The Reno Bar on 4th Street was open from at least 1950 through at least 1971-1972.

The phone number on your matchbook (3-7228) is the one listed in the 1951-1955 phone books.

(In 1950 the number was Reno-7228, in 1956 it was FA-?????--I didn't bother to write the numbers down!)

I searched the 1955 yellow pages, trying to find a display ad that might mention gambling. I couldn't find a display ad, so I searched several categories and could only find one listing for the Reno Bar...under the heading "Beer Parlors".
Reno Bar was NOT listed under Restaurants, Liquor Stores, Clubs or Cocktail Lounges. In those days they didn't have a casino category.

FWIW...the 1939 phone book listed the Reno Bar on 2nd Street. The 1945 phone book didn't have any listing for Reno Bar.