Police say Stephen Paddock set up a number of cameras in and around his hotel suite.

Two cameras in the hallway and one in the peephole allowed him to see if “law enforcement or security” were approaching, they said.

Although the authorities are still unable to explain why a 64-year-old gambler and retired accountant should want to carry out a mass shooting by hauling such a vast arsenal of weapons to the hotel, they do know there was a high degree of planning.

The authorities in Las Vegas revised the death toll down from 59 on Tuesday evening, saying that one of the bodies was that of the gunman.

Clark County Sheriff Joseph Lombardo told reporters: “It was pre-planned extensively and I’m pretty sure he evaluated everything he did in his actions.”

Undersheriff Kevin McMahill suggested the attack may have stopped when Paddock was disturbed, shooting a security guard.

President Trump is in no doubt. He described Paddock as “a sick man, a demented man”.

But a senior US homeland security official, speaking on condition of anonymity to news agency Reuters, said there was “no evidence” of “mental illness or brain damage”.

Reports on Wednesday said Paddock was prescribed an anti-anxiety drug in June, but this has not been officially confirmed.

Nor have police found links to any foreign or domestic terrorist organisations, despite the claims made by the group known as Islamic State that the gunman was acting on their behalf.