Why? Earle starts with the form book. He reckons that "Dexy" had Go Ballistic, a leading fancy for the National, beaten when the latter fell in the Agfa Chase at Sandown, which the grey went on to win. It is not a view shared by many bookmakers: Dextra Dove is available at odds of 40-1 with Ladbrokes for the big race.
But Earle has more than the form book on his side. He also believes that the grey's curmudgeonly personality and dislike of hard work will actually work in his favour at the Merseyside course. "You don't have to switch him off to conserve energy," Earle explained. "He switches himself off. I'll be very happy if at half distance he's way down the field and looks like he has no chance at all. That would be perfect."
Because Dextra Dove always finds a little extra: if the jockey throws the kitchen sink at him on Aintree's 494-yard run-in, the gelding will respond. It is in his blood: he belongs to the extraordinary family of Doves bred by the Price family in Leominster from the prolific mare Red Dove. His close relations include Shadey Dove, who won 13 races, and her daughter Flakey Dove, who won the 1994 Champion Hurdle. Dexy has now won more races - 19 - than any other member of his family.
Doves traditionally look like they should be pulling rag-and-bone carts, but Dexy does not take after his forebears in this respect. He is a rather beautiful dapple grey, with a flashy silver mane, and he is sure to attract sentimental support for the Grand National along with the other grey in the field, Suny Bay, despite the fact that no horse of this colour has won the race since Nicolaus Silver in 1961.
Dextra Dove has been with Earle since he was a four-year-old. He owes his name to the stable's sponsors, Dextra Lighting Systems, a company belonging to Earle's brother- in-law. The yard is small - only 14 horses this year - and well situated on good galloping ground on a hill with sensational views over the Blackmoor Vale in deepest Dorset.
This is not a travelogue: the views are important. "Dexy gets bored terribly easily," Earle said. "He needs things to watch - cars in the distance, the hunt running across the fields - to keep him sharp."
The man tasked with keeping him awake and up to his work at Aintree is Chris Maude, something of a course specialist. "Chris knows the horse and the course. He knows that you have to give Dexy a whack to get him going. If whips had been banned, Dexy would never have won a race."
Maude will not be short of advice from the trainer, who as a jockey led the Grand National on Mister Christian in 1991. "People say they have made Aintree easier," he said. "But there is no way that the National has become an ordinary race. The way that the fences there are built, the horses have to take off very steeply, which means they land steeply. Anyone who thinks it is easy should go and take a close look at The Chair - it's awesome. And the drop is still the same at Becher's."
Such obstacles naturally concern Earle, whose affection for Dextra Dove is clearly limitless. The gelding was his last winner as a jockey, and his first as a trainer, one day at Worcester. "That was a fairytale. We had all the family there for a real party." The winnings topped up Dextra Dove's total earnings, which at present stand at pounds 99,000. "Aintree would be a wonderful place to take it over pounds 100,000," Earle said. "But the main thing is that we get Dexy back in one piece."
Earle has ridden the horse in all his final preparation work since he returned from the care of Mary Bromiley in Lambourn, where he was treated for a little shoulder niggle. At the end of last week Earle schooled him over some undemanding show-jumps, to sharpen his rhythm, and over an Aintree- style fence.
Back in his box after exercise, Dextra Dove received visitors. He is not a biter, but he has other methods of expressing resentment that his personal space has been invaded. He put his white nose down and sniffed for a Polo mint. Having established that no sweeties are on offer, he nudged the visitor gently towards the door of his stable. How about a tip from the horse's mouth - "How are you going to get on at Aintree, Dexy?" Very slowly and deliberately, Dextra Dove turned round so that his rear end faced the questioner, lifted his tail and let fly with a mighty fart.