This hand was presented as a bidding problem on our local Danish bridgesite, and most (including experts) saw it as an easy 3♠.
Obviously, I understand the arguments for that bid, but still I personally went for the direct 3NT. That may not always end the bidding, but 4♠ will typically only be reached if Responder has a 3-card support.
In contrast, the more popular 3♠ is forcing, and could lead to 3NT (frequently with 0 or 1 spade, rarely with 2 spades) or 4♠ (frequently with 2- or 3- card support).
Where I come from, a vulnerable pass followed by 2♥ over 1♠ will typically show exactly 5 cards and 9-10 hcps (or perhaps 6+ hearts with too many (3+?) spades for a decent 2♦(Multi)/2♥/3♥-opening, planning to support ♠ no matter what next round - if any!).
Thus, I assume it will be quite rare for Responder to follow up with a bid of 4 Minor or even 4♥, whether Opener rebids 3♠ or 3NT.
Please feel free to comment on:
- Openers 2nd bid
- Any of the above assumptions
- Your expectations of winning 3NT and 4S, respectively, if Responder has exactly 2-5 in the majors, and 9-10 hcps. Maybe someone can run a simulation?
/Niels

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Pass-Pass-1♠(5+)-Pass, 2♥(5+)-Pass-?