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Robertson has joined Ali Carter, Stephen Maguire, Mark Allen, David Gilbert, Jimmy White and Graeme Dott in withdrawing from the event over health fears with nearby Spain reporting 50 deaths so far from the pandemic.
The 2010 world champion said he is not feeling well and would prefer to look after his daughter, who is also recovering from illness.
Trump raises the Gibraltar Open trophy to an imaginary crowd
"Just a quick one regarding my Gibraltar withdrawal," said Robertson on Twitter. "Not feeling the greatest myself and my daughter is very unwell but on the mend. Usually this would be enough for me to withdraw especially so close to the Tour Championship. Health comes 1st before any bonus on offer."
Carter, who has battled testicular and lung cancer, lives with Crohn's Disease. He was advised not to travel on medical grounds due to a "compromised immune system and previous lung issue" ahead of Friday's first round of matches.
World champion and world number one Judd Trump is bidding to become the first man in the history of the sport to claim six ranking tournaments in a season. He has been drawn to face Gibraltar’s top amateur player Lee Prickman in the round of 128. Prickman and Gareth Lopez - who faces Joe Perry - were handed wildcards as Gibraltar's leading two players.
Trump could pick up a £150,000 bonus in an event restricted to only 100 fans due to the coronavirus outbreak.
The winner of the event picks up a £50,000 first prize with the runner-up claiming £20,000, but there is also the not so trivial matter of £150,000 to be won by either Robertson or Trump, the two leading players in the world rankings.
If either man won the tournament they would claim the top prize plus a £150,000 bonus from tournament sponsors Betvictor. Robertson leads the BetVictor European Series having amassed £115,000 from three events so far with world champion Trump £35,000 behind in second place.
Trump and Robertson, officially one and two in the world rankings, were seeded to meet in the last four, but Trump can deny Robertson if he wins the event on Sunday.
Robertson won the first of the European series with a 9-0 whitewash of Zhou Yeulong in the European Masters final before Trump downed Robertson 9-6 in the German Masters final.
With neither player competing at the recent BetVictor Shoot-Out, Trump needs to win the event to deny Robertson his lucrative bonus.
This is one of only three ranking events left this season. With the cancellation of the China Open at the end of March due to the coronavirus outbreak, only the Gibraltar Open and Tour Championship remain on the schedule before the World Championship begins in Sheffield on April 18.
World rankings one-year list (after Players Championship)
- 1 Judd Trump 656,500
- 2 Shaun Murphy 383,000
- 3 Mark Selby 282,500
- 4 Neil Robertson 274,500
- 5 Ding Junhui 261,250
- 6 Yan Bingtao 206,500
- 7 Mark Allen 165,500
- 8 John Higgins 158,500
- 9 Stephen Maguire 152,000
- 10 Graeme Dott 136,250
- 11 Thep Un-Nooh 131,000
- 12 Kyren Wilson 130,000
- 13 Joe Perry 127,000
- 14 Mark Williams 113,250
- 15 David Gilbert 104,000
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