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Slam invite question

The auction proceeds to you


and you hold a strong two bid in spades. (The actual hand in the Soloway was AKJxxxx, --, AKx, AQT but the post mortem was the source of some theoretical discussion.) It would seem that you would like to have a "bid 6 with second round hearts", a "general I need some help", and perhaps "I need a trump filler." You have three possible auctions: 5S, DBL...5S, and 4N...5S. However, the problem with doubling with long spades is that partner may choose to convert so I am not sure that is really an option.

So, I am soliciting thoughts. As this is not a common problem, I think you need some sort of "meta rule" to apply in circumstances of this genre. In high level competition I believe that, "partner always has a trick." (Comment?)

Assume the auction we faced.

Please select up to 4 choices.

DBL is never a single suit slam try
DBL...5S is something (explain)
5S is asking for H control
5S is asking for spade help
5S is a need some general help
4N...5S is asking for H control
4N...5S is asking for spade help
4N...5S is need some general help

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