nullve

Yes, why not.

The hidden game of "rock-paper-scissors" in a game of bridge with bidding boxes: Players: the two members of a bridge partnership Moves: gaps between consecutive bids by one player that are either * 'small' (plays the role of, say, 'rock') * 'mid-sized' (plays the role of, say, 'paper') * 'large' (plays the role of, say, 'scissors') Since the players take turns to bid and thereby make a physical move in this game, it's not at first sight a simultaneous game like "real" rock-paper-scissors. But as long as the players focus on the bids instead of the gaps, the last player to move will have no advantage except possibly due to subconscious effects. So at least we can pretend it's a simultaneous game, albeit one played unwittingly.

It would be nice to have good names for different views expressed here and on BW about what it takes to prove (table behaviour-restricted) cheating. I'll go first and propose the names 'emissionism' and 'transmissionism' for the views that in order to prove cheating, it's sufficient to prove that an illegal signal has been given ("emitted") and transmitted, respectively, and 'collusionism' for the view that in order to prove cheating, one must prove not only that an illegal signal has been transmitted, but also that the signal was preagreed.

Some ideas: 1M = "8-10", 4-5 M, (semi)bal. / "10-21", 5+ M, unbal. 1M-?: 1♠ = 4+ S 1N = "5-14(15)", 3- M. Also 3- S if M=♥. To play opposite "8-10" (semi)bal. (...) 2M = "4" M, PRE opposite "8-10" (semi)bal., F1 opposite unbal. hands (idea: Law protection) 2♠(M=♥) = WJS [not sure about the exact range, but < inv values] 3M = "5" M, PRE opposite "8-10" (semi)bal, GF opposite unbal. hands (idea: Law protection) (...) 1♥-1♠; ?: 1N = "8-10" (semi)bal., 3- S 2♣ = "10-18", 6+ H or 4+S5+H ("10-12", 3S5H4+m possible?) / "16-18", 2-S5H4+D [2♣ is partly a two-under transfer to hearts] ...2♦ = relay, GF opposite "13+" .......2♥ = "10-12", 3-S6+H ..........2N = GF relay .......2♠ = "10-12", 4+S5+H (or 3S5H4+m?) ..........2N = GF relay (?) .......2N = "13-15", 6+ H or 4+S5+H ..........3♣ = relay .............3♦-3♠ = M2 .............3N = 4522 .............4m = 4+S5+H, SPL m .............(...) .......3♣ = "16-18", 2-S5H4+D ..........3♦ = relay .............3♥+ = part of M1 .......3♦-3♠ = "16-18", M2 .......3N = "16-18", 4522 .......4m = "16-18", 4+S5+H, SPL m .......(...) ...2♥ = to play opposite "10-15", 3-S6+H ......P = "10-15", 3-S6+H ......2♠ = "10-12", 4+S5+H (or 3S5H4+m?) ......2N = 16-18, 5H4D ......3♣ = "15-17", 6+H4+m / "16-18", 4+S5+H" .........3♦ = GF relay ............3♥/♠ = part of M2 ............3N = 4522 ............4m = 4+S5+H, SPL m .........3♥ = to play opposite 6H4m ......3♦ = 15-17, 5H5D ......3♥ = "16-18", 2-S6+H ......3♠ = "13-15", 4+ S ......