eldest hand vs elder hand

eldest hand and elder hand both are nouns.

Word	Noun	Adjective	Verb	Adverb
eldest hand	Yes	No	No	No
elder hand	Yes	No	No	No

As nouns, eldest hand and elder hand are synonyms defined as:

eldest hand (noun)	elder hand (noun)
the card player on the dealer's left	the card player on the dealer's left