David Moyes takes this competition very seriously, as appearances in the final and semi-final stage within the past four years suggest, and he will choose a strong side here.
As such, faith should be invested in the Toffees to overcome a two-goal handicap against their League One counterparts at 5/4.
The Merseyside club have already hosted a League One side in cup competition this season, when they bested Leyton Orient 5-0 in the Capital One Cup.
A repeat of that scoreline is 12/1, whilst the 5-1 win Everton recorded away to Cheltenham means the Blues would have comfortably dealt with a two-goal deficit on two of the occasions they have faced lower league sides this term.
Of course, Oldham managed to avoid succumbing to an emphatic defeat in the initial meeting of this pair, and the 2-2 draw they achieved at Boundary Park will lead some to back another stalemate at 6/1 here.
They managed to open the scoring in that match, and should the away side take the lead here, Ladbrokes will refund losing first scorer bets as a free bet.
And the Latics do have previous at Goodison Park, winning an FA Cup third round bout here via a 1-0 scoreline back in 2008.
They can be backed to gain another unlikely triumph in normal time at 14/1, whilst the third-tier outfit are 9/1 to qualify by any means.
The fact that Everton are 1/25 to advance by any means shows just how heavily they are favoured to progress though.
5/4 is the price attributed to the possibility of a 90-minute Everton win featuring at least 3.5 goals, and it is an outcome which appears very plausible.
Half markets could too provide useful betting opportunities for punters, with the 4/11 about the hosts leading at the half-time whistle and at full-time an appealing prospect.
What looks a better bet though, at a greater value 23/20, is for the Toffees to win both halves, against a side that has shipped 27 goals on the road in League One this season.
Nikica Jelavic could be afforded another chance to play his way back into form for the home side, and this game represents a great opportunity to end his recent goal drought.
The Croatian striker is 7/2 to break the deadlock, and his last goal came in this competition facing lower league opposition.
All Odds and Markets are correct as of the date of publishing.