Each player found he had a run of cards from an ace through to the 10, completed by a jack, queen and king flourish.

Ieuan Griffiths, Meirion Hopkins, Mike Harwood and Owen Williams found they had matching 13-card runs while playing Crash at the at Brynamman Industrial Club, South Wales

The freak outcome happened last week as Owen Williams, Meirion Hopkins, Ieuan Griffiths and Mike Harwood sat down to play at Brynamman Industrial Club near Ammanford, South Wales.

They were so intrigued by their fortune that they called Cardiff School of Mathematics to find out what the odds on their incredible hands were.

Lecturer Rhyd Lewis astonished them further by calculating the odds at 61,204,166,001 to one.

‘I was just amazed when I sorted my cards and I realised what I had,’ said Mr Williams, 63, a commercial finance broker.

‘It was the first deal of the evening and I was the first one to finish sorting my cards.

‘A run through takes the kitty – so I thought I’d won £1.65.’

But as the other players sorted their own hands, each found he had an identical mixed suit run.

The friends were so amazed at the outcome they called over other club members to witness the four hands.

Mr Owen insisted the group had been playing with a ‘well-used pack of cards which were cut and shuffled in the normal way’, before being dealt.

He added: ‘If you wanted to get this outcome on purpose I would have thought that it would be impossible.’

Mr Lewis said: ‘The probability of this occurring in a single deal is 0.000000000016339. In other words the odds are around 1 in 61,204,166,001.

‘Given that the odds of winning the lottery are around 1 in 16 million, this demonstrates that it is a very unlikely event.’

Despite the unlikely outcome, he calculates that an identical deal should happen somewhere in the world about once every year.

The calculation is based on the estimate of 10 million people playing cards around the world every day, with each game requiring 10 deals.

That means 36,500,000,000 deals take place each year.