Question: Am I failing to get a point here?

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> Collins English Dictionary:
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> [as often as not](http://www.collinsdictionary.com/dictionary/english/as-often-as-not#as-often-as-not_1): **quite** frequently
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> [as likely as not](http://www.collinsdictionary.com/dictionary/english/as-likely-as-not#as-likely-as-not_1): **very** probably
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Considering the meanings of these phrases, to my eye, they come to have connotations not in line with their real meanings.

Before consulting my dictionary I envisaged that **as often as not** would most probably mean **just about never** rather than *quite frequently*, and that **as likely as not** would be associated more with **impossibility** than with *high probability*.In short, I expected **not**, in the phrases above, to have the same implication as **nothing** does in, for example, **as good as nothing**. 

Do you think **not** in these phrases is of some connotation different from what its commonplace definitions convey? Do you ever believe the component words preserve their meanings after these phrases are broken down and thus, are we supposed to treat the phrases the way idioms are treated?

I found [one answer](https://ell.stackexchange.com/questions/14174/how-to-understand-as-often-as-not-literally), but with no reference so far.

Answer: 
This is the same ellipsis as in, say, *as good as gold*:

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> It is ***as good as gold (is good)***.
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Everything except the contrasting material is deleted:

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> This is true ***as often as (it is) not (true)***.
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If something is true *as often as not* it is true at least half the time, and generally more often.
The "not" in this context refers to a 50-50 chance of either the positive or negative outcome.

A substitute I might use is "the converse": As often as the converse. As likely as the converse.