[Stephen Tu]

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On the other hand reaching game is more valuable than
reaching the correct part score, and you have a reasonable
partscore, 2S - a 5-2 fit.

Stylistically, some of us like to rebid 1nt on 13(54), 1444 minimums, although this is up to partnership agreement. This allows us to play 1nt which may be the best spot, and also allows us to play 2H when responder has 4-5 hearts, when 2h NF . Bidding 2S is not necessarily reasonable in this style.

Even if you have agreed never to rebid 1nt with a stiff, there is still considerable danger that you miss a substantially better heart contract when responder has 4 & especially 5 hearts. At MP, this is definitely not any less valuable than reaching games, you'll lose MP every time hearts takes extra trick(s). Even at IMPs, if this is the difference between making & down 1, this costs about the same as NV game bidding mishaps.

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And the difference in frequency between weak hands
with 5-4 in the mayors and inv.+ hand with 5-4 in the
mayors is not that large.
After all responders will hold on average 8-9, assuming
opener showed 12-14.

You are going to invite game with 8-9 hcp opposite 12-14?

There is no way it's going to be close in overall frequency, the partscore range is like 5 pt range, the invitational range is around 1.5 pt range. Even with that range being more frequent than the lower end of the partscore range, the number of partscore hands are going to be much larger.

[keylime]

Elianna,

Check Garozzo's Ambra notes - I think he applies it to this case as well.

[awm]

Garozzo's Ambra notes do use an artificial 2♣ rebid after 1♦-1M. However, this doesn't appear in the various online descriptions of Gazilli and I would consider it a distinct conventional treatment rather than part of the Gazilli structure. Note that this method differs from Gazilli in many ways, including:

(1) In Gazilli, virtually all strong hands rebid 2♣ after 1M-1Y. Over 1♦-1M in Ambra, the 2♣ bid is only used with strong hands that are awkward to bid in standard methods, particularly 18+ balanced with a fit and game-forcing one-suiters (and natural club rebids of course).

(2) Gazilli is primarily a method for handling "tweener" hands that are awkward in standard because partner could easily pass a wide-ranging simple suit rebid (or would be forced to bid on dubious hands over wide-ranging simple suit rebids to handle the rare "tweener" opener hand). The Ambra notes use 1♦-1M-2♣ as artificial, but the various strong meanings are generally game-forcing (or nearly so) hands which are simply hard to describe in standard methods.

(3) In Gazilli, over 1M-1Y-2♣, we have 2♦ as a relay promising GF values opposite the strong option. Over 1♦-1M-2♣ in Ambra, we have 2♦ as a weakness signal and NF opposite the weak option. In fact there is no rebid over 1M-1Y-2♣ which promises more than minimum values without game interest opposite 11-16 with ♦/♣.