An artist named Coolidge was the originator of these paintings and there have been many prints made !! Look through the pics at the link and see if you can find yours !!
https://www.google.com/search?q=Wm+Smith,,+artist,,+Dogs+playing+poker&client=firefox-b&tbm=isch&source=iu&ictx=1&fir=F3J_Dj8ronv0LM%253A%252CtM8Qru9i69eh1M%252C_&usg=AFrqEzfm9zzjsb5gM_eZxh4P89pL_5qFXA&sa=X&ved=2ahUKEwjo1du3_bzdAhVJb60KHbMJBvAQ9QEwD3oECAAQDA#imgrc=F3J_Dj8ronv0LM:
Isn`t the first one same as yours ?? Its one of CM Coolidge paintings even though I used the Wm Smith in the search !!