Selby completed a 13-7 victory over the No.2 seed when taking two of the opening four frames of the morning session at the Crucible.
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A 91 in the opening frame of the day had moved Selby within one of victory, but his march to the semis was delayed as Robertson valiantly won the next two.
Another tight frame just before the interval this time went Selby's way, and the 2014, 2016 and 2017 winner is now just two wins away from another world crown.
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A last-four meeting with Mark Williams or Ronnie O’Sullivan awaits Selby, who is now the bookies favourite to win a fourth world title.
Williams holds a 6-2 lead over O’Sullivan in their quarter-final, which resumes in Tuesday’s afternoon session on Eurosport.
McGill closes on victory
Anthony McGill has moved within three frames of a first-ever World Championship semi-final, but has been made to fight by Kurt Maflin going into their evening session tonight.
In the battle of the two remaining unseeded players, McGill led 7-1 going into the morning session, but Maflin took the opening two frames to cut the gap to four.
An 86 helped McGill open that lead back up to five frames, only for Maflin to hit back again with an 87 as three wins on the spin made it 9-6.
A crucial final frame of the session saw both players miss big opportunities, but it was McGill who held his nerve to make it 10-6.
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