[DavidKok]

This thread is an offshoot of this thread. In this thread I'll present a set of competitive agreements after a natural overcall of a nebulous opening bid (this includes e.g. transfer overcalls, as long as the opponents have promised a suit these methods can reasonably be applied with some modifications). In particular, this structure works well when opener frequently has a balanced hand. The goal is to frequently enter the auction with competitive values without going past our most common safety levels, while retaining maximum accuracy should we prove to be able to force to game.
The two core ideas are:

• Showing shape is often more important than showing strength, provided the bidding hasn't gotten to a level yet where it is unsafe to enter with a relatively weak hand.
  
• By using transfers we are guaranteed to get a rebid with strong hands while we can stay low on misfit minimum hands.

For constructive-but-not-GF bids we need some rules on how to respond to partner's bid. I think these rules themselves also deserve to be optimised for each situation, but here's a simple set that covers most of the questions:

• Completing a transfer shows a minimum in context and is not forcing.
  
• Superaccepting (i.e. raising the suit shown by) a transfer shows a fit and is constructive but not forcing.
  
• Bidding the opponents' suit is a forcing raise confirming a fit.
  
• Rejecting a transfer with the cheapest NT call is not forcing and tends to show an unbalanced or semibalanced hand with length in the opponents' suit and shortage in responder's suit (balanced minima tend to complete the transfer instead). Note: this can be awkward if opener rebids a NF 2NT on certain auctions, you could instead change this rule out for something more nuanced.
  
• Bidding a new suit instead is natural and forcing.
  
• Forcing natural or cue bids at the 3-level are forcing to game (again, you can introduce exceptions to this as you please).

This is somewhat similar to "respond as if partner had made a negative free bid, completing the transfer exactly if you would pass" but covers some of the edge cases and clarifies some (though not nearly all) details.

While originally this system was intended to be used after interference over a strong club, I've since modified it for a Dutch Doubleton 1♣ opening. With the kind help of several friends we've managed to refine the structure somewhat. I am now translating this back for use over a strong club including the refinements, and as a result some details might seem out of place. I'll remark on those whenever they come up, and you may wish to change the structure to be more in line with a strong club approach.

In general it is more important to show majors than minors, more important to bid when we are short in the overcalled suit (as the auction is more likely to get bounced) and would really like to put opener on lead on 1♣-(<something>)-?, both because this means the strong hand is declaring and because it puts overcaller on lead. Transfers can achieve all of these reasonably effectively.
The allocation of bids will necessarily depend on the amount of bidding space available and the suits still in play. As a result this is a complicated method, but with some core design ideas:

• Most bids will be will be 'semipositive+' or 'negative free bid plus' transfers. Facing a Precision 1♣ opener this means approximately 5+ HCP or an ace. Facing a Dutch Doubleton 1♣ opening this means approximately 8+ HCP. As always you may take liberties with extra length or well placed values or choose to be conservative with unsuitable hands, a point count is no substitute for hand evaluation. I'll abbreviate this with SP+.
  
• It is often valuable to have multiple ways to bid with a major suit, to best clarify our holding as early as possible. Having undisclosed length in a major suit can lead to awkward guesses on further rounds, so (when available) multiple bids are allocated to clarifying this.

With all that out of the way, let's begin with the actual system.

1♣-(X)-?. This auction is special - the X gives us extra bidding space, but usually anticipates jumping around by fourth hand. To properly defend against this we need a defence that depends on the meaning of the double, e.g. 'both majors'. The suggestion below is instead optimised for a Dutch Doubleton 1♣ opening, but I think it ports over reasonably well.

Spoiler

• Pass = weak (0-4) any
  
• XX = SP+ 5(+)♦, Walsh style (denies a 4cM if exactly semipositive).
  
• 1♦ = SP+ 4(+)♥, Walsh style. Note: over a Dutch Doubleton 1♣ I think it is instead interesting to require 5(+) hearts for this bid, giving up on the 4-4 major suit fit facing a standard takeout double. 4-4 fits are allegedly less frequent on that auction, and might not play well even when available.
  
