Crossword Genius

A choice of one in two, or possibly one in three (6)

Ross

I believe the answer is:

either

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'a choice' is the definition.
(I have seen 'Choice of two' mean 'either' so perhaps 'choice' could also mean 'either')

'one in two or possibly one in three' is the wordplay.
I cannot really see how this works, but
'one' could be 'the' (both can introduce a definite example of something) and 'the' is present in the answer.
The remaining letters 'eir' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

'of' acts as a link.

Can you help me to learn more?

(Other definitions for either that I've seen before include "Word introducing first of two 16s" , "Each of two; moreover" , "Her tie (anag.)" , "offered a choice" , "One of two alternatives" .)

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