ETM Gadget can be used to provide a cheapest bid relay over 1m-1M;2m sequences, thus providing the ability for game forcing hands to describe themselves, and to provide an extra bid after two level fourth suit forcing sequences. It works by having the relay being either any GF hand, or a signoff in 2M, or, only when the relay is 2D and M=Ss, a signoff with both Ss & Hs.
The last bid in each of the following sequence can be used as ETM Gadget:
In sequences 1), 3) and 4), the relay is either any GF or a signoff in M. In the 2) sequence, responder if not a GF may have a signoff in just Ss or a weak signoff with both majors, at least 5-5. In the 5) sequence, if not a GF responder has either a signoff in just Ss, of a signoff with both majors, usually 5Ss & 2Hs.
Opener assumes that responder has a signoff and bids correspondingly. If the Gadget bid was 2D and M=Ss (sequences 2 and 5 above), opener assumes responder has a weak signoff in both majors and bids correspondingly, and responder will correct a 2H rebid to 2S with just a signoff in Ss – for example 1C-1S;2C-2D(Gadget);2H-2S(just signoff in Ss). If opener replies to Gadget above 2M it shows a hand that is interested in game even opposite a signoff in M.
If opener rebids 2M or below in reply to ETM Gadget, then all of responder’s bids above 2M are GF, natural. So, for example, to establish a GF in Cs, responder can bid 1C-1S;2C-2D(Gadget);2S(in case signoff)-3C(natural, GF).
If opener rebids above 2M in reply to ETM Gadget, showing a great hand, then responder, with a hand that used Gadget with GF values, must bid fourth suit forcing (if available), or 3D if a new suit, or on the four level. So, for example, 1C-1S;2C-2D(Gadget);3C (game interest opposite signoff)-3D(natural, GF).
When playing ETM Gadget, the direct bid of 2M is available, since with signoff values responder bids Gadget. 2M by responder shows useful values (ETM defines “useful” as approximately constructive to limit) with 5+ in M, 4+ in the suit the Gadget bid would be made in. It is NF. If the Gadget suit was Hs, after 1D-1S;2D, then 2S denies GI with 5+Hs, since 1D-1S;2D-3H shows 5-5+, GI.
If responder could have used ETM Gadget but instead bids on three level it shows GI values. If responder bids 3D as a new suit it shows 6+ in the Ds, exactly 4 in M and GI values. If responder makes a new suit rebid in Hs or Cs it shows 5-5+, GI. If responder rebids 3M it shows a good GI or shapely GI (make a ETM Useful Jump Shift otherwise).
1C-1S-2C-2H shows useful values, 5+Ss, 4+Hs, if 5-5+ & GI bid 3H over 2C.
1H-1S-2C-2H is a signoff in Hs, but only 4Ss.
1D-1S;2D-2S: Useful, with 5+Ss, 4+Hs, NF.
1D-1S;2D-2H: Signoff in Ss, or any GF.
1D-1S;2D-2H;2S-3D: GF in Ds.
1D-1S;2D-3C: GI with 5+Ss, 5+Cs.
1D-1S;2D-2H;2S-3C: GF with Ss & Cs.
1C-1S;2C-2D;2H-2S: Signoff with just Ss (6+Ss).
1C-1S;2C-2D;2S-3C: GF with C fit.
1C-1S;2C-2S: Useful with 5+Ss, 4+Ds.
1C-1S;2C-2H: Useful with 5+Ss, 4+Hs.
1C-1S;2C-2D;2S-2NT: GF balanced.
1C-1H;2C-2D;2H-2S: GF with Hs and Ss.
1C-1H;2H-2D;2H-3H: GF with Hs
1C-1H;2C-2D;3H: Would bid 1C-1H;2C-2H;3H in standard.
1C-1H;2C-3D: GI with 6+Ds, 4Hs.
1D-1S;2C-2H;2S-3D: GF with D fit.
1D-1S;2C-2H:3S Would bid 1D-1S-2C-2S-3S in standard.
1D-1S;2C-2S Useful with 5+Ss, 4+Hs.
1D-1S;2C-2H;2S-3C: GF with C fit.
1D-1S;2C-2H;2S-2NT: GF balanced.
1H-1S;2C-2D;2H-2S: Signoff with Ss, 6+Ss.
1H-1S;2C-2D;3H: GI with 3+Hs.
1H-1S;2C-3D: GI with 6+Ds, 4Ss.
1H-1S;2C-2S: Useful with 5+Ss, 4+Ds.
1H-1S;2C-2H: Signoff in Hs, usually only 4Ss.
1H-1S;2C-2D;2H-3C: GF with C fit.
After 1D-1H-2D, there is no bid below 2M to use for ETM Gadget. Instead standard bidding is used here with one recommended exception: 1D-1H-2D-2NT should be played as forcing to at least 3D, since 2D promises at least 6Ds here. Over 2NT, opener first assumes responder has just GI values and bids only above 3D with values to accept a GI.
After 1C-1D-2C in standard, which shows 6+Cs, it is recommended to play 2NT as forcing to 3C here, with at least GI values. Opener, without values to accept the GI bids 3C, and otherwise bids above 3C.