(...) 2♦ = "10-12 or 19-21", 5H4+m / "16-18", 3S5H4+m [2♦ is Muiderberg-like] ...2♥ = to play opposite "10-12" ......2♠ = "16-18", 3S5H4+m ...2♠ = (5)6+ S, NF ...2N = GF relay ......3♣+ = M1 ...3♣ = pref. opposite "10-12" ......(...) ......3♥ = "16-18", 3S5H4+C, NF ......3♠ = "16-18", 3S5H4+D, NF 2♥ = "13-15", 5H4+m [2♥ is Muiderberg-like] ...P = 2-3 H, < GF values ...2♠ = 5S1-H, scrambling [didn't respond 2♠(WJS) to 1♥] ......P = 2-3 S ...2N = GF relay ......3♣+ = M1 ...3♣ = P/C, < 5 S 2♠ = "8-10" semibal., 4 S ...2N = GF relay 2N = 16-18, 2-S5H4C ...3♣/3♥ = to play ...3♦ = GF relay ......3♥+ = part of M1 3♣ = 15-17, 2-S5H5C 3♦-3♠ = "19-21", M2 3N = 19-21, 4522 4m = "19-21", 4+S5+H, SPL m (...) 1♥-1N; ?: P = "8-10" (semi)bal. 2♣ = "10-18", 6+ H / 16-18, 5H4+D or 4+S5+H [2♣ is partly a two-under transfer to hearts] ...2♦ = relay, GF opposite "13+" .......2♥ = "10-12", 6+ H ..........2N = GF relay .......2♠ = "16-18", 4+S5+H ..........2N = GF relay .............3♣+ = M3 .......2N = "13-15", 6+ H ..........3♣ = relay .............3♦-3♠ = M2 .............3N = 4S6H .............4♣ = 4S7H .............4♦ = 5S6H .............(...) .......3♣ = "16-18", 5H4+D ..........3♦ = relay .............3♥+ = part of M1 .......3♦-3♠ = "16-18", M2 ...2♥ = to play opposite "10-15", 6 H ......P = "10-15", 6+ H ......2♠ = "16-18", 4+S5+H .........2N = GF relay ......2N = 16-18, 5H4D ......3♣ = "15-17", 6+H4+m .........3♦ = GF relay ............3♥/♠ = part of M2 .........3♥ = to play opposite 6H4m ......3♦ = 15-17, 5H5D ......3♥+ = "16-18", 6+ H, one-suited 2♦ = "10-12", 4S5H / "10-12 or 19-21", 5H4+m [2♦ is Lucas-like] ...2♥ = to play opposite "10-12" ...2♠ = P/C opposite "10-12" ...2N = GF relay ......3♣+ = M1 2♥ = "13-15", 5H4+m or 4S5H [2♥ is Lucas-like] ...P = 2-3 H, < GF values ...2♠ = P/C ...2N = GF relay ......3♣+ = M1 2♠ = "19-21", 4+S5+H ...2N = GF relay ......3♣+ = M3 2N = 16-18, 5H4C ...3♣/H = to play ...3♦ = GF relay ......3♥+ = part of M1 3♣ = 15-17, 5H5C 3♦-3♠ = "19-21", M2 1♠-1N; ?: P = "8-10" (semi)bal. 2♣ = 4+ H ...2♦ = relay, GF opposite "13+" ......2♥ = "10-12" .........2N = GF relay ............3♣+ = M3 ......2♠ = "13-15" .........2N = GF relay ............3♣+ = M3 ......2N+ = "16-18" .........3♣ = relay ............3♦+ = part of M3 ......3♣ = "16-21", 5413 (5404) .........3♦ = range ask ............3♥ = "16-18" ............3♠ = "19-21" ......3♦+ = "19-21", part of M3 ...(...) 