• 1♥ = SP+ 4(+)♠, Walsh style.
  
• 1♠ = SP+ (semi)balanced.
  
• 1NT = SP+ 5(+)♣ - note that most hands with exactly 5 clubs are best treated as (semi)balanced, so this usually shows 6.
  
• 2♣ = SP+ 6(+)♦ single-suited (over a Dutch Doubleton I'd consider making this bid weak, e.g. 4-8 HCP, instead).
  
• 2♦ = SP+ 6(+)♥ single-suited.
  
• 2♥ = SP+ 6(+)♠ single-suited.
  
• 2♠ = 5(+)♠5(+)other (2NT asks), GF.
  
• 2NT = 5(+)♥5(+)♣, GF.
  
• 3♣ = 5(+)♣5(+)♦, GF.
  
• 3♦ = 5(+)♦5(+)♥, GF.

The last few bids require some additional explanation. Over a Dutch Doubleton 1♣ the idea is to play these bids not forcing, approximately 7-10 HCP. This allows for negative inferences on the other shape-showing bids whenever we are too weak to bid again in further competition. This requires putting the spades two-suiters in 2♠. Over a strong club I think the constructive NF range, i.e. semipositive, is probably too narrow a target. In keeping with principles of the transfers it's then probably best to also swap around the order, e.g. 2♠ = 'a two-suiter not containing spades' (2NT asks, bid the other suit you don't have - very awkward if that bypasses your suit(s) though) and 2NT+ showing the suit above and spades, or the likes.

1♣-(1♦)-?

Spoiler

• Pass = weak any or a trap pass of diamonds.
  
• X = SP+, 4(+)♥.
  
• 1♥ = SP+, 4(+)♠.
  
• 1♠ = SP+, (semi)balanced.
  
• 1NT = SP+, 5(+)♣ (as before, usually 6(+)).
  
• 2♣ = GF three-suiter with short diamonds. Over a natural 1♣ opening you may wish to use this as a simple raise. It is also very reasonable to leave it idle for the sake of simplicity. Over a truly nebulous bid I think treating the transfer to their suit as a strong three-suiter is useful, as that hand type can anticipate future competition.
  
• 2♦ = SP+ 6(+)♥ single-suited.
  
• 2♥ = SP+ 6(+)♠ single-suited.
  
• 2♠ = 5(+)♠ + 5(+)♣, GF
  
• 2NT = 5(+)♠ + 5(+)♥, GF
  
• 3♣ = 5(+)♥ + 5(+)♣, GF

As before, shuffling the two-suiters around is probably wise. I'm going to stop commenting on that from here on out.

1♣-(1♥)-?

Spoiler

• Pass = weak any or a trap pass.
  
• X = SP+, 4-5 spades.
  
• 1♠ = SP+, (semi)balanced.
  
• 1NT = SP+, 5(+)♣.
  
• 2♣ = SP+, 5(+)♦.
  
• 2♦ = GF three-suited short hearts.
  
• 2♥ = GF, 6(+)♠.
  
• 2♠ = SP, 6(+)♠.
  
• 2NT = 5(+)♠ + 5(+)♣, GF.
  
• 3♣ = 5(+)♣ + 5(+)♦, GF.
  
• 3♦ = 5(+)♦ + 5(+)♠, GF.

This is an adaptation of a standard scheme over 1m-(1♥). In standard we'd assign 2♥ = weak or GF with 6(+)♠, 2♠ = NF invitational. Over a strong club that doesn't make too much sense. It is probably better to split out some of the hands with 5 spades from X and put them in 2♥ or 2♠, I'd love to hear people's thoughts about this.

1♣-(1♠)-?. This is the first annoying one, as we have no transfer to NT. In standard it is common to play 1NT = 8-10 natural here, and I've copied that over. Arguably this is a silly idea and should be eliminated in a strong club context for the 'obvious' club transfer.

Spoiler

• Pass = weak any or a trap pass or semipositive hands with clubs and no good bid.
  
