D. H. Lawrence seems, as a prelude to describing how Paul is able to pick winning horses by riding his rocking-horse, to be suggesting that all children possess extrasensory perception. Paul and his two sisters can all hear the voices the author describes.
And so the house came to be haunted by the unspoken phrase: There must be more money! There must be more money! The children could hear it all the time, though nobody said it aloud. They heard it at Christmas, when the expensive and splendid toys filled the nursery. Behind the shining modern rocking horse, behind the smart doll's house, a voice would start whispering: "There must be more money! There must be more money!" And the children would stop playing, to listen for a moment. They would look into each other's eyes, to see if they had all heard. And each one saw in the eyes of the other two that they too had heard. "There must be more money! There must be more money!"
This is the kind of thing that many of us can remember from our childhoods. We seemed to possess some intuitive knowledge that was lost to us after a certain age. We knew that certain things were going to happen before they happened. If we can relate to these three children in their hearing the voices crying for more money, then it becomes easier to accept the notion that Paul should also be able to use that same intuitive ability to see into the future and predict the names of horses that would win races yet to be run. Paul, it would seem, is only making use of the extrasensory perception that all children bring into the world with them.
Whether or not this is literally true, it seems true enough to make us believe in D. H. Lawrence's assertions that the children can hear the voices crying, "There must be more money!" and to make us believe that Paul could actually foretell the future with the same ESP (extrasensory perception). After all, he is able to convince his uncle and Bassett the family gardener. These grown men have lost the magical powers of childhood, but are more than willing to place their money on Paul's picks. Paul's mother is more than willing to take the money and spend it.