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1D= 4+Hs


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How about 1 as GF relay and other bids approximately standard as if opener bid 1 promising 4+? I guess that makes 2m natural invites rather than 2/1 GFs, but otherwise it should work. Responding 1 or 1NT may just be looking to improve the contract (0+ pts if unwilling to pass 1), and could both be played as non forcing.
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You might find it helpful to look up the Australian submarine opening system which has been played at BB level. From memory they use 1H as an INV+ relay but the full CC is available online if you look around. (Just an additional note, the system uses a strong club so the 1DHS openings are limited - however I believe the structure will be adaptable.)
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Playing MOSCITO I strongly prefer to play 2/1s as natural and non-forcing.

I don't think that this is playable given the wide range of your opening bid.

 

Personally, I'd lean towards using 1 as a GI+ relay and use a transfer response scheme

 

1N = Clubs

2C = Diamonds

2D = good raise to 2H

2H = preemptive raise to 2H

2S = fit showing (6 Spades and 3 Hearts)

2N = Limit raise+

3m = fit showing

3H = value raise

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I'm a fan of the newer moscito structure and I think it may be workable with your opening even though it's large ranging.

 

Something like:

1 = general relay to let opener describe his hand (any balanced or any GF hand)

1 = natural, F1

1NT = s, less than GF

2 = , less than GF

2 = good raise, 3

2 = weak raise, 3+

2 = weak 6+ (or INV if you prefer that)

2NT = INV+ with 4+ fit

3m = INV, good 6+ card suit, 3

3 = mixed raise

3/4m = splinters

3NT open for discussion (you may use this as a splinter to show different ranges or difference between singleton/void).

1-3m is a bit strange, with invites you could also just transfer and rebid 3m. Therefore it makes sense to show the difference between 3 card support or not.

 

After 1-1 you can play something as follows (here the limited range has it's advantages to stay low):

1 = natural, 4 (perhaps even any strength and forcing, to create extra bidding space for strong hands)

...1NT = balanced

...2 = GF relay

...2NT = balanced INV

1NT = unbalanced, longer m (or 1=4=4=4, but I prefer to open these with something else)

...2 = P/C

...2 = GF relay

...2NT = balanced INV

2m = min, 5+, 4+m

...step = GF relay (not 2)

...2NT = balanced INV

2 = min, 6+

...2 GF relay

2 = extra's, natural (or longer m if you use 1 as any strength)

2NT = extra's, longer m

3m = extra's, 5+, 4+m

3 = extra's, 6+

 

This gives you full relays when opener is minimum, but might give you trouble when opener is max. You can't have it all... ;)

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