If you should vs If you happen: which is 'more possible'? :)

[Tamara]

I was taught that the pattern 'If you should' is rather formal and is used in the case when a speaker supposes an event (condition) to be very unlikely, just a chance possibility.

If your should see Ann, please ask her to phone me tomorrow.

OK.
My question is:

Is If you should equivalent (in the above sense) to If you happen or the latter still means 'more possible'? Or the latter is exactly the same, but just a bit less formal?
_________________
It’s impossible to learn swimming without entering the water…

[Alan]

Hi Tamara,

You asked:

[Yankee]

Hi Tamara

In American English, "If you happen to see" would be a much more typical expression. "If you should see" sounds fairly formal in AmE.

I'm not sure that I would think of "happen to" strictly as being used for "very unlikely" situations, though. It might be used in a situation where the degree of likelihood is simply unknown.

Amy

[Conchita]

[Tamara]

Hi all