• X = SP+, almost always exactly 4 hearts.
  
• 1NT = SP, natural NF (may be semibalanced with clubs). Alternatively: give up on showing this hand type and utilise this as a club transfer.
  
• 2♣ = SP+, 5(+)♦.
  
• 2♦ = GF, 5(+)♥.
  
• 2♥ = SP, 5(+)♥. NF. Note: on this auction we don't have a three-suited GF transfer bid, as it is too valuable to have an extra way to clarify our hearts holding.
  
• 2♠ = GF (semi)balanced or long clubs.
  
• 2NT = 5(+)♥ + 5(+)♣, GF.
  
• 3♣ = 5(+)♣ + 5(+)♦, GF.
  
• 3♦ = 5(+)♦ + 5(+)♥, GF.

1♣-(1NT)-?. This bid is (or should always be) artificial, and you are probably best served playing something like 'Unusual versus Unusual' against this if it shows a specific 2-suiter. Nevertheless here's a generic scheme. In the Dutch Doubleton setting there is significant value to be had in putting overcaller on lead.

Spoiler

• Pass = weak any or SP with clubs.
  
• X = SP+ (semi)balanced.
  
• 2♣ = SP+ both majors, at least 54+ either way. 2♦ asks for the longer or better major, responder jumps with a GF hand.
  
• 2♦ = SP+ 5(+)♥.
  
• 2♥ = SP+ 5(+)♠.
  
• 2♠ = SP+ 5(+)♣. Note: since this forces us to the 3-level this promises extra length if minimum.
  
• 2NT = SP+ 5(+)♦. Note: since this forces us to the 3-level this promises extra length if minimum.

I've omitted the two-suiters, you can add those back in if you wish. Keep in mind 5-5 in the majors can bid 2♣ and make sure to stay below 3M with a hand with that major to cheaply set trumps.

1♣-(2♣)-?

Spoiler

• Pass = weak any or a trap pass or semipositive with no good bid.
  
• X = SP+ takeout, at least 43 in the majors either way or a GF hand with no good bid.
  
• 2♦ = SP+ 5(+)♥.
  
• 2♥ = SP+ 5(+)♠.
  
• 2♠ = GF (semi)balanced.
  
• 2NT = GF 5(+)♠ + 5(+)♥.
  
• 3♣ = GF 5(+)♥ + 5(+)♦.
  
• 3♦ = GF 5(+)♠ + 5(+)♦.

1♣-(2♦)-?. This overcall represents a cutoff point. We no longer have transfers to both major suits, so instead we swap the structure entirely. This is a work in progress, but the basic idea is to use a Rubensohl structure.

Spoiler

• Pass = weak any or a trap pass or a SP hand with no good bid.
  
• X = SP+ takeout, at least 43 in the majors either way or a GF hand with no good bid.
  
• 2♥ = SP, 5(+)♥. NF.
  
• 2♠ = SP, 5(+)♠. NF. System aficionados may prefer to play 'switch' here, using 2♥ as SP+ 5(+)♠ and 2♠ as SP+ 5(+)♥ (or possibly make this second call forcing to game, or promise a sixth heart if minimum). This is likely an improvement, but since it would be a unique deviation from the system I've elected to stick with the hopefully easier to remember Rubensohl).
  
• 2NT = SP+ 5(+)♣, promises a 6th if minimum.
  
• 3♣ = GF three-suited with short diamonds.
  
• 3♦ = GF, 5(+)♥.
  
• 3♥ = GF, 5(+)♠.
  
• 3♠ = GF, (semi)balanced, this should perhaps be a stopper ask.
  
• 3NT = To play.

Quite a few of the bids here leave something to be desired. The direct 3♠ bid has overlap with the (much cheaper) takeout double, and voluntarily forcing ourselves to the 3-level with a 5-card major suit can backfire if opener has an unbalanced hand. In both Dutch Doubleton and strong club systems a natural 2♦ overcall can wreak havoc, and I do not have a satisfactory solution.

1♣-(2♥)-?

