Partner, nv at imps. opens 1♦ and bids 3N over our 1♥ response, showing a good hand with a good, long and strong ♦ suit, black suit stoppers and usually short ♥s.
The panel, and all responders, wrestled with two different issues: are we content with the bird in the hand... and almost certainly cold game, or do we go seeking bigger game (slam)... whether in ♠ or ♦s?
And if we venture out in search of ♠s, how certain are we that partner will understand what we are doing?
Not very, seems to be the consensus of the experts. Frances goes further (well, actually, it was Jeffrey who went further): We would like to bid 4♠ natural but the last time this auction came up (Ed: the last time? You mean this has happened before?
Fred (and Ben similarly) said that 4♠ was ambiguous...both as to whether it shows a suit and as to whether it is passable. My own thoughts are closer to those of Frances: to me this auction does not permit finding a 3rd suit as trump. Add to the relative infrequency of such hands the problems we have distinguishing forcing and non-forcing meanings (just how does opener advance a natural forcing 4♠ bid?... and how clear is that?) and 4♠ is a bid in search of a meaning... not a solution to a problem.
Justin felt that ♠s were unreachable, thus implicitly agreeing with Frances about it being a cue bid....Phil Clayton also mentioned that 4♠ was a slam try, but did not specify whether it was natural and forcing or a cuebid. Justin (and Phil) decided that he'd take his plus score, via pass.
Fred chose 4♦, rather than 4♣, which he agreed was a cue. He felt that 4♦ left him better positioned to control the auction: which is needed because he is not committing to slam: he will cue 5♣ over 4♠ but otherwise signoff in 5♦... a plan echoed by Ben. Fred added an extra and subtle dimension to his reasoning. He felt that a cue bid now, followed by a signoff in 5♦, would be too likely to encourage a possibly winning trump lead.
Henri (ritong) joined Justin with a pass that he described as cowardly. If he knew that partner's club stopper was the Ace, he'd reconsider, (but lesser cards would probably be wasted in a ♦ slam).
The 20 votes (one more set arrived after I did hand 1) included 8 for pass, 4 for 4♦, and 5 for 4♠ with individual votes for 5♦, 6♦ and 5♣.
I think that 4♠ is misguided and am demoting it in the scoring. None of the 4♠ bidders provided comments, and thus I do not know whether they felt that it was forcing or passable, which impacts the assessment of the bid for scoring purposes. Furthermore, as Justin observed, even if partner holds Kxx in ♠, we may not want to play in 4♠, and certainly no higher.
I was inclined to significantly upgrade the 4♣ call, chosen only by Frances: I will upgrade it but Fred's comments about the advantages of 4♦ (less encouraging to partner than 4♣ and less informative to the opps should we stop in game) persuade me that 4♣ is not as attractive as I had originally thought: when I put the problem on the net (I cribbed it from an old BW), I was torn between 4♣ and 4♦, but now think that 4♦ is much the better bid.
My scoring:
4♦ 100
Pass 80... I don't like it, but it was popular and could work out
4♣ 70
4♠ 50 I'd give it less, but it got a lot of votes
5♦ 40.... not a slam move, and a lower scoring game
6♦ 40..... too committal, risks a minus score

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