Bashir only has access to two games of chance at Quarks Bar; Dabo and Tongo.
Dabo appears to be roughly analogous to roulette and is essentially immune to the sort of high level statistical analysis that Bashir is capable of. On top of that, Quark describes the rules as "easy to learn" but the stakes seem pretty low. It's only when people double and triple down that the winnings (and losings) become even slightly interesting to Quark.
BASHIR : Please. You and I both know these so-called games of chance are no such thing -- the odds are in the house's favor.
QUARK : Shh. Don't say that. (looking at the other players)
People are trying to have fun.
Bashir places his bets...
BASHIR : (to Quark) Sooner or later, no matter how perfectly I play, no matter how well I hedge my bets, I'm going to lose.
The sole occasion that Bashir plays Tongo is in DS9 : Change of Heart, it's made pretty clear that this is usually a Ferengi-only game and that he feels that Bashir's enhanced brain will be pretty useless:
QUARK : Tongo is more than just number-crunching. They have yet to
create the computer that can master this game.
BASHIR : Then you shouldn't have anything to worry about.
Quark sizes him up for a beat.
QUARK : You realize we're not playing for drinks. This is a