This makes you wonder: did people start playing backgammon more in the 30s? They did. Maybe. This site says there was one backgammon-related magazine in the 20s, and nineteen in the 30s. This site says it declined somewhat during the Depression. The rules were codified for US audiences in 1931, so that may have kicked off a vogue.

Note how she's drawing a Lucky from a pack that really isn't there at all.