Is there a name for the psychology behind lowering your bets?
The answer I was searching for is Creeping Normality. It fits better examples and has a clearer definition for what I was attempting to express.


  Creeping normality refers to the way a major change can be accepted as
  the normal situation if it happens slowly, in unnoticed increments,
  when it would be regarded as objectionable if it took place in a
  single step or short period.