If everybody in the world flipped coins for the rest of their lives, they would have to live about a billion years before anyone replicated your sequence of 150 tosses. They might allege you couldn't have done it without supernatural aid. One can't logically argue that because something highly improbable happens, some occult force had to make it happen that way. Whatever the pretensions to objectivity, design theorists, like biblical creationists, are apt to be impelled by religious sensibilities. Why they should find the concept of a designer comforting, rather than unsettling, is perhaps best explained by psychologists.
Nature is a huge killing field rocked by ceaseless internecine combat.
Living creatures spend much of their time ripping other creatures apart or trying to avoid being ripped. Billions of people have died agonizing deaths from genetic flaws subtly shrouded in the innermost recesses of their DNA molecules. The list of ailments that afflict humans and other animals is longer than an anaconda. No human imagination is capacious enough to grasp the quantity of excruciating pain that animals have endured, generation after generation, throughout what Shakespeare called the dark and backward abysm of time. The concept of design raises more questions than it answers.