In a book's dialog, there are two characters: Smoke and Delaney (he's the kid)
I don't know what "draw short" means.
When it says "Here's yours and I'm drawing mine", I assume this means that cards are being dealt, but there may be a bit more to this.
It was Smoke’s deal. With the final card, there was a thousand-dollar pot. The kid had a pair of jacks showing. Smoke had a possible straight. But Smoke had been plunging for a long, long time. The kid was used to his empty bluffs.
“Make it a thousand,” said Smoke. “I’ll draw short.”
“A thousand, and another thousand,” responded Delaney.
“Here’s yours and I’m drawing mine.”
“Call,” said Delaney, thrusting out an IOU.
Smoke had his filler.
That was the first big pot Delaney had lost. It did not bother him.
From L. Ron Hubbard, The Toughest Ranger.