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.
This usage is slightly archaic, and contracted. As you've probably guessed, the format is a comparative phrase. For example:

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> He went **as far** east **as** I went west
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> I have **as many** melons **as** you do
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The repetition adds to the confusion, but if I said

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> I have **a larger number** of melons **than** you
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... hopefully it doesn't look as weird. It's the same style of sentence.

I mentioned that the phrases you mention are a shortened form. Expanded out, the first is easy to read:

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> He won at bingo **as often as not**
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> He won at bingo **as often as** he did **not** win
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The second is almost slang, and is harder to follow:

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> My mate is descended from royalty, as likely as not
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It is just **as likely** that

*my mate is descended from royalty*

**as** it is that

*my mate is **not** descended from royalty*

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> If you're still confused at the end of all that, don't worry. You won't ever use this language construct, as likely as not!
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