unfortunately I think all 4+ assessments are a crap shoot - it all depends if your child is clingy on the day (if a 3 year old is coming down with a cold, they won’t be happy to go into a new place and behave without crying!), is offered activities they like (some kids like trains, some kids like animals - they might be happy to count trains and not cats!), and had a good sleep the night before!
Generally, I think Falkner are looking for curious kids who can follow instructions, sit still, and have some age appropriate ‘academic’ ability (interested in letters and numbers rather than can write a sentence!). More importantly, they don’t seem to take kids who can’t go into the assessment without being clingy or crying, or is disruptive.
i think they’d be the first to agree that 4+ is not a great time to assess children - they are just too young to know what they will be like at 10. Lots of boys who make the 4+ aren’t the most academic in later cohorts (I think those are the ones who join on occasional places later, when academics can be more rigorously tested), but the school is still very supportive of children for whom Harrodian/Ibstock is the right level academically.
i do think they assess for parents too. There are plenty of non British parents, but most parents are ones are happy to trust the school, able and willing to support with homework further down the line, and are not pushing for Stpauls/westminster or die narrative.
if you are a fairly chill parent who are quite academic yourself, trust and believe in the school, and have a well-behaved (and probably older in the year) boys, you have a good chance.
most parents towards the older years are genuinely choosing not to apply to St Paul’s etc as many feels the deeply ingrained competitive environment is not right for their kids, and FHB is fully on board with that.