Here's Blackie. The scuffle is well underway at this point. There's been a gunshot. Oswald has cried out in pain 4 distinct times. And now they are wrestling with the guy with the gun, who is bent on shooting again. Notice that Blackie has his hand on his little cigar as he takes a drag.
But then, as he brings his arm down, to use it in the fight, he leaves the cigar there.
Blackie may be the only man in history who engaged in a physical altercation while smoking a cigar. You might think he had his hand up to his mouth to remove the cigar and ditch it, but not Blackie. This wasn't that big a deal. He could subdue "Ruby" and continue smoking. No problem. And hey, those cigars cost money, and he wasn't made of money. Here's Blackie a little later, the cigar still perched there:
I hope you enjoyed your cigar, Blackie Harrison, truly one of Dallas's finest.