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When I play in robot tourneys I open a lot of 14-18 counts 1N. The fringe hands where partner makes an invitational raise opposite 14, or where partner passes opposite 18 and we miss a good game, seem to be sufficiently infrequent in comparison with other benefits that it seems to pay off, although I confess that I have not been keeping a tally. Not saying that this policy translates well into the real world.
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Some people around here play 15-18 in face to face bridge for reasons that I do not understand.
Years ago, we opened 1N on balanced hands ranging from a good 15 to a poor 18 Milton Work Points, depending on non HCP considerations (like shape and texture). And that is how we declared and explained our understanding :) Nowadays, I suppose those playing such methods would explain them as 16-17 HCP or some other fiction, expecting opponents to read between the lines and so allow for the possibility of so-called "upgrades" and "downgrades" :(
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or "good 15 to flat 18" which we commonly hear here (admittedly, more often as "good 14 to flat 17"). If people want to know how *you* define a "good" hand, they can ask (People certainly asked fairly frequently when we announced "good 11-14", to which the answer was "A, A, K, or supporting honours in long suits.")
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My partner and I play Mexican 2, which we explain as 18 to bad 20. When asked what a "bad 20" is, I say that it essentially means we practically never open 2NT with a 19 count.

 

Last night partner opened 2, and he played in my major after a Texas transfer. When we opened the traveler I was surprised to see that most other pairs were playing it from his side as well, since Mexican usually changes who plays these contracts. I asked him if he had a hand that other players might have upgraded to 2NT, and he said yes. After the game, when I went out with other players to the pub to discuss the hands, I saw from the hand record that he had a 21 count. :)

 

In case you're curious, his hand was AKQ KJ KJT A7532.

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There are three or four different versions of "Mexican 2" floating around, all of which, if I'm not mistaken, were played as part of Romex at one time or another. The current version, based on Rosenkranz's latest book, Godfrey's Angels, published in the early to mid 2000s, is "21-22 balanced, or a GF with primary diamonds". The responses are somewhat complicated, but the structure is based on the assumption that opener has the balanced hand, which he will some 85% of the time.
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Is the version the Italians play identical to a Romex form? I had thought they had modified the responses a little.

I don't think so, but I'm not all that familiar with the Italian version.

 

It is interesting to note that the last four books Rosenkranz has written (all with Phillip Alder) have four different versions of the convention, the differences being mostly, but not all, in the responses. The difference in the bid itself is that the strong 4441 hands which were originally included were moved to other bids in the third book, and dropped entirely in the fourth.

 

On Romex and the GCC: to the best of my recollection, everything in Bid to Win, Play for Pleasure and Godfrey's Bridge Challenge is GCC legal with the exception of the 4NT opening bid, which is Mid-Chart. It's a pretty rare bid, and could easily be dropped for GCC events. Godfrey's Stairway to the Stars adds two new Mid-Chart openings: 2NT showing a weak preempt in either minor (again, not absolutely essential to the system) and 2 showing a Precision 2 opening (when playing the Romex Forcing Club (RFC) introduced in this book). The purpose of this one is to allow the system to keep the Mexican 2 opening when playing RFC, so it kind of kills the "two card" approach in GCC events. The fourth book (Godfrey's Angels) mostly adds some bits and pieces, all of which are, to my recollection, GCC legal. I haven't checked the system against other regulatory structures, although it's mentioned in "Stairway" that the 2NT is brown sticker under WBF rules.

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