2♦ = "10-18", 6+ S / 16-18, 5S4+D [2♦ is partly a two-under transfer to spades] ...2♥ = range ask, GF opposite "13+" ......2♠ = "10-12" .........2N = GF relay ......2N = "13-15" .........3♣ = relay ............3♦-3♠ = M2 ......3♣ = 16-18, 5S4+D .........3♦ = relay ............3♥+ = part of M1 ......3♦-3♠ = 16-18", M2 ...2♠ = to play opposite "10-15", 6 S ......P = "10-15" ......2N = 16-18, 5S4D ......3♣ = "15-17", 6+S4+m .........3♦ = GF relay ............3♥/♠ = part of M2 .........3♠ = to play opposite 6S4m ......3♦ = 15-17, 5S5D ......3♥ = "16-18", 6S3H, one-suited ......3♠+ = "16-18", 6S2-H, one-suited 2♥ = "10-12 or 19-21", 5S4+m [2♥ is Muiderberg-like] ...2♠ = to play opposite "10-12" ...2N = GF relay ......3♣+ = M1 ...3♣ = P/C opposite "10-12" 2♠ = "13-15", 5S4+m [2♠ is Muiderberg-like] ...P = 2-3 S, < GF values ...2N = GF relay ......3♣+ = M1 ...3♣ = P/C 2N = 16-18, 5S4C ...3♣/S = to play ...3♦ = GF relay ......3♥+ = part of M1 3♣ = 15-17, 5S5C 3♦-3♠ = "19-21", M2 Modules: M1: 1M-1N; 2[M-1]/M-2N; ?: One idea is to play similar stuff whether 2M-1 is a Muiderberg- or Lucas-style rebid, so e.g. 3♣ = 4+ D ...3♦ = relay ......3♥ = 5M242 or 5M5D .........3♠ = relay ............3N = 5M242, not 19-21 [haven't decided what to do with 19-21 yet] ............4♣+ = 5M5D. Relay structure? ......3♠ = 5M143 (0544) ......3N = 5M341, not 19-21 ......4♣ = 5M341, 19-21 3♦(M=♥) = 4S5H ...3♥ = anti-SPL C / relay ......3♠ = 4513 (4504) ......3N = 4522 ......4♣ = 4531 ......4♦ = 4540 ...3♠ = anti-SPL D 3♦(M=♠) = undefined! 3♥ = 5M224 or 5M5C ...3♠ = relay ......3N = 5M224 ......4♣+ = 5M5C. Relay structure? 3♠ = 5M134 (5M044) 3N = 5M314, not 19-21 4♣ = 5M314, 19-21 M2: 1M-1♠/N; 2[M-2]-2[M-1]: 2N-3♣; ?: / 1M-1♠/N; 2[M-2]-2[M-1]: ?: / 1M-1♠/N; ?: (...) 3♦ = one-suited 3♥ = 6+M4+C 3♠ = 6+M4+D M3: 1♥-1N; 2♣-2♦; 2♠-2N; ?: / 1♥-1N; 2♠-2N; ?: / 1♠-1N; 2♣-2♦; 2♥/♠-2N; ?: If M = opened major, (...) 3♣ = 5M4OM13 (5M4OM04) 3♦ = 5M4OM31 (5M4OM40) 3M = 6+M4OM 3♥(M=♠) = 5+S5+H 3♠(M=♥) = 5S6+H 3N = 5M4OM22 (...) ---- Could something like this be playable, or is there a big flaw somewhere? ------------------ 21 Oct: Hmm, the above doesn't look good even to me. I think i need to try: 1♥-1♠; ?: 1N = "8-10", (semi)bal., 2-3 S 2♣ = "10-12", 5+H4m / "10-18, 4+S5+H / "16-18", most (all?) shapes [Gazzilli-like] 2♦ = 6+ H [could be "10-15", as I know how to handle the "16-21" range by other means] 2♥ = "13-15", 5H4+m [Muiderberg-like] 2♠ = "8-10", (semi)bal, 4 S 2N+ = "19-21", relay structure 1♥-1N; ?: P = "8-10", (semi)bal. 2♣ = "10-12", either 5+H4m or 4S5H / "16-18", most (all?) shapes [Gazzilli-like] 2♦ = 6+ H [could be "10-15", as I know how to handle the "16-21" range by other means] 2♥ = "13-15", either 5H4+m or 4S5H [Lucas-like] 2♠ = ? 2N+ = "19-21", relay structure 1♠-1N; ?: P = "8-10", (semi)bal. 2♣ = "10-15", 4+ H / "16-18", most (all?) shapes [Gazzilli-like] 2♦ = "10-12", 5S4+m [Muiderberg-like] 2♥ = 6+ S [could be "10-15", as I know how to handle the "16-21" range by other means] 2♠ = "13-15", 5S4+m [Muiderberg-like] 2N+ = "19-21", relay structure which in some ways is much closer to what I actually play in a 2/1 context.

