Jones will celebrate a successful month if the Wallabies are dispatched in the final autumn international with wins over South Africa and Japan so far offset only by a controversial defeat to New Zealand.
Australia have won a mere four of their last 12 Tests, placing Cheika under pressure with less than a year to go until the World Cup.
Jones and Cheika played club rugby together for Randwick and while England’s head coach has won all five meetings between the rivals since taking over in 2015, he refuses to underestimate his long-standing friend.
“Cheika is my old mate, he’s always at his best when they’re under pressure and he loves that,” Jones said.
“He’s a street-fighter and that makes them dangerous. But at the same time we’ve had a tough year too and we don’t mind a scrap either, so it should be a good scrap.
“Australia had a good win against Italy and they’ll be ready for the battle. They understand where we’re strong and we understand where they’re strong.”
England survived a scare against Japan on Saturday by conceding a 15-10 half-time deficit that eventually morphed into a 35-15 victory sealed by Joe Cokanasiga’s 72nd-minute try.
Eleven changes had been made to the side that faced the All Blacks and it was only when Owen Farrell was introduced after the interval that the tide turned.
Farrell has become irreplaceable, a point underlined this autumn by his heroics against the Springboks and the galvanising effect he had on his team-mates as Japan threatened an embarrassing upset.
Jones rejects concern over England’s reliance on their Saracens playmaker, however.
“If I was Japan and I had Michael Leitch off the field, I’d be a bit worried too,” Jones said.
“If I was us with Owen Farrell off the field, I’d be a bit worried. If I was Ireland with Sexton off the field, I’d be a bit worried.
“Do you want me to keep going? He’s an influential player. Of course he’s important to us.”
Farrell replaced Alex Lozowski at half-time after his Saracens team-mate waved Ryoto Nakamura through for Japan’s opening try.
It is the latest in a series of decisive and hard-nosed substitutions made by Jones, who withdrew Teimana Harrison and Luther Burrell inside 30 minutes in Australia two years ago.
Bath lock Charlie Ewels reveals the threat of being hauled off can act as a powerful motivator.
“At half-time Eddie is hard. He knows what he wants, he is questioning your character which, as a rugby player, is something that hurts – and so it should,” Ewels said.
“He’s firm in what he’s saying and ultimately, if you are not doing it, he’ll bring you off. That is obvious, he doesn’t need to say that. He’s proven that in the past – bringing guys off.
“If you’re not delivering, if you’re not doing your part and if your attitude isn’t right and you are not winning your collisions, he can’t have you on the pitch. The guys know that.”
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