Raise your stealth skill enough that you get the update that you "riff through the discard pile for a better hand, while the dealer pretends to ignore you". At the end of the game, you'll get called out for it and the mission will continue. Also in my experience, the best way to eat money from people through poker is to spam low value bets. Starting at $20 they'll fold every other hand, unless they have a god hand.
I get the dealer ignoring me because my stealth is already as high as it can get, plus everything but channeling is too, so I think a trigger must have not been hit right.
Taking a look at the console I'm getting a bunch of errors when I hit Play Poker:
AccidentalMind - Alpha 3.0D.html:79512 Error: <<set>>: bad evaluation: Cannot set properties of undefined (setting '0')
<<set $poker.mind[$i] to "Two pair">>
AccidentalMind - Alpha 3.0D.html:79512 Error: <<set>>: bad evaluation: Cannot set properties of undefined (setting '1')
<<set $poker.mind[$i] to "Pair">>
AccidentalMind - Alpha 3.0D.html:79512 Error: <<set>>: bad evaluation: Cannot set properties of undefined (setting '2')
<<set $poker.mind[$i] to "Three of a kind">>
AccidentalMind - Alpha 3.0D.html:79512 Error: <<set>>: bad evaluation: Cannot set properties of undefined (setting '3')
<<set $poker.mind[$i] to "Two pair">>
AccidentalMind - Alpha 3.0D.html:79512 Error: <<set>>: bad evaluation: Cannot set properties of undefined (setting '4')
<<set $poker.mind[$i] to "Pair">>
AccidentalMind - Alpha 3.0D.html:79512 Error: <<set>>: bad evaluation: Cannot read properties of undefined (reading '1')
<<set $see2 to $poker.mind[1]>>
AccidentalMind - Alpha 3.0D.html:79512 Error: <<set>>: bad evaluation: Cannot read properties of undefined (reading '2')
<<set $see4 to $poker.mind[2]>>
AccidentalMind - Alpha 3.0D.html:79512 Error: <<set>>: bad evaluation: Cannot read properties of undefined (reading '3')
<<set $see6 to $poker.mind[3]>>
AccidentalMind - Alpha 3.0D.html:79512 Error: <<set>>: bad evaluation: Cannot read properties of undefined (reading '4')
<<set $see8 to $poker.mind[4]>>