cherdano, I'll ask you again: Can you (cherdano, not Balicki) control your hand movements enough not to signal numbers on every second hand you defend after the screen is opened? If 'Yes', how do you know?

The ♣/♥ swap makes sense even without the strong option in 2♣, because it allows 1♠-1N; 2♣(4+ H)-2♦ = range ask instead of e.g. 1♠-1N; 2♥(4+ H)-2N = nat. inv.

If the 1N response allows you to pass bare minimum hands with 5S4C, you can play something like 1S-1N; 2H*-?: (...) 2N = inv+ relay (GF opposite 5S4C) ...3C = 5+S5+C, NF ...3D = 5134 (GF) ...3H = 5314 (GF) ...3S = 5+S5+C, FG ...3N = 5224 3C = pref., < inv (...) * 6S4C not included

Can you? How do you know?

I play 1S-1N; ?: (...) 2D = 5S4+m (Muiderberg-like) 2H = 6+ S, extras 2S = 6+ S, min ("10-12") (...) I actually pass 1N(5-12, NF) with 10-12, 5S4m, so the 2D rebid is easier to handle than one might think.

From a comment on Bridgewinners: "If someone is cheating, do we have to disclose their full method to prove guilty? No, we don't.Since B-Z use 3 ways to bid(small, normal, large gaps), so if they are innocent they are doing it unconsciously, and it will be quite random. If evidence show that randomness is violated then it is serious, regardless of the exact meaning." (http://bridgewinners.com/article/view/a-different-approach-on-b-z-bidding-gap-issue-3/) This got me thinking about the game of rock-paper-scissors: "Proponents of the “Chaos School” of RPS try to select a throw randomly. An opponent cannot know what you do not know yourself. In theory, the only way to defeat a random throw is with another random throw – and then only thirty-three percent of the time. Critics of this strategy insist that there is no such thing as a random throw. Human beings will always use some impulse or inclination to choose a throw, and will therefore settle into unconscious but nonetheless predicable patterns. The Chaos School has been dwindling in recent years as tournament statistics show the greater effectiveness of other strategies." (http://worldrps.com/advanced-rps/)

Maybe. But: "During a practice match between Junior Teams conducted over twenty years ago, I witnessed a new player placing his opening bid in the center of his space when he held an average hand, to the far left with a great hand and somewhere between those physical points with an intermediate hand. Given that he had only been playing for a few months and sitting in a new partnership, it was obvious that this was not an effort to cheat. It was simply that he was unconsciously leaving room for the bidding cards to be comfortably placed for the expected duration of the auction." (http://bridgewinners.com/article/view/the-unintentional-and-its-offspring-part-1/) On the face of it, this is not very different from what B-Z allegedly were doing.

Do the von Ostens and Clever Hanses of bridge actually cheat? If not, how can we as spectators tell the difference between them and real cheaters?

"Years ago I took to filming my players as they trained for competition in order to ascertain what tells they owned. One certainty became apparent virtually immediately: every single player possessed at least one and typically three or more. The worst ones I revealed to them, primarily because they were placing themselves at an extreme competitive disadvantage. I also became concerned that their partners would subconsciously learn them, too." (http://bridgewinners.com/article/view/the-unintentional-and-its-offspring-part-1/)

Consider how Hans and his owner were unwittingly using a code to "cheat" at arithmetic.

