So, just what are your limits as a passed hand in terms of bidding? I would say one free bid or, at the very most, two. Of course, you should answer partner's opening bid normally if you have responding values—that's not a "free" bid. You might even make a 2/1 bid since he will know that you cannot have opening count. And if partner forces you to bid again, you will honor his request. You may raise his suit, even his preempt although you will be careful about doing so since he may have been making a pressure bid.
But if the auction gets competitive, you can't just keep on bidding till the cows come home! I recall a hand from a year or two ago where my partner made three bids after having passed originally and hearing only the one bid from me. The result wasn't pretty but fortunately the details of that hand are lost.
Here's a classic example of what I mean from a recent random game on BBO (I changed partner's name to protect the guilty but used Victor Mollo's favorite epithet):
Admittedly, North made only two bids after he had passed, one of which was not a free bid. But the jump to 5♦ was itself the logical equivalent of two bids. We can make 3♦, they can make 3♠. It's hard to be sure what East would have done over 3♦. Probably with a singleton diamond, he would take the push. What would the effect of a 4♦ bid by partner have been? Hard to tell. I would guess that the opponents would either go quietly (we lose 1.7 IMPs) or bid on to 4♠ (we gain about 5 assuming we don't double which would be more like 10 or 11). As it was, they didn't double 5♦ and we "only" lost 4.3.
In the following hand, the BBO Robots were kind enough to furnish me with another example (see the following).
The first diamond call by partner isn't really a free bid, given that he has 8 points. To pass would be Quixotic. The support double in round two confirmed a full opening bid (11-21 hcp) with three-card diamond support, and suggests a balanced hand, although presumably doesn't deny a 5-card club suit. The likely result of the double, it seems to me, would be +200 or -790. Predictably perhaps, we suffered the latter fate and a (shared) bottom.
Personally, I don't think the North robot has any business making a double with no surprises in store for the declarer, and having already made two bids after passing at his first turn.
So, to conclude: once you are a passed hand, resolve all marginal calls by taking the more conservative action (often that would be pass). The only justification for bidding aggressively is having very good shape. Doubling for penalties without having the goods, is just asking for trouble.
[Note: 2014/09/18: I changed the title back to the original]
The double on the last hand is laughable but it is based on the absurd notion that your raise to 3C shows extras. The bots are really bad about this. I've written numerous robot reports lambasting them for not letting me compete after suit agreement has been reached. So far no one is listening. If I wanted to try for game, I would bid a new suit.
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