But the stand-up who has become famous for his comic creation the bigoted loud-mouthed Pub Landlord has another matter on his mind. His wife was due to give birth on Sunday and the baby is now almost certain to arrive during the final week of the Fringe.
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Murray has previously said he might go ahead with the show, since it normally takes more than an hour to give birth in any case. At this stage, he is keeping quiet on plans for the baby's arrival and how it might affect the remainder of his run.
The title of his show this year is And A Glass of White Wine for the Lady. It is scary to think what this might become once the Pub Landlord has his own child.
But for Murray, who was temporarily banned from the Perrier prize for becoming too well known, this looks set to be a week of reasons to celebrate.
Mobile man
Another proud father on the comedy circuit is Dominic Holland, who boasts a grand total of three children. In his stage routine, he admits he is exhausted by the strain of having to look after them.
Holland has given his eldest the nickname Nokia, because he only ever seems to need an hour to lie down and recharge and is then up for the rest of the day. Following this precedent, he refers to his two more recent arrivals as Ericsson and Motorola.
In his show, Holland recounts his experiences running around after his offspring. He describes chasing after them and picking up Ericsson and Motorola. "By this point," he adds, "Nokia is hands-free."
It is certainly the corniest line in his routine, but for some reason it got the biggest laugh.
The cannabis side-show
More worldly issues have dominated the Scottish news during the Festival thanks to the publicity efforts of the Bishop of Edinburgh, who has admitted to having both tried cannabis ("a bit disappointing") and thinking it should be made legal, in interviews about his new book.
The clergyman has won the support of some other religious leaders and a number of Scottish politicians. There is a feeling abroad that the Scottish Parliament might take a bold step and make cannabis available for recreational use - although it actually has no powers over drug laws.
Inevitably, not everyone agrees. Both Scotland Against Drugs (SAD) and Mothers Against Drugs (MAD) argue so-called soft drugs lead to heroin and the creation of ridiculous, self-defeating acronyms (clearly I made that last bit up, but the organisations are real).
But the Newsrevue team playing at the C Too venue offers the most compelling argument in favour of the status quo. It is not clear if the world is yet ready for the arrival of the first deep-fried hash cake.