Spoiler

• Pass = weak any or a trap pass or a SP hand with no good bid.
  
• X = SP+ takeout, almost always exactly 4 spades. May be a GF hand with no good bid.
  
• 2♠ = SP, 5(+)♠. NF.
  
• 2NT = SP+ 5(+)♣, promises a 6th if minimum.
  
• 3♣ = SP+ 5(+)♦, promises a 6th if minimum.
  
• 3♦ = GF three-suited with short hearts.
  
• 3♥ = GF 5(+)♠.
  
• 3♠ = GF, (semi)balanced, this should perhaps be a stopper ask.
  
• 3NT = To play.

1♣-(2♠)-?

Spoiler

• Pass = weak any or a trap pass or a SP hand with no good bid.
  
• X = SP+ takeout, almost always exactly 4 hearts. May be a GF hand with no good bid.
  
• 2NT = SP+ 5(+)♣, promises a 6th if minimum.
  
• 3♣ = SP+ 5(+)♦, promises a 6th if minimum.
  
• 3♦ = SP+ 5(+)♥, promises a 6th if minimum (with a SP hand with 6 hearts bidding surely beats passing, so we stretch the bid to include hands too weak to force to game).
  
• 3♥ = GF three-suited with short spades. Note: it is superior to swap this bid with 3♠ below, making opener declarer in 4♥ on the hands where we have a heart fit. Again this would be a unique exception from general principles, so I hesitate to recommend it.
  
• 3♠ = GF, (semi)balanced, this should perhaps be a stopper ask.
  
• 3NT = To play.

1♣-(2NT)-?. Another weird overcall, this is sure to be some two-suited or artificial bid. I don't have a recommended defence, but you can play the 1♣-(1NT)-? generic defence one level up if you wish.

1♣-(3♣)-?. For 3♣ we can still play a relatively sound system, though trying to stop at the 3-level is now probably foolish. At this point it is useful to start including (artificial) 4-level bids. Unfortunately I don't know how to allocate those, and I'd love to see more discussion on this. I've included some more suggestions below but all of these are work in progress.

Spoiler

• Pass = Any hand too weak to force to game, or a trap pass.
  
• X = GF takeout, at least 43 in the majors either way.
  
• 3♦ = GF 5(+)♥.
  
• 3♥ = GF 5(+)♠.
  
• 3♠ = GF, (semi)balanced, this should perhaps be a stopper ask.
  
• 3NT = To play.

1♣-(3♦)-?. Starting with 3♦ circularly swapping around bids is as reasonable as anything, so:

Spoiler

• Pass = Any hand too weak to force to game, or a trap pass.
  
• X = GF 5(+)♥.
  
• 3♥ = GF 5(+)♠.
  
• 3♠ = GF takeout, may be offshape. Good luck.
  
• 3NT = To play.

1♣-(3♥)-?

Spoiler

• Pass = Any hand too weak to force to game, or a trap pass.
  
• X = GF 5(+)♠.
  
• 3♠ = GF takeout. Does not particularly promise 4 spades.
  
• 3NT = To play.

I hope this set of suggestions can spark some interesting discussion. Personally I think a set of agreements similar to the above can work well over a lot of nebulous opening bids, especially if those opening bids are frequently balanced or semibalanced. One design principle that I failed to incorporate, but am eager to explore, is sometimes sacrificing definition on hands with length in opps' suit (e.g. balanced, especially balanced with a stopper) since it is least likely that fourth hand will raise the suit. Theoretically this can free up bidding space for better definition on hands with shortage in this suit.

[awm]

We generally play something similar, but I think you somewhat underrate the differences depending on the opening.

For example, take the auction 1♣-(1♠)-2♦(hearts)

Could opener have seven clubs and a heart void? I think if this is a possible hand, it would be nice to be able to bid three non-forcing clubs somehow; when we open a strong club we use a 2nt rebid (sort of like lebensohl) for this purpose. The options of 2♥ or 2nt NF are pretty unsatisfying here.

