The first game of Sunday's triple treat sees West Ham attempt to end a 50-year wait for a win at Anfield when they travel to Merseyside to take on Liverpool.
However, they will have to do so by finding the away goals that have been lacking so far this season - and they must do so without Andy Carroll, who is blocked from playing against his parent club.
"Most of the time Liverpool were so much better than anybody else, you wouldn't have expected it," said Allardyce of the half-century wait.
"Other people have won there - West Brom and that - so they have slipped up now and again.
"You just hope when you go it's your turn to catch a big boy who slips up on the day.
"On any given day you hit your best form, then anybody can win any football match.
"It happens less often at some places like Anfield than it does others."
Liverpool vs West Ham Starting XIs
Liverpool: Reina, Johnson, Carragher, Agger, Enrique, Lucas, Gerrard, Henderson, Downing, Coutinho, Suarez.
Subs: Jones, Skrtel, Coates, Shelvey, Suso, Assaidi, Sturridge.
West Ham: Jaaskelainen, Demel, Collins, Tomkins, O'Brien,O'Neil, Diame, Jarvis, Vaz Te, Nolan, Cole.
Subs: Henderson, Collison, Maiga, Taylor, Pogatetz, Chamakh, Potts.
Tottenham vs Everton Starting XIs
Tottenham: Lloris, Walker, Caulker, Dawson, Vertonghen, Parker, Dembele, Sigurdsson, Holtby, Dempsey, Adebyaor.
Subs: Friedel, Naughton, Assou-Ekotto, Livermore, Huddlestone, Carroll & Ceballos.
Everton: Howard, Coleman, Baines, Heitinga, Distin, Jagielka, Gibson, Mirallas, Osman, Barkley & Anichebe.
Subs: Mucha, Jelavic, Oviedo, Naismith, Hitzlsperger, Stones & Duffy.
Newcastle vs Fulham Starting XIs
Newcastle: Krul; Simpson, S.Taylor, Yanga-Mbiwa, Santon; Marveaux, Sissoko, Cabaye, Gutierrez; Gouffran, Cisse.
Subs: Elliot, Williamson, Anita, Bigirimana, Obertan, Campbell, Ameobi.
Fulham: Schwarzer; Riether, Hangeland, Senderos, Riise; Manolev, Karagounis, Enoh, Duff; Ruiz; Berbatov.
Subs: Etheridge, Hughes, Richardson, Frimpong, Emanuelson, Frei, Rodallega
Chelsea vs Sunderland Starting XIs
Chelsea: Cech, Azpilicueta, Ivanovic, D Luiz, Bertrand; Ramires, Mikel; Oscar, Mata, Hazard, Ba.
Subs: Turnbull, Ferreira, Terry, Lampard, Marin, Benayoun, Torres.
Sunderland: Mignolet, Bardsley, Rose, O’Shea, Kilgallon, N’Diaye, Gardner, Larsson, Johnson, Sessegnon, Wickham.
Subs: Westwood, Graham, Colback, McClean, Mangane, Mandron, Laidler.
QPR vs Wigan Starting XIs
QPR: Cesar, Bosingwa, Samba, Hill, Traore, Townsend, Jenas, Mbia, Hoilett, Remy, Zamora.
Subs: Green, Park, Taarabt, Mackie, Granero, Onuoha, Ben Haim.
Wigan: Robles, Kone, Alcaraz, McCarthy, Maloney, Gomez, McManaman, Boyce, Beausejour, Figueroa, Scharner.
Subs: Al Habsi, Caldwell, Di Santo, Henriquez, McArthur, Espinoza, Stam.
Meanwhile, the race to secure qualification into next season's Champions League heats up with both Spurs and Chelsea in action against Everton and Sunderland respectively.
Spurs' bid to finish in the top four suffered a huge setback when star player Gareth Bale suffered an ankle injury during their midweek Europa League clash with Basel, but manager Andre Villas-Boas believes his side will cope without Bale.
"We have suffered setbacks before and managed to jump out of them so lets wait and see," Villas-Boas said said.
"We've had his absence before in different moments of the season and we had people stepping up to the game."
When asked if it was a chance for other players to come in and shine, the Portuguese replied: "I think so. When an injury happens to a player who has played most of the time it another player to step in.
"We have those players - [Gylfi] Sigurdsson has gone back to his goalscoring form, scoring two during the internationals and once against Basle and [Lewis] Holtby was also at a very, very good level."
Meanwhile at Stamford Bridge, Paolo Di Canio makes his managerial debut for Sunderland, and Blues captain John Terry believes the appointment of the controversial Italian will prove to be beneficial for the Black Cats.
"I can only speak highly of him (Di Canio)," Terry told the London Evening Standard.
"I played against him when he was at Charlton. His movement was fantastic and I found he was just a real nice guy on the pitch.
"I was only young at the time when I was playing against him when he was at West Ham and sides like that.
"He always gave a battle. If there was a little tussle he'd get up and shake your hand after and that kind of thing.
"So very fair, very passionate, as we've seen with his character, and his ability was fantastic. He was a credit."
Elsewhere, relegation battlers QPR and Wigan Athletic do battle with both looking to pick up all three points in a bid to survive in the Premier League, while Newcastle attempt to recover from their demoralising loss to Chelsea last weekend with a win against Fulham.
Sunday's Premier League Fixtures
Liverpool vs West Ham
Tottenham vs Everton
Newcastle vs Fulham
Chelsea vs Sunderland
QPR vs Wigan
Monday's Premier League Fixtures
Man United vs Man City
Saturday's Premier League Results