Imps, NS Vul
K x x x x
J x x
A J x
We agree with your valuation. This hand is worth an invitation only. Assuming your 9 HCP are 8 WP, we will reason like this.
We know that our SST will be at worst 5. But that only happens if North has 5-3-3-2 with the same doubleton as you. Since expecting that is overly pessimistic, we assume that our SST will be 4 or less (partner is twice as likely to have a doubleton diamond or heart than a doubleton club). To make a game then, partner needs 15 WP or more. Alternatively, he may have a red suit singleton, so that our SST will be 3. Then, a minimum opening will be enough for game. In both cases, partner will know that he should bid 4. No need for us to bid his cards.
If you should bid 4 over a potential 4 is not so clear. True, 4 won't be very expensive, but going -100 (or rarely -300) instead of +100 (or +200 if you dare to double), is costly at any form of scoring. Heart bids by the opponents increase the chance that East has a singleton there, but then why didn't he bid 4 all by himself? Suppose his reason for passing over 4 was that he had wasted values in their suit. Then, your jack of hearts may play a big role on defense against 4.
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