Counter invites or maximum flat hand with fit ?

W
N
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1NT
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2
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3
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2 was invitationnal natural with 5+.

My question is not only for this particular case but for similar cases.

What is the best use for 3S.

Counter invite or maximum hand with fit but flat shape (COG between 3NT and 4S)

Another example would be when 2 show 4 invitationnal. Its fairly standard that its something like

2NT = minimum only 2 or 3 but no ruffing power.

3Y = maximum, 3 and some ruffing power. (3 can possibly show 5 and a max)

3Nt = maximum only 2 or 3 without ruffing power.

4S - maximum 4 trumps.

Should 3S be a counter invite or a COG (maximum 4 trumps but flat hand) ?

COG are more important than counter invites.
If you are maximum +fit (but flat hand) just bid a new suit even if this bid tend to deny a full fit.
flat hand with 4 trumps are rare so when its 4-4 fit its a counter-invite but when its 5-3 fit its a COG bid.
Counter invites in all cases.

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