Bath companion has a number of games with no score (6,4)

I believe the answer is:

rubber duck

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'bath companion has a number' is the definition.
I know nothing about this answer so I cannot judge whether it can be defined by this definition.

'games with no score' is the wordplay.
'games' becomes 'rubber' (rubber can mean a group of matches).
'with' means one lot of letters go next to another.
'no score' becomes 'duck' (duck is a kind of score. I am not sure about the 'no' bit.).
'rubber'+'duck'='RUBBER DUCK'

'of' is the link.

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