No matter what I do, I always seem to get into trouble.
For the record, I was the east hand, and my periodic partner and I had not discussed this situation. Rightly or wrongly, he was showing a heart stopper after my non-pre-accept 3D response, searching for the best game. This is one way to play it, I guess. On this hand, I didn't really know what 3H meant, so I chose what I thought was the safest game contract. Shoot me (but please use a silencer. My wife hates loud noises.)
To play 3H as showing shortness with slam interest seems to be the way many play this sequence.
There is another possible meaning to 3H that is more matchpoint oriented. The prerequisite is that the partnership is playing that Stayman followed by 3 of a minor shows a weak 4-6. If so, then the meaning of 3M after transfering to diamonds might show 4 of the M, or 4 of the OM with GF or better values.
Perhaps no one plays the weak 4-6 method any more.
DHL

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