The trapped Chilean miners have given a video tour of the underground space in which they pray, play dominoes and plan for their release.

Most of the 33 men who have been trapped since the roof collapsed on Aug 5 feature in the grainy film, all shirtless and sporting scraggy beards but apparently in good health and most in good humour. They wave at the camera, make victory signs and link arms and shout: "Long live Chile. Long live the miners."

The 45-minute video was shot after colleagues on the surface sent a camera down the narrow hole through which they have been providing supplies since the group was found alive last Sunday.

It was shown on a large screen to emotional families living at "Camp Hope" near the mouth of the mine.

In the video, a miner uses a head torch to light the way to show their minimal comforts, which include first aid boxes, cards and a domino set. A thermometer showed the temperature to be 29.5C.

The guide showed some mats in a corner to lie on and pointed out a "cup to brush our teeth". "We have everything organized," he said.

Filming men playing dominoes, he added: "This is where we entertain ourselves, where we play cards. We plan, we have assemblies here every day so that all the decisions we make are based on the thoughts of all 33."

One domino player joked: "This is our casino." Another gestured at a colleague and said: "This guy doesn't want to get out of here because then he'll have to take a shower."

One miner jokes about his comrade's "mattress" as the man sleeps on some rocks.

But there were signs of stress, with some of the miners' voices trembling as they spoke, and some bitterness against the mine owners.

The guide said: "This place should have been prepared to shelter us, but when this happened the power was cut, everything was cut."

One miner could be heard saying "get us out of here soon", but another looked at the camera and told his family: "Be calm. We're going to get out of here."

The men have now been told it could take until December to dig a shaft big enough to lift them out. Doctors said the biggest risk is how they will cope mentally until then.

Psychologists who viewed the video said the men displayed a trait that is key to keeping motivated and optimistic - a sense that they have a role in their own destinies. The men have divided themselves into three working parties: one for the "doves" - the metal tubes that carry food, messages and medication; another for ensuring there are no more rock falls, securing the 32ft by 16ft [10m by 5m] chamber in which they are living and the third group is in charge of health.

On Thursday, the miners received their first proper meal - apple puree with nuts and bread.

Jaime Manalich, the Health Minister, said four Nasa officials will arrive in Chile this weekend to advise how to care for people in confinement.

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