The difference between As often as not and More often than not
As often as not is also phrase with the meaning: more or less half of the time.
More often than not is also adverb with the meaning: usually.
check bellow for the other definitions of As often as not and More often than not
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More often than not as an adverb:
Usually; more than half the time; more likely to be the case than not to be the case.
Examples:
"'More often than not, tomato seeds will sprout even if they are a couple of years old."