I think it's an old blue Playskool block under the brown-painted, carved stool upon which this wonderful figure sits, holding forth their checkerboard seemingly in perpetual hopes of soliciting a partner for a match. I love everything about this, including the fact that the figure seems both quite specific and also ambiguous in terms of gender, ethnicity, race--and temperament--such that this feels all about devotion to a game and a longing to play! 

5 1/8" t x 2" w x 3" d. Unsigned. Later 20th century I believe. Very good condition, sturdy and not fragile, with a little discoloration/staining to the paint on one side, as pictured.