Player’s Navy Cut was discontinued in 2016. Not a bad run.
One of its slogans in the 1920s was “Player’s Please”. It’s a long shot, but I think it’s possible this was an early version of the more recent “Playa please.”
And yes, “Me likee” is a racist stereotype. Don’t do that.
Detail: Notice the “Hero” on the sailor’s hat.
And just because, here’s a possible origin for “Put that in your pipe and smoke it.”
The ad copy:
Player’s Navy Cut
J.C. Me likee your Tobacco.
J.T. I should think you do, it’s Player’s.