Crossword Genius

Six out of nine go, I stay -- one considers no one else (6)

Ross

I believe the answer is:

egoist

I'm a little stuck... Click here to teach me more about this clue!

'six out' is the definition.
Although both the answer and definition are singular nouns, I cannot understand how they can define each other.

'nine go i stay one considers no one else' is the wordplay.
'EGOIST' is hidden within the letters.
But, I am unsure how this is indicated.

'of' is the link.

Can you help me to learn more?

(Other definitions for egoist that I've seen before include "A seld-centred, conceited person" , "Self-absorbed person" , "Person with very a good opinion of himself" , "Conceited and self-centred person" , "Excessively conceited person" .)

I've seen this clue in The Telegraph.
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