Patterns
Humans always search for patterns in everything. From constellations to serial killers, it has to have a pattern.
They also think death has a pattern. Better yet, whole religions have been built upon these patterns. Karma, they call it. Luck and stupidity, with the Darwin Awards as crowning achievement.
Searching for patterns of death in the mysterious ways of this God-guy, or Allah or Jahweh or however you want to call it.
Thinking they can cheat the perceived deathly pattern by praying or dieting to 'save the old ticker', prolonging live through surgery and medicine, all the while trying to find the meaning of death.
It makes the shinigami laugh and laugh, laughing until their eyes bleed.
Patterns? A shinigami has no pattern. With its eyes the shinigami sees the life span, the unavoidable drawing ever closer. Humans who've received the special eyes always try to find patterns in those numbers. They must mean that something up there has a bigger plan, a purpose. Why else would their number turn up, if not for some grand purpose? Humans are egoistical like that.
The shinigami have never really thought about those patterns. They can live like parasites and gamble the years away in their dull world. Their eyes have stopped searching for patterns, because they simply don't care. The numbers they see floating about only represent how much years they can steal.
A proper shinigami selects at random. Some might prefer a certain gender, some only steal the lives of old people. The humans create patterns around these random selections. They write papers about the increase of deaths in retirement homes in summer and during heat waves. All it really means is that a conscience-heavy shinigami is on the loose, prowling through the pleasant heat to prolong its own live.
A smart shinigami steals from toddlers, and the humans call it crib death.
Patterns, patterns everywhere.
That's who it's so interesting for Ryuk when Yagami Light plays his game. The boy is big on patterns, and so is his opponent. They seize each other up, prodding and poking for behavioral patterns, twitches of the eye, any weakness they can prey on and weave into their pattern of logic.
At the end of it all, Ryuk laughs and laughs. All the benefits the humans have gotten with their patterns is an early grave. Ryuk grins and for the heck of it randomly writes the name of a famous actor in his Death Note.
Make a pattern of that, humans.