Origami is the art of paper folding. It has nothing to do with folding in the game of poker, but there have been puns. “Never play poker with origami makers; they always fold” was posted on Twitter on May 21, 2009.
 
“I played an origami expert at poker once. He folded” was posted on Twitter on November 23, 2009. “I played poker last night with an Origami expert. Waste of time, he kept folding” was posted on Twitter on April 19, 2010.
       
 
Wikipedia: Origami
Origami (折り紙, from ori meaning “folding”, and kami meaning “paper” (kami changes to gami due to rendaku)) is the art of paper folding, which is often associated with Japanese culture. In modern usage, the word “origami” is used as an inclusive term for all folding practices, regardless of their culture of origin. The goal is to transform a flat square sheet of paper into a finished sculpture through folding and sculpting techniques. Modern origami practitioners generally discourage the use of cuts, glue, or markings on the paper. Origami folders often use the Japanese word kirigami to refer to designs which use cuts, although cutting is more characteristic of Chinese papercrafts.
     
Twitter
Ben Combee
@unwiredben
Never play poker with origami makers; they always fold.
9:26 AM - 21 May 2009
 
Twitter
John Richard Hewitt
@JohnHewitt
Replying to @MrsStephenFry
@MrsStephenFry I used to play origami poker but I kept folding #MrsFryGags
5:17 PM - 1 Jul 2009
 
Twitter
Tim Halbert
@timhalbert
Played a master of origami at poker yesterday. He folded most of his cards.
4:51 AM - 13 Oct 2009
     
Twitter
Ross Teddy Craig
@RossTeddyCraig
I played an origami expert at poker once. He folded.
8:23 PM - 23 Nov 2009
 
Twitter
Wyre Forest RT
@WyreForestRT
I played poker last night with an Origami expert.
Waste of time, he kept folding.
4:48 AM - 19 Apr 2010
 
Twitter
Greg Lockwood
@greglockwood
Origami artists would be terrible at poker. They’d want to fold all the time.
9:38 AM - 6 Aug 2010
   
Twitter
sickipediabot
@sickipediabot
I took part in the most predictable game of poker last night with the local origami society.
They kept folding.
9:00 AM - 10 Jun 2012
     
Google Books
5,000 Sidesplitting Jokes and One-Liners
Compiled by Grant Tucker
New York, NY: Skyhorse Publishing
2013
Pg. ?:
I played poker last night with an origami expert. Waste of time–he kept folding.
   
Reddit—Jokes
Why did the Origami Artist never win a poker match?
submitted August 3, 2013 by Stroke_n_Smoke
Because he will always fold.
 
Twitter
carl, certified hoe ™
@ascendingcarl
Someone called my bluff in origami poker so I folded.
10:28 PM - 6 Jul 2014
     
Reddit—Jokes
Why can’t origami masters play poker?
submitted July 20, 2016 by Sgp15
Because they keep folding
   
Reddit—3amjokes
Why do origami enthusiasts suck at poker? self.3amjokes
Submitted November 1, 2016 by yeeah_suree
They’re always folding.
 
Reddit—Jokes
Why was the origami master terrible at poker?
submitted November 28, 2017 by ripjaw92
He always folded.
 
Reddit—Dad Jokes
Why are origami so good at poker? (self.dadjokes)
submitted March 6, 2018 by BlissedIgnorance
Because, they always know when to fold.