EDIT: Trying to use the hand editor since the original format caused some confusion for some.[Question: how to get it to show a ? under West's 2nd bid]
IMPs. Dealer South. None Vul.
* 3♠ = Pre-emptive
You are West, your bid.
A number of alternative bids were given, Pass, 4m, 4H, 4S, 4N.
I find anything beyond 4H as being a bit nuts tbh with a balanced 10-count. Pass also seems manic, since their 3S suggests 9 trumps (although the discussion was in a 4cM area, it doesn't really matter I think since they are suggesting a 9-card fit whatever their basic system) and the LTT tells us that 3S-X is likely to be a good score for them however it turns out. Essentially Pass should have a surprise for them in trumps along with some values.
That leaves a choice between 4C & playing 4H on a possible Moysian. I plumped for 4H at IMPs, but would probably go for 4C at MPs - even though that could be a 0 count from partner's viewpoint.
The discussion around this seems to centre on two areas:
1. How many hearts does partner guarantee for the X?
2. What does 4S mean and does that affect what 4N means? (N.B. Not saying that they're sensible on this hand, just to discuss what they mean systemically).
For 1, there is a question as to whether partner is obliged to bid 4H with any 5-card or longer holding, even say Q9xxx (or even 65432?). If so, does the X suggest that he has only 4 hearts. And does it promise 4 hearts? Note that in this we're ignoring the possibility that he may have a very strong hand that needs to start with a X, since that will not be a problem hand.
If they were bidding hearts then we would of course expect partner to bid 3S with 5+ cards and X with 4, but we're in a different boat now that 4H may end the auction and we may play a 5-1 fit.
Re question 2, there were all sorts of suggestions re these bids - some saying that 4N is rkc for hearts, some that it's a general force, some saying any 2-suiter with hearts goes that way so 4N is minors. If it has hearts then it must be a slam try to go beyond 4H, so... I thought it would be interesting to see what people here think. The 3S pre-empt certainly causes some problems for people.