Sean Dyche's side were denied a vital victory by Manolo Gabbiadini's stoppage time equaliser for Southampton last weekend and have now failed to win any of their last 12 matches.
The Toffees, meanwhile, have lost their last five fixtures away from Goodison Park.
Three of the last four fixtures that the Clarets have contested have ended all square and the odds compilers offer 2/1 (3.0) that this match also ends all square.
The visitors have won just one domestic fixture away from home this season and Allardyce's side are chalked up as a 2/1 (3.0) chance to come out on top at Turf Moor.
The Clarets have no fresh injury concerns, but Sean Dyche is hoping to have Jon Walters available after a lengthy injury lay-off.
Eliaquim Mangala is out for the Toffees, but Leighton Baines could return.
Everton have scored more than once in just one of their 14 away Premier League matches this season, failing to score in three of their last five away fixtures on their travels in league.
Preview and predictions
There have been fewer than three goals scored in 12 of the 14 Premier League matches played at Turf Moor and it is no surprise that the odds compilers offer just 10/21 (1.48) that there are no more than two goals in this game.
The 29/20 (2.45) quote, however, from SportPesa for fewer than two goals to be scored could represent excellent value.
This selection would have landed in more than half of Burnley's 14 home league matches so far this season.