Toffees boss manager Ronald Koeman names an unchanged XI from the side that claimed a memorable win over Manchester City last time out, meaning that 18-year-old midfielder Tom Davies keeps his place after finding the net against Pep Guardiola's side.
Maarten Stekelenburg is fit again after overcoming problems with a dead leg but is left on the bench in favour of Robles, who is marking his 50th appearance for the side.
The Eagles begin the game in the relegation zone following Swansea City's surprise win at Liverpool in the early kickoff, and Allardyce makes a bold call to switch to three at the back against Koeman's side.
The fit-again Loic Remy is selected to partner Christian Benteke up front, with Andros Townsend dropping to the bench, while Jeffrey Schlupp earns his full club debut in the middle of the park at the expense of Joe Ledley.
Crystal Palace: Hennessey; Ward, Dann, Delaney; Tomkins, Schlupp, Cabaye, McArthur, Puncheon; Remy, Benteke
Subs: Speroni, Kelly, Lee, Ledley, Flamini, Townsend, Kaikai
Everton: Joel; Holgate, Funes Mori, Williams; Baines, Coleman, Barry, Davies; Mirallas, Barkley; Lukaku
Subs: Stekelenburg, Schneiderlin, Jagielka, McCarthy, Valencia, Oviedo, Lookman