S,1 or 1,S as a condition for maths offers

Hi, does it ever happen that Cambridge colleges give an 'S' (in either StepII or III) as a condition in their offers? I've heard this is the case for St. Johns and Trinity, but what about the others?

Also, is it true what I've heard that 1/3 of Cam mathmos got an 1,2?

Supposing 600 people do the StepIII every year (given 550 offers and some 50 people doing it for fun or in advance), 33% of these, or around 200 people, get 'S' or 1 (out of 250 acceptances). Does this mean an applicant with 1,1 trumps another who has higher grades but 1,2? And what if the former is a foreigner? Foreigners made up 30% of Cam application rate in 2020, but only 18.6% of the final acceptances.

Thank you very much for you answer Theloniouss, very informative.
In the link Gurbir Johal asks "I would like the No, of offer holders making Grades X,Y in II and III and how many of those got a place/acceptance".

Is this what the table is showing in the column 'offers', or is it instead showing total offers conditional to x,y?
I take it to mean the latter, but given the precise question they might have given him what he asked for.

They look at scripts in detail and sometimes acceptances are weakly correlated with raw marks. You can get rejected having missed your offer by 1 mark, or get in having missed it by a considerable number. (presumably if you have a promising script or many marks lost were silly mistakes and you had good ideas)

I would avoid colleges that pool most who miss their offer out of hand, (though this is contrary to official advice that college choice doesn't matter) even if just to avoid the 2-day stress of the pool.

Hi there OP. Offers which include an S grade (so S,1 or S,S - we don't specify which exam the S should be achieved in) are relatively common. Partly this is to stretch the strongest mathematicians and partly if we're not sure about someone - clearly if they get the S grade, they've done extremely well!

Every year, there are plenty of mathematicians who are admitted with grades lower than 1,1 at STEP. This is partly because of the flexible offer scheme operated by some colleges (see here for more information) and partly because Admissions Tutors and Directors of Studies not only get grades, but also marks for each paper and can see the papers. Our Admissions Tutor goes through the papers of all applicants who've missed their offer very carefully to see how they did on the questions they answered. If there working was good, or they only narrowly missed the offer, they may be reprieved.

@Theloniouss is absolutely right about international offer holders. International students may struggle with fees and are probably more likely than UK students to be holding offers from other universities outside the UK, whether that be in the US, China or Singapore or their home country (if it's not one of the ones I've listed).

Hope this helps!