Something other than rum in each bridge-player's hand (2-7)

I believe the answer is:

no-trumper

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'something other than rum in each bridge-player's hand' is the definition.
I can't tell whether this defines the answer.

'other than rum in each bridge-player's hand' is the wordplay.
'other than' becomes 'not'.
'in each bridge player's' becomes 'pe' (I am not sure about this - if you are sure you should believe this answer much more).
'hand' becomes 'R' (abbreviation for right, as in the right-hand side).
'not'+'rum'+'pe'+'r'='NO-TRUMPER'

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