Dyche's arrival was announced earlier this week as he replaced Frank Lampard who was sacked with the club winless in 10 games in all competitions.
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The former Burnley boss has been tasked with turning the season around for his new side but he is faced with the toughest possible challenge to welcome him to Goodison Park.
League leaders Arsenal are Everton's first opponents under their new manager and with the Gunners unbeaten since September, they will have to pull off a shock result.
To make matters worse, Dyche himself has only lost more Premier League games against Manchester City than he has against Arsenal.
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He has been beaten 10 times by the Gunners and lost every single game of his first nine meetings with the north London side.
However, in more recent years, the new Toffees manager seems to have worked out how to stop this horrible run of form, losing only one of his last five games against Arsenal.
And it's the same for Everton as a whole, who have won three of their last four Premier League fixtures against Arsenal after only winning three of their previous 26!
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At Goodison Park, the Toffees have come out on top in their last two games against the Gunners, winning 2-1 in both meetings.
They will now be aiming to pick up a huge three points and pull off a shock result by making it three wins in a row.
This is a feat that has not been achieved by the club in almost 45 years, last winning three on the bounce against Arsenal between March 1977 and August 1978.
If Everton and Dyche can continue their recent positive results against the Gunners, they will give themselves a huge boost in the fight for Premier League survival.