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1. Should I pass in the 1st round or double? Any opinion?
I would double and accept the occasional 2C bid.
Most of the times, 2C will be a 5 card suit in pard's hand, so that should not be a disaster.
The advantage of bidding right away is to be "in-quick, out quick" at a low level, and is right on values.
It is indeed offshape, but oh well... :-) taking a chance here has 2 chances out of 3 that pard likes our suit.
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2. Questionable pass by North. Probably they are playing precision.
a. pass does not llok right even playing Precision
b. if they do play Prec, they should alert
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3. Don't think south hand worth this 2♣ bid.
Agree. Too much of a balanced hand.
However, if playing Precision, at matchpoints, it is not unreasonable to resolve the shape of the nebulous diamond in order to be able to contest the partscore.
At IMPS, a clear pass.
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4. This double should be OK, right?
In my view, yes.
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5. This is the most critical bid. What different hands will be shown by 2♠ or pass?
I think 2S should show an overcall with slightly less than an opening bid but not completely broke.
Ideally, something like the following hand, with extra length:
QJxxxx-Axx-x-Qxx or so
Instead, RDBL would be semibal with full opening hand, jump to 3S = full opening hand playing strength with length in spades, jump to 3m = fuill opening hand, 2 suiter.
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6. Should I jump to game directly? What should I expect from my pd's 2♠ bid?
If pard bids 2S, promising what I showed above, then 4S looks right.
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7. Should my pard accept my invitation?
Nope, he has terrible minimum hand, forced to balance to protect you.
"Bridge is like dance: technique's important but what really matters is not to step on partner's feet !"