It's a Puzzlement

A K 2
A 10 8
Q 9 7
A 9 8 7
Q 7 6 5 4 ------
2 K Q 9 6 4 3
10 6 5 4 A K J
K J 5 Q 6 4 2
J 10 9 8 3
J 7 5
8 3 2
10 3 Vul: No one

WestNorthEastSouth
Pass 1 NT Dbl* 2
Pass 3 3 3
Dbl Redbl All pass

This was a puzzling use of the redouble (and I confess that when I first printed it out, I thought it was South who'd redoubled, which was even more puzzling than the actual case). It made no sense in either of the two common uses of the redouble -- the S.O.S. and a ringing announcement of confidence in making the contract -- when I thought it was South, and doesn't make a whole lot more sense here, except that the S.O.S. can be ruled out, it would seem. The redouble can only be interpreted as indicating good support in his partner's suit, which cannot be denied, and utmost confidence in his partner's acumen, which on this hand at least, was disastrously misplaced. Further, 3 spades doubled has gotta be a good board if you make, while a redouble invites an excessive penalty if you don't.
First to the bidding: the double of a no trump looks like a Brozel bid, wherein it shows a one suited hand. South's free bid with two hcp's strikes me as a bit aggressive, though just barely in the ballpark, non-vul. North's 3 club bid is way out of whack. The fit in spades has been located and a no trump opening announces point count within a fairly narrow range. By Goren's terminology, South must be the captain on this hand from knowing more about North's hcp's than North know about his. So North should go along. After all, South may even be a tad overbid here, for all North knows! [Or could that have been a misunderstanding about the 2 spade bid? I vaguely recall a convention some years back where 2 spades opposite a no trump opening invited a club transfer, 2 no a diamond.]
But the three spade bid is totally out of whack: South has already overbid, for God's sake, and should have been happy to have been taken off the hook. Further, his partner might want to double 3 hearts with a pretty good holding in that suit. The actual hand in 3 hearts looks too close to call, and North isn't necessarily going to double. Anyway, the first reason given is enough: South has already overbid. Where's there any percentage in taking another free bid? The hand clearly demonstrates the dangers of overbidding on top of an overbid -- in spades! Where 3 hearts might well be defeated with repeated spade leads and at worst would bring N-S minus 140, South's bidding the same meagre values twice, coupled with the redouble, doubtless influenced in no small part by South's confident bidding, brought minus 1000! There isn't necessarily a place where you can improve your situation over the 3 heart bid -- especially in view of holding fewer hcp's than the opposition, which South should know. Sometimes you just have to hunker down, take your licks and figure that if your bidding is sound, you'll have some company , though not necessarily as much as you'd like.
If opponents bid over 2 spades -- well, then, over 3 clubs -- South can breathe a sigh of relief. Let 'em have their partial -- if they can make it. They hafta lose two hearts, the ace of clubs and another club -- and could have trouble on repeated spade leads. Can the 13th diamond be used? It doesn't appear so. They've got only one entry to dummy for the diamond hook, though it takes only one defensive misplay to upset the applecart. Anyway, you've gotta let 'em have it, and if they do take the bid, it will almost surely be no worse for N-S than anything that can come out of three spades -- when 2 spades itself was rather aggressive.
When East bids 3 hearts, why on earth would either N or S want to enter into the bidding again? They've both bid all their values. Good heavens! Why would you contract for 9 tricks to their 4 when they've got the preponderance of the points? Twice as many tricks on fewer hcp's? Oh yes, a superfit can make hands competitive, with minimum hcp's, with say, 20 and the right vulnerability. Even a sound 9-card suit with even breaks might justify the three level. But everything looks a little too balanced here to expect much compensation from a fit for a shortfall in hcp's.
Let me offer a few critiques. Goren offered the sage advice that the captain on any hand should be the person who knows most about the two hands, as referred to above. So the captain on any hand is not necessarily the stronger hand, and indeed, with a no trump opening, the most specific of opening bids, the stronger hand must turn over the captaincy to his partner as the one who knows the most about the combined hands. So the redouble is way outta line. South knows the strength of the partnership (roughly), must be recognized as captain, as just postulated, and we may hope wouldn't have dreamed of a redouble.
To be sure, South deserves a fair share of the blame here. He starts with a very questionable 2 spade bid, escapes a double which alone would have been more costly than any partial the opponents could make, (evidently, 2 spades could have been set two tricks for minus 300, already more than any partial the opps might dig into) and then when he's relieved of any need to bid again with so few hcp's as to make his first bid risky, he jumps back in and deservedly ate a thousand-point set.
I have discussed the risks and dangers of bidding to the two and three level on half or fewer than half the hcp's (except on superfits) here. I have said that even an eight-card fit is a very modest fit that won't make up a whole lot for a shortfall in hcp's, and so I have said that when you have no better than an 8-card fit and possibly not even that, and when you concurrently have at most half the deck or less, the two level is a little risky and the three level is downright dangerous. A word to the wise . . .
The local expert has teased me about this reference to 20 points ever since it appeared in the Bulletin, circa 1983. I have presumed that his point has been that, well, everyone knows this, for heaven's sake, though I've never asked him. Anyway, I have always maintained that there are more than a few who don't pay heed to the significance of 20 hcp's on balanced hands, who play fast and loose with their bidding in this dangerous territory. This hand is only a particularly disastrous example among the many I could conjure up.
The bottom line, to return to the topic at issue here, is that the redouble is totally uncalled for and would have been with even a couple of more kings. When you're doubled in a partial of two hearts or higher, doubled "into game" as some people put it, you've got a good board right there if you can make it. Not necessarily an absolute top, but near top at least.
Now when you are slambound, I've pointed out that if you let a double at the 5 level hold, you don't do as well as people bidding and making slam. But with a redouble, you'll do better than those making (an undoubled) slam -- with a cushion to boot, in that it may be an 11-trick hand after all. And it's necessary not to be suckered into an acceptance of the 5-level double. But the same logic doesn't hold with an "into game" partial. If you feel confident you'll make, you'd do well to wipe the smile off your face and listen for three consecutive passes. And if there is any reasonable chance that you won't make, well, the redouble is obviously counterproductive. A dangerous bid, costly if you don't make, unnecessary if you do.