https://en.wikipedia.org/wiki/Clever_Hans

I don't think there's enough symmetry in your design, because although you play 1C-1D; 1H-1N = 4H5+C, GF 1C-1H; 1S-1N = 4S5+C, GF 1C-1D; 1H-2C = 4H5+D, GF 1C-1H; 1S-2C = 4S5+D, GF you also play 1C-1S; 1N-2N = 4+D5+C, GF 1C-1N; 2C-3C = 5+D4+C, GF So you're actually putting more hands into e.g. 1C-1N; 2C-3C than into 1C-1D; 1H-2C even though you're a whole level higher! To rectify this, I think you should give up the idea that 1N is always a transfer to clubs. I also think you should be able to stop in 1N with something like 15-17 bal. opposite 6-8 bal., so I suggest the following (while trying to interfere with your design goals as little as possible): 1C-?: 1D = 0-5, any / 6-8, 4-S4-H (or possibly 5M(332)), unsuitable for 1C-2C+ / 9+, "H" ...1H ......1S = 0-5, any ......1N = 6-8, 4-S4-H (or possibly 5M(332)), unsuitable for 1C-2C+ [Opener will pass with 15-17 bal.] ......2C+ = 9+, "H". Specifically: ......2C = 4H5+D ......2D = 6+ H ......2H = 5S4H ......2S = 4H5+C [think of 2S as a (two-under) transfer to C, not as a (one-under) transfer to N] ......2N = 1444 [think of 2N as a (two-under) transfer to D, not as a (one-under) transfer to C] 1H = 9+, "S" / 12+ bal. [edit] ...1S ......1N = 12+ bal. [puts an upper limit on 1C-1S; 1N-2C] ......2C = 4S5+D ......2D = 4S5H [but what do you do with 5S5H?] ......2H = 6+ S ......2S = 4S5+C [think of 2S as a (two-under) transfer to C, not as a (one-under) transfer to N] ......2N = 4144 [think of 2N as a (two-under) transfer to D, not as a (one-under) transfer to C] 1S = 9+, "D" or 9-11 bal. ...1N ......2C = 9-11 bal. [necessary to put an upper limit on 2C here IMO] ......2D = 5H4+D ......2H = 5S4+D ......2S = 5+D4+C [think of 2S as a (two-under) transfer to C, not as a (one-under) transfer to N] ......2N = 6+ D [think of 2N as a (two-under) transfer to D, not as a (one-under) transfer to C] ......3C = 4441 [think of 3C as a (two-under) transfer to H, not as a (one-under) transfer to D] 1N = 9+, "C" ...2C ......2D = 5H4+C ......2H = 5S4+C ......2S = 6+ C [think of 2S as a (two-under) transfer to C, not as a (one-under) transfer to N] ......2N = 5+D4+C [think of 2N as a (two-under) transfer to D, not as a (one-under) transfer to C] ......3C = 4414 [think of 3C as a (two-under) transfer to H, not as a (one-under) transfer to D] 2C+ = inspired by decent 1N defence (such as Multilandy), but with 6-8 and possibly allowing 5M(332).* *Alternatively, and conforming to your scheme: 2C = 6-8, 5M(332) [would have responded 1D with (4333), (4432) or 5m(332)] 2D = 6-8, 44(41)/(50) or 4H6+m or 5+ H, unbal. [would have responded 1D with 1444 or 3-S4H5m and 2C with 5H(332)] 2H = 6-8, 4S6+m or 5+ S, unbal. [would have responded 1D with 4144 or 4S3-H5m and 2C with 5S(332)] 2S = 6-8, 6+m4Om or 7+ m, one-suited [would have responded 1D with 6m(322) or 6m(331), not wanting to preempt p, who is often minimum with a 5c major] 2N = 6-8, 5+D5+C [would have responded 1D with 22(54) or (31)(54) and 2S with 6+m4Om, allowing p to ask for the longer minor] 3m = 6-8, 7+ m, one-suited [my suggestion, allows 2S to be 6-8, 6+m4Om unambigously]

