What kind of partnership does Paul have with Bassett?

In D. H. Lawrence's "The Rocking-Horse Winner," Paul and Bassett—the young protagonist and his family's gardener—have partnered together to gamble on horse racing. The partnership is equal in the sense that its success hinges upon both partners holding up their end of the agreement.
Paul is too young to make the bets himself. He also does not wish his mother to find out, as he believes she would put a stop to it. For these reasons, he must rely on Bassett to place the bets for him. On the other hand, Bassett must also rely on Paul, as he is the one picking the winners.
Bassett used to be "batman" (i.e., servant to a British Army officer) to Paul's uncle, Oscar Cresswell. After injuring his foot, Oscar helped Bassett get a job as a gardener for Paul's family. At the start of "The Rocking-Horse Winner," the pair have already been partners for a while, building up quite a stockpile of money. In a sense, Bassett has now also become "batman" to Paul, though it does not take away from the latter's reliance on the former.
The pair's process is as follows: Paul rides his rocking horse, where he gets an idea of who to bet on:

"Sometimes I'm absolutely sure, like about Daffodil," said the boy; "and sometimes I have an idea; and sometimes I haven't even an idea, have I, Bassett? Then we're careful, because we mostly go down."

As Paul is too young to do so, Bassett is the one who must go place the bets. He is also responsible for holding on to their winnings for safe keeping. The two of them only place large bets on horses that Paul is "absolutely" certain will win. Until Uncle Oscar discovers Paul's gift of luck, the pair keep this a secret from everyone else in the family.

Bassett and Paul have a partnership to place bets on horse races. Paul can determine the winner of an upcoming horse race by riding his rocking horse very hard. But he is too young to go to the racetrack and bet, so Bassett does that for him.
We learn that Bassett is the young gardener for Paul's family. His foot was wounded in World War I. Uncle Oscar helped him get him the job with Paul's family, because Bassett had been his batman in the war. (A batman was a personal servant the British army assigned officers like Uncle Oscar.)
Because Bassett and Uncle Oscar had a prior close relationship, Oscar is inclined to support their betting partnership. When Oscar questions Paul about it, he learns that Bassett had lent Paul the money—five shillings—to make his first bet. Oscar is surprised to find out the large sums the two are now winning on the races.