"I'm sure Gene knows the answer."
Partially.

Accoutability for chips is carried in the Cage Float.
Issue chips, add to Float.
Destroy chips, account for the destruction in the Float.
It is a misnomer that each $1 chip must have $1 backing it.
That is a different story. Its called a Bankroll.
Bankroll is determined by a very complicated formula of chips, number of table games, number of slots, Keno limits, progressive jackpots, Sport book limits, etc, etc, etc.
We have a BB contributor that could explain it better. Maybe he will.