I play something close to the following in 1st and 2nd seat NV: 1C = nat. or 14-19 bal. 1D = nat., unbal. 1C-(P)-?: 1M-1 = 0+, 4+ M ...1M = 3 M or 14-16 bal. or 17-19 bal. w/ 4-5 M ...1N = 17-19 bal. w/ 2-3 M 1S = "0-6 or 10+", 3-S3-H unless GF ...1N = 14-19 bal. 1N = "7-9", nat. (to play opposite 14-16 bal., FG opposite 17-19 bal.) 1C-(1H)-?: X = 0+, 4+ S ...1S = 3 S or 14-16 bal. or 17-19 bal. w/ 4-5 S ...1N = 17-19 bal. w/ 2-3 S 1S = "0-6 or 10+", 3- S unless GF ...1N = 14-19 bal. 1N = "7-9", nat. (to play opposite 14-16 bal., FG opposite 17-19 bal.) 1C-(1S)-?: P = 0+, 4+ H ...X = 3H or 14-16 bal. or 17-19 bal. w/ 4-5 H ...1N = 17-19 bal. w/ 2-3 H X = "0-6 or 10+", 3- H unless GF ...1N = 14-19 bal. 1N = "7-9", nat. (to play opposite 14-16 bal., FG opposite 17-19 bal.) Of course, some additional sci-fi stuff is needed to sort everything out, not least after 1C-(1S)-P; X, when Responder still has to bid on nothing.

Maybe Fisher had read this: http://bridge.thomasoandrews.com/valuations/2nt-3nt.html#z_hcp_121

Confession: I seem to have missed Adam Meyerson's (awm's) comment in http://bridgewinners.com/article/view/transfer-responses-to-1c-gcc/ where he clearly outlines a T*-Walsh structure (the first ever?) where Responder has to bid 1D(=4+ S) first with both majors and hence also on FR-type hands. I actually do the same in a version of T-Walsh, but over 1C-1D; 2C I then play DRFR to help find 5-3 spade fits. In the corresponding T*-Walsh structure I'd play DFR over 1C-1D; 2C to help find 5-3 heart fits.

This is the essence of board-a-match (BAM) scoring.

Classically, a direct bid shows a weaker hand than a takeout double followed by the same bid, so you might consider doubling 3C and rebidding 3H to show an invitational hand with 5+ H. The problem is that partner would bid 3S on a minimum hand with 4 S, and then you'd already be too high. In theory, though, I suppose you could play ...(3C)-X; ?: P = LoTT decision 3D = 3H5+D, NF 3H = 5+ H, inv3H = 4S3H, min 3S = 4S3H, extras etc., as I can't think of any (other) natural use of the 3H bid that would make sense.

I've seen Welland-Auken do this.

