. 4, col. 6:
As our wit has all been Ann T. C. Pated, we will Ann T. Up and pass the buck.—Weekly Ledger.
 
22 January 1868, Watertown (WI) Republican, “The Seven Sleepers,” pg. 1, col. 5:
Behold, the jig is up—let me ante up and pass the buck.
 
Google Books
Roughing It
By Mark Twain
Hartford, CT: American Publishing Company
1872
Pg. 332:
“You ruther hold over me, pard. I reckon I can’t call that hand. Ante and pass the buck.”
 
5 December 1877, Chicago (IL) Tribune, “Quips” (Boston Commercial Bulletin), pg. 7, col. 4:
A companion song to “Pull Down the Blind,” entitled “Pass the Buck,” has just been issued.
   
7 November 1898, Independent Democrat (Las Cruces, NM), pg. 1, col. 5:
An officer seldom has time to pass the “buck” when in pursuit of outlaws.
 
4 December 1900, St. Paul (MN) Globe, “Pertinent or Partly So,” pg. 4, col. 4:
In the popular game of the nation Judge Collins would probably “pass the buck.”
 
25 August 1903, San Bernardino (CA) Daily Sun, pg. 8, col. 4:
SACRAMENTO, Aug. 24.—Governor Pardee is credited by a local paper with having said the State Board of Prison Directors was trying to “pass the buck” to him in the matter of the investigation into the prison break. Governor Pardee said this morning that while there had been talk about “passing the buck,” it was all said in a joke.
 
16 October 1904, San Francisco (CA) Sunday Call, “Tooth Talk for Pa and Children” by Dr. William Merrill Tryon, pt. 2, pg. 3, col. 5:
The present day habit of “buck passing” is taught us in childhood. As the child with bad teeth must of necessity bolt his food, the mouth calmly “passes the buck” to the stomach and that patient subservient menial stands the indignities until patience ceases to be a virtue and we find a full fledged dyspeptic on our hands.
 
,a href=“https://www.urbandictionary.com/define.php?term=Pass%20the%20buck”>Urban Dictionary
pass the buck
A transfer of a problem from person to person.
Rather than taking a trip to the post office, the stamp-lacking asian asked her friend to drive over to her house and bring her stamps. She passed the buck to him.
by Johnny Rocket January 02, 2004
 
Twitter
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@DavidBDiehl11
Replying to @VeteransHealth and @PucciniCobb
The VA hospital IS the problem. I didn’t expect any help from you anyway.
Nobody wants to take responsibility, just pass the buck..
Maybe I DO need to make a trip to DC and get this taken care of personally. Or let the papers run the story.
6:22 PM · Oct 3, 2019·Twitter for Android