where did the word river come from when talking about the poker game texas holdem?

Answer 1

From the phrase "going up the river" (doing well) or "going down the river" (out of luck) --- the 5th card often sends a player one way or the other

Answer 2

Partly correct. Poker became popular on the riverboats of the Mississippi. Hence when you lost on the last card, you were down the river...