Allen Iverson tested his luck in Chicago this week ... hitting up a local casino while his BIG3 team was in town for a game.
The Answer posted up at the roulette table at the Rivers Casino on Thursday -- where witnesses say he was flanked by private security during his gambling run.
No word on how much he was betting. We're told he was drinking water.
A.I. has a penchant for the casinos -- he was spotted at the SugarHouse Casino in Philly earlier this month while the BIG3 was there.
There have been reports over the years that Iverson has a gambling problem -- but he's publicly denied that.