Allardyce got off to a winning start with the Toffees with a 2-0 victory against Huddersfield in the Premier League, but missed the 3-0 win at Apollon Limassol in the Europa League to attend a pre-arranged medical appointment.
Harry Charsley - Capped by Ireland at Under-21 level, Charsley is an energetic and versatile midfielder who has regularly weighed in with goals for Everton's age-group sides.
With Big Sam watching from home ahead of Sunday's Merseyside derby, former Leicester boss Craig Shakespeare took the reins.
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Everton's XI, which featured two debutants - Harry Charsley and Fraser Hornby - was the youngest an English club had selected for a European group-stage fixture in eight years, and Shakespeare also brought on three teenagers for their bows, including 16-year-old Anthony Gordon.
A youthful core of Under-23 and Under-18 regulars have also travelled, including 17-year-old defender Michael Collins and Ireland Under-21 worldwide midfielder Harry Charsley.
Beni Baningime starts at right-back in a defence with Morgan Feeney and Muhamed Besic in the centre.
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Everton have a long way to go before they can compete with Liverpool, both on the pitch and financially.
The Toffees, already eliminated from the competition, face Apollon Limassol in Nicosia this evening.
Alex Denny - England Under-17 global Denny is a ball-winning defensive midfielder by trade, but has also stepped up admirably to fill in at centre-back for David Unsworth's second-string team at times this season.
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After that, it's an extremely inexperienced side that makes up the squad for the game in Cyprus.