I have played all of the above and some others as well.

Personally, my preference is to play shortage (or some variant) in these positions. I also dislike the 3♠/3N flip for several reasons:

1) I struggle to remember it
2) It is hard to exploit (e.g v suitable hands can pass NS 3N)
3) Additional system is needed for when serious isn't used (do we flip em back, do we play something else).
4) It has little advantage over standard and some deficits. It definitely is not a win-win convention.

Your priority should be shortage showing in my view. If I was playing the scheme I would follow something similar to Martens proposal of Stayman+Transfers.

I am in the X=T/O of ♠ camp too. X=Balanced is a very popular defence to M2♦ known as Dixon here in the UK. I think people like it as:

a) It fits with 1N-(2♦*)-X = Values
b) (2♦*)-X-(2M)-? = You can now treat this like 1N-(2M)-?.
c) Simplicity

From my experience though, it is far too fiddly for my liking hence the X=T/O route. This also fits in with the rest of my X of ART bids style which is nice.

Lot of probables, but I am tired.

As Michael I would bid 4♦ as 4♥ should be to play probably (or stronger/weaker) I would then make some sort of move over it as necessary.

On your auction I would bid 5♠ probably.

South should open
North should potentially open more than 1♠ (2♠/3♠/4♠)
North should bid more than 2♠
South should definitely bid on

Oh and what is 2♠ in 4th. If intermediate then isn't 2♠ here somewhat stronger thus, even more of a reason for South to bid on.

Seems like both N/S are equally to blame

I think shape showing has more merit than controls but to each their own.

When I was playing this style last year with someone who liked it he preferred 2♦ as the positive as this allowed for a more comprehensive Kokish style.

2♣-2♦ = Positive:

2♥ = Bal or ♥
2N = ♣
3♣ = ♦
3♦+ = minors or 4441 shapes

The purpose was that partner can complete the minor transfer and then we can continue to show shape. E.g 4M-5m.

Over
2♣-2♥:
2♠ = bal GF or nat (there were followups)
2N = NF
3♠ = 4♠-5♥
Others = nat

Essentially if you are going down this route you should try and get the most out of your 2♦/2♥ bids in terms of making up for lost time. Thus for me, I would pack all the good hands into 2♦ since they are the slam-interested ones.

Only 4? Partner must have solid 20count over there!

1♥ could be as bad as xxx, QJTx, x, xxxxx for me :P

So where do I rank this hand (hmm).

As Simon.

Play 2♦ as Mild INV here and 2N as a more clearcut game-try. All bids higher than 2♥ are as per 1♥-2♥.

Definitely bidding. Partner has 6♥-5m or 7♥-4m and wants us to pass only if we have a penalty double of 4♠.

Bidding 5♣ as the info both sides give might help us judge 5♠ vs 6level better.

in which case they have 5♥ and a FNJ. If partner doubles then they have even more dummy ruffing potential.

Not convinced by the line of logic that defending 2♥x is right. RHO almost certainly has 6♥ and possibly a Fit Non Jump with ♦ which we cannot shorten sufficiently to take control fast enough. Hands like x, AKQTxx, xx, xxxx spring to mind where 2♥ x looks to be in rude health, no? We are basically gambling on the black suit breaks + partner not straining too hard it seems.

Floating between 3♣ and 3♦. Don't think 2N is right at all as LHO will lead stiff through partners possible Kx. Pass could be right but I feel 3N is too likely to be on the cards.

Hopefully 3♣ will show partner interest (they will put me on approx 6♣ + outside A) and then they can judge accurately whether 3N is good. The problem with this is we hold the A♠. This is a really bad card for our hand as it means partner cannot be sure whether Kxxxx, Ax, xxx, xxx is 9 tricks.

Tempted by 3♦ but the vuln and the fact that Niall is likely my partner makes me stray to the conservative action.

Since I guessed/proposed the 4♦ two-way treatment, I should say that Andy is technically correct. However, I also think a sign-off is more important than a diamond slam-try full stop.

The hand we have picked up is among the most powerful “without shortage” hands that we can pick up and it is still borderline sign-off after 3N-4♣. This tells me that we definitely need a sign-off. If you do want the diamond slam-try then the two-way bid seems like a reasonable compromise.

See my point above as to why I would long suit try in ♥. Hopefully, partner will move with heart cards or heart length+other values which is probably our best shot.

Neither do I, since for me a mixed raise contains shortage. However, I think they both fall within the parameters specified. 4333 is apparently on the border

Kxxx, xxxx, KQx, xx is a better example as you won't need to pick up ♣.

Richard has somewhat illustrated my point. To my mind, you bid 3N primarily to hear shortages from partner and evaluate accordingly. If partner bids 4♣ you will want to do 2 things:

a) Stop in 4♠ as you needed shortage from partner
b) Make another slam try.

Since I know Frances puts a lot of work into her system, I was curious. My initial guess was:
3N-4♣
4♦ = Slam try with ♦ or Sign-off in 4♠

then:
4♥ = Which was it please?
4♠ = No interest opposite either

This also works over 1♥-3♥ assuming 3♠ is now the ask. There are other solutions but this seemed to fit most easily into the above structure.
………………………………..

So on the particular hand if we can bid 3N “free of charge” then we definitely should since some days partner will show ♥ shortage which is great for us. To my mind then the problem becomes what to do over 3N-4♣.

Assuming we have no sign-off option and we have bid 3N, I would probably make a slam try in ♥ over 4♣. Partner is often 4=3=4=2 or 4=2=4=3 so I have reasonable chances of making all 4♣ regardless of their club holding. Therefore it makes sense to get them to evaluate for ♥.

(Sorry btw about not reading the problem properly but was rushing out)