For those that are having trouble with xTGE's method here are the five games that I did on the way to unlocking this achievement. They are all listed as 'City Games' in the game if you hover over their icon whilst using the map.
Head to one of the three bars in the city and complete one session.
Play one round of this, win or lose to add this game to your tally.
Simply play one round to get your third game unlocked.
If you spin the machine once, win or lose then you're done here.
Once the cards have been dealt the game adds one more point to your total. If you've followed the guide as I've written it then you should have your achievement.
Good Luck, and if you have any questions please stick a comment below rather than -1'ing me anonymously without a reason as to why. I don't mind negative votes, just please let me know as to why I receive them so that I can make changes to my solution.