You’ve added a “raise with extras but not GF” with 3♥: this makes sense in a context where opener needs a LOT extra to GF (opening was 11+ and transfer is 5+ for example) where you need to be able to encourage but stop short of game. But opposite a strong club this makes less sense — 5 opposite 17 is not far from game and if you give opener a four card fit and/or a bit extra it’s okay to commit to game. We prefer 3♥ here after the strong club as GF, which frees 2♠ for another use. We actually like natural, certainly over something like psycho suction where the overcall could be based on ♣+♦.

[awm]

Another difference for us is the 2nt bid. When a strong club is opened, we have found it is useful to have a natural GF 2nt available. This gives opener space to show a suit of his own in case we are better off in a suit game or we have a suit slam! Neither blasting 3nt nor an off-shape double really appeals.

Opposite our 1♦ opening, such a 2nt is much less valuable. Opener can’t have a one-suiter and he’s limited enough that slam is quite rare with responder having wasted values in the opponents’ suit. Blasting 3nt is okay here, and we play 2nt as a club transfer over 1♦-(2M) as you suggest.

[DavidKok]

The idea of the not-GF raise is that completing the transfer denies a fit and preserves maximum room in case responder has extras, since that's the scenario where we don't know about the optimal strain yet. The jump accept is a 'support with support' style bid, allowing responder to better evaluate their hand. With a void and a 7-card side suit completing the transfer is not an option, but most balanced and semibalanced hands will play best in the long suit of the weak hand in case of a misfit with neither side having extras. It's also one of the cheapest contracts available.

Ditching the jump accept with fit makes sense, forcing to game whenever you find a fit is playable. I think by frequency it's still a useful bid to have, as it also clarifies that we're usually not looking for a slam anymore.

You could very well introduce some NF responses to certain transfers, though most of the time you won't need them. This makes it more difficult to show stronger hands and I tried to keep responses to the most common transfers simple for now, but I'm eager to learn more about good rebid systems for opener. As an aside 1♣-(1♠)-2♦ is forcing to game, but there's other example auctions where these issues are very relevant. On the Dutch Doubleton auction 1♣-(1♠)-? I would play 2♥ NFB (approx 6-9, 5(+)♥, NF) with 2♦ being inv(+) 5(+)♥, so opener still doesn't need a mountain of a hand to initiate a game force.

On low level overcalls responder has a way to make a transfer to notrump, rightsiding an eventual 3NT contract while preserving space for opener to show shape. On the overcalls where this isn't available that's a serious issue, and reserving 2NT natural GF is an interesting idea!

[foobar]

What do folks play over 4th hand interference? The common situations are 1♣ - (P) - 1♦ (negative) - (bid), 1♣ - (P) - (GF positive response) - (bid), 1♣ - (P) - (semi-positive non-GF response) - (bid).

Over 1♣ - (P) - 1♦ - (bid), one treatment is to "pretend as if the opponents opened the bidding", so for example after 1♣ - (P) - 1♦ - (1♠) - 2N (minors), and so forth. Over the positive GF response, playing PDI at some level appears to make sense.

[DavidKok]

I think this depends a great deal on what the responses show, and haven't given this much thought. But very briefly:

• If partner's bid set up a game force we can use general rules for game forcing auctions, e.g. pass = forcing and no good bid, X can be either takeout(/'values') or penalty-oriented depending on preference, bidding shows a long suit.
  
• If partner's bid was a generic negative treating it as if they had opened seems very reasonable. I wonder if there is room to improve here but don't know of any discussion on this topic.
  
• If partner's bid was some invitational+ bid, perhaps a transfer or coded bid, I think it is wise to bid the same as if second hand had overcalled/play a generic transfer response structure.

Forcing pass and PDI can help generate more sequences at relatively low cost, and are probably wise to implement in most situations. There's a serious risk of misunderstandings though. I'm also really not happy with the very popular "1♦ is any negative, 1♥ through 3NT are some positives" approach that a lot of strong club systems have, and dealing with fourth hand interference is going to be very different in systems that are not of this type.