We have some Reno phone books from that era...

1945, 1955 & 1956 have nothing under Reno Club (white or yellow pages)

1951 has a listing for: Reno Club Bingo Inc., 232 N. Virginia. The listing is not in the 1952 phone book.

TGT, audit edition, shows:

Billings, MT
1940's-1950's

232 N. Virginia St.
Reno NV
1932-1941 (hmmm...same address as 1951 phone book...)

32 W. Douglas Alley
Reno
1931-1931

Galveston, TX
1940's-1957

Hot Springs, AR
1940's- closed: yes

Reno Club, Harrah's
232 N. Virginia St.
Reno
1941-1945 (There's that address again)