First, a couple of handy definitions: Recall that Reverse Flannery by Responder (RFR) is a response to 1m showing hands with 5(+)S4+H in some range below GF strength. So let 'Flannery by Responder' (FR) similarily be a response to 1m showing 4S5(+)H hands in some range below GF strength. Then we can also say that a hand is of 'Flannery by Responder-type' (FR-type) if it's consistent with a FR response. Whether FR-type hands pose a problem in a T*-Walsh structure s* may largely depend on the T-Walsh structure s. But this post will be about the kind of problems that may arise from using an artificial 1S rebid over 1C-1H in the desired structure s* when we start with a mundane-looking T-Walsh structure s, e.g. one where 1C = nat. or 12-14/18-19 bal. 1C-1M-1; ?: 1M = 3 M 2C+ = XYZ1S(M=H) = 4+S2-H4+C, NF1N = 12-14 bal., 2 M (and 3- S if M=H) 2C+ = XY-NT, In s*, the 1S rebid over 1C-1H(=4+ H) will now probably just show 3c H support, as in 1C-1OM-1; ?: 1OM = 3 M 2C+ = XYZ1S(M=H) = 2-S4+H4+C, F11N = 12-14 bal., 2 M 2C+ = XY-NT, so the danger is that 4-4 S fits may be lost in s* unless we pay attention. For example, if Opener's has to rebid 2C in s* on AQ9x-x-Kxx-KTxxx [corrected 11 August, was 'AQxx-x-xxx-KTxxx'] because 1S would have shown 3-card H support and 1N 12-14 bal. with a doubleton heart, a 4-4 S fit could easily be missed in favour of a silly 5-1 C fit opposite something like Txxx-Kxxxx-A9x-x. The situation is not as bad as it looks, partly because the analogous problem in s with x-AQ9x-Kxx-KTxxx opposite Kxxxx-Txxx-A9x-x could easily be solved in s* after (say) 1C-1D(=4+ S); 1S(=4+ H). But we can also imagine a problem after 1C-1H(=4+ H) in s* that doesn't similarly correspond to a problem in s after 1C-1H(=4+ S). For example, the problem of locating a 4-4 spade fit with AQ9x-xx-Kxx-KTxx opposite Txxx-Kxxxx-A9x-x after 1C-1H(4+ H); 1N in s* doesn't have a counterpart in s, because with xx-AQ9x-Kxx-KTxx opposite Kxxxx-Txxx-A9x-x the bidding would simply go 1C-1H (nat. or 12-14/18-19 bal.; 4+ S) 1N-2H (12-14 bal., 2 S; 5+S4+H, weak) P. So the problems in s and s* don't always cancel out by symmetry. Knowing this, we might decide to use FR on weak FR-type hands, which will solve both problems in s* above, but unfortunately at the cost of a potentially useful two-level response to 1C. (I have to admit that this is the only simple solution I could think of at the time I wrote the OP, and it might show.) Another solution involves what I for convenience shall call 'Delayed Flannery by Responder' (DFR), denoting any rebid by Responder showing a FR-type hand. But interestingly, solving the latter problem in s* involves little more than a simple trick using XY-NT, provided Opener is not allowed to bid anything else than 2H or 2S over Responder's GF relay: 1C-1H; 1N-?: 2C/2H+: as in standard XYZ 2D = weak DFR (the trick, made explicit for the sake of full disclosure) / ART GF 2H = 3-S2H (can be viewed as preference opposite weak DFR) 2S = 4S2H (can be viewed as preference opposite weak DFR) So, using the trick with AQ9x-xx-Kxx-KTxx opposite Txxx-Kxxxx-A9x-x, the bidding would go 1C-1H (nat. or 12-14/18-19 bal.; 4+ H) 1N-2D (12-14 bal., 2 H; weak DFR / ART GF) 2S-P (4S2H; weak FR-type hand). As for the former problem, I don't see a good reason for solving it unless we'd also be interested in solving the analogous problem in s. But maybe: In s*: 1C-1H(=4+ H); 2C-?: 2D = weak DFR / ART GF 2H = 3-S2H (pref. opposite DFR) 2S = 4 S or 3S1-H (pref. opposite DFR) 2N = 4D6+C 3C = 3-D7+C2S = inv DFR Similarly, in s (where 'DRFR' = 'Delayed Reverse Flannery by Responder'): 1C-1H(=4+ S); 2C-?: 2D = weak DRFR / ART GF 2H = 4H or 1-S3H (pref. opposite DRFR) 2S = 2S3-H (pref. opposite DRFR) 2N = 4D6+C 3C = 3-D7+C2H = inv DRFR [i have used small letters 's' and 's*' to name structures in this post, to avoid confusion with the 'S' denoting spades.]

Since my previous post I've discovered a couple of errors in my OP grave enough to render it largely unreadable. I think those are corrected now, but still: Sorry! A clarification: Since we can take 'T-Walsh' as denoting any structure characterised by 1C-?: 1M-1 = 4+ M, may have longer D if < GF, let 'T*-Walsh' denote any GCC legal structure characterised by 1C-?: 1OM-1 = 4+ M, may have longer D if < GF I didn't make it sufficiently clear in the OP, but what I'm dreaming of is a way of assigning to each T-Walsh structure S a T*-Walsh structure S* that is in some predefined sense the closest (GCC legal) approximation to S. (That's how S* can be a GCC legal "substitute" for S and, ultimately, T*-Walsh a GCC legal "substitute" for T-Walsh.)

That's an understatement.