Punters are placing 100-1 bets on Princess Eugenie naming her baby after her scandal-hit dad Prince Andrew.
The Queen's granddaughter, 30, revealed she was expecting her first child with Jack Brooksbank last week.
Arthur is the 4-1 favourite for the royal baby's name but punters are hoping they'll look past the furore surrounding the Duke of York.
Coral spokesman Harry Aitkenhead told the Daily Star: "Although we haven't seen many bets on Andrew, there have been a couple of punters place small stakes on it.
"These are only £1 or £2 bets, as is often the way in markets like this, and a £1 on Andrew would return any lucky punters £100 winnings if their predictions came true, with odds of 100-1."
He added: "We always include any family names in our betting for each Royal and there is always a wide range of choices from bettors having a flutter."
Prince Andrew stepped back from public duties after giving a car crash Newsnight interview on his links with the late paeophile financier Jeffrey Epstein last November.
He sensationally claimed he was at a Pizza Express in Woking on the night he was accused of sleeping with alleged teenage sex slave Virginia Roberts when she was 17.
The Queen's favourite son denied wrongdoing saying her claims could not be true due to his "inability to sweat".
Prince Andrew has since been keeping a low profile and did not appear in his official photos of his other daughter Princess Beatrice's wedding in July.
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Mr Aitkenhead said Arthur could be the "perfect" name due to its historic links with both the Royal Family and 34-year-old wine merchant Mr Brooksbank's ancestry.
He added: "Arthur is a name that appears in Jack's family history, as well as the Royal family, so we think it could be the perfect one for the their first child if it does turn out to be a baby boy."
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Oliver was the second favourite with 5-1 odds whilst Mary is the 6-1 third favourite and the shortest odds of the girls' names.
Mr Aitkenhead said: "If it is a baby girl, we make Mary the most likely name according to the betting, whilst the likes of Lily and Alice are in the frame too."
The odds are: 4-1 Arthur, 5-1 Oliver, 6-1 Mary, 8-1 Edward, 8-1 Lily, 10-1 Alice, 10-1 Alexander, 12-1 Hugh, 12-1 Nicola, 14-1 Isabella, 14-1 George, 14-1 Alastair, 16-1 Thomas, 16-1 Ruby, 16-1 Philip, 16-1 Mia, 20-1 Elizabeth, 20-1 Henry, 20-1 Zoe, 25-1 Stephen, 33-1 Michael, 33-1 Emilia, 50-1 Maya, 66-1 Sarah, 66-1 Maya, 100-1 Andrew
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