Mostly people choose a top 2 aspirational, two in the middle and one lesser.
This is standard MN advice, repeated year after year, often by the same posters. But that does not make it correct.
DC who are predicted more or less straight A*s, and whose school believes are capable of thriving on a top course, should aim for one. As discussed above, it can be a lottery. So:
- Apply to the top 4
- Treat it as a two year process.
Obviously allow more width for your second application, but if you are applying with A*s in hand rather than predicted your chances will be slightly better anyway.
Given what I read on MN I think one reason why some schools have much better acceptance rates for top courses, is because they give better advice. You normally get one chance to go to University. You might as well aim for one that will be a strong fit.
Back to the percentage example I gave earlier. When DS was applying there was one place for every 11 qualified applicant at LSE, and similarly high numbers elsewhere. A good applicant might have a 25% chance of getting a place at a specific institution. So some end up with 4 offers, some none. That's the lottery bit. And this year it might be down to 20%.
And why is it important to aim for a top course. I would say maths. DS' fifth choice expanded their department and were taking applicants with a B in Maths. Graduates on technical courses will be hired partly on the technical skills acquired and salary levels will be bases partly on the rarity of those skills. It is pretty obviously that a course where most applicants have an A* in FM will be able to go faster and cover more ground.
Getting on a top course is a bit of a lottery. Why not do everything you can to maximise your chances.
(I would put a firm bet on the fact that your DDs school has changed their approach for gifted mathematicians in the decade of so since your DDs left, simply because the competition has increased so much.)
And yes Oxbridge interview. Each top course has a slightly different recruitment approach. It depends on the applicant which approach they are more likely to do better in. As a broad generalisation and based simply on the London applicants we knew, Cambridge economics likes confidence. The type who walks into an interview room and is there with a ready and interesting opinion. Without exception the people we knew who went there had parents who were (very) senior bankers. LSE in contrast seemed to like quieter mathematicians, who perhaps shine better on paper. Warwick liked linguists. A small, possibly inaccurate, sample but observation nonetheless.