Punchboards such as the one you see above originated during the 1700s, and by the early 1900s were being produced at a rate of millions per year. They hit the peak of their popularity during the 1930s and 1940s and were generally found in bars and other places of merriment. So, what were they? Basically, you’d pay pennies to select numbers and if you punched out the right one you’d win something. That something used to be money, which made these similar to lottery tickets, but when that type of gambling came under legal pressure from state governments, the prizes became goods such as beer, cigarette lighters or, in this case, cigarettes. What makes this Odd Pennies punchboard particularly collectible is the art by pin-up king Rolf Armstrong. Probably 1940-ish on this item. 

Update: We got an email from Joe R., who writes: "RE: the Lucky Pennies post, the Lucky Strikes package went from green to white in 1942 (the famous "Lucky Strike Green has gone to war" ad campaign), so there's a good possibility that this punchboard goes back to the 1930s.

Joe: Thanks for writing in. Now that you mention it, we think you're right. We took a detailed look around the interwebs and some of the other punch boards Armstrong illustrated actually go all the way back to the late 1920s, apparently. So mid-1930s seems like a good deduction on the date here.