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ATB: In competition, how much do you need to support partner's 2-level overcall?

This happened in the last round of a matchpoint game against decent opponents.

West
93
1054
KQ8763
J4
North
AKJ107
K8
A9
10865
East
Q52
AQ6
J52
A932
South
864
J9732
104
KQ7
W
N
E
S
1
P
2
2
3
3
P
4
P
P
P
D
4 North
NS: 0 EW: 0
The result is 4S -2.

3D by W make 3 would give NS a poor score.

3S by N -1 would give NS an average+.

4S by N -2 gave NS average minus.

South's point:

    - You (North) should pass 3S which is the only chance for us to get a decent score.

    - No matter what we get from 3D, we will get a bad score, thus I had to compete up.

North's point:

    - I expected a much better hand from you when you compete to 3-level.

    - Something like mixed raise (7-9) with 4 spades or limit raise with 3 spades.

    - For example, with 2 cover cards (any 2 of SQ, HA, DK, CAK), 4 spades, and a short in either minor, 4S is reasonable.

 

What do you think?

If you would not bid 3S with south hand, please comment on what more do you need to compete up?

Below are some examples:

    - Change H2 to SQ.  S Q864 H J973 D 104 C KQ7

    - Change D4 to SQ.  S Q864 H J9732 D 10 C KQ7

    - Change HJ to HA.   S 864 H A9732 D 104 C KQ7

North is 100% right. South had definitely overbid.
North is more right. South did overbid but North should pass since 3S is competitive.
Both North and South had overbid. They are equally wrong.
South is more right. South overbid with a purpose in a matchpoint game.
South is 100% right. His bid was the only way to get a good score.
None of the above.

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