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4N (RKC). I know partner has 5+ S and 2+ D, and East's failure to support hearts suggests that partner also has heart length and therefore club shortness. So I don't expect any club losers and can practically count 11-13 tricks depending only on how many aces partner has. Did 5♦ also deny the ♣A? If so, what is partner supposed to believe?

First thing you have to determine is whether that hand is worth a game force. That depends on the location of your honor cards, your support for opener's hearts, spot cards like 10's and 9's, etc. Also, whether your partner tends to open light. Do you have 3 card heart support and are you playing 5 card majors? Then, what bidding system are you playing. I don't (and won't) play Acol, but I'm guessing that 2♣ would be a common response. In a "standard" 2/1 game force system, if you decide this hand is worth a game force, then 2♣ would usually be the response (i.e. if club were ♣xxxxx you may decide to treat clubs as a 4 card suit and respond 1♠. If you decide that hand is only an invitational bid, then 1♠ would be the choice. I'm not going to say anything bad about MAFIA responses, but just note that if responder bids 2 suits, the suit lengths are ambiguous and you need well defined agreements on subsequent rounds to figure out what's going on.

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Thanks for the input. An old criterion I learned for evaluating 6-card invites was to think of them as weak-two openers (given that a balanced hand opposite a weak-two opener needs around 15 to make a move towards game). Here this is a worse than average weak-two, so I would transfer and pass. Any better guidelines you can suggest? We cannot directly show shortness in an invitational hand, but we can bid Stayman followed by 2♠ (nominally a 5-card invite) and partner can ask for shortness over that. I notice that no-one commented about this option?...

I did a SIM opposite for 4S with that hand with 12, 13 and 14 points, and had the figures 23%, 49% and 57% respectively. 19%, 34% and 68% were the respective figures for 3NT, so there is something to be said for inviting with 2NT, and if partner goes back to 3S, I will add a fourth as the ninth trump rates to be useful.