Two Bits Against a Penny

J 3 2
A 7
A K 5 4
K 10 5 3
A K Q 10 7 6 5 4
K Q J 6 5 3 2 10 9 8 4
Q 3 J 8 6
------ J 9
9 8
------
10 9 7 2 Vul: Both
A Q 8 7 6 4 2 Opening lead: A of spades

WestNorthEastSouth
3 * 3 NT Pass 4
4 5 5 6
Dbl RedblAllpass
* Alerted
First, a look at the bidding. The 3 club opening bid was alerted and means, well, I guess what you see (though if it means a transfer to hearts, I don't know why he doesn't just pre-empt 3 hearts). Anyway, I'm not familiar with whatever convention that is. Now, when the bidding goes like this, starting at the 3 level and both sides are showing an unbalanced hand with good potential if they can name trump, it's awfully difficult to know who's bidding to make and who to sac, even when the bidder is yourself! Five clubs can't make, but would certainly be a good sac over 4 hearts. Five hearts can't make. When you've pushed the opponents to 5 of a major, I would recommend letting it ride, i.e., on these competitive auctions where it's not clear who's bidding to make, who to sac. If you were slambound before a 5-of-a-major by the opposition, then of course you'd want to pursue that slam. Also, the vulnerability enters in. If they're bidding a vulnerable game and you're not-vul and believe you can't lose more than two tricks, you might bid over it. But what will you do if they continue on to slam? Bid over it? Let it go? Or do you want to double for a really good board or a really bad one? Myself, I feel I've done well if I've pushed the opps to 5 of a major. That's often not a very good place to be: one more than needed for game, one short of a slam bonus if it's a 12-trick hand. We've put them in what may be an unmakable contract that many of their confreres have not had to bid, which was the case here.
Well, that's largely personal. And if 5 clubs can't make, then we're sure 6 clubs can't. Since we don't know who's bidding with what intent here, I don't think I'll belabor the bidding except for saying . . . . The redouble was off the wall, and I want to explain why.
Well, first it's optimistic in the extreme. North is looking at three small spades and can't know whether his partner was bidding to make or not, even aside from the possibility of overbidding when he thought he could make. Then there's the third round of diamonds. But looming over all is the sheer effrontery of expecting to lose at most one trick when the bidding has been crowded and the opponents are indicating a few good tickets of their own. Further, if you can make, you've got a good board on a double already, for God's sake. How can North feel confident that they're cold for 12 tricks? Beyond that, there is the matter of what you stand to gain vs. what you stand to lose.
Only two people bid slam, which I guess shouldn't surprise us since neither side can make more than 10 tricks. Both who bid slam were in 6 clubs and both got doubled. The other pair landed right smack dab in the middle of the scoring with 50%. After all, they beat all pairs in 4 hearts. If it's evident that they would have done still better to pass 5 hearts, or double five hearts, well, that's an awfully close call and nobody's gonna get 'em all right. The redoubling pair, need I say, got zero. Now if this slam had made, this pair would have been at the top, the redoubler besting the other (doubled) pair by maybe getting 100% to the other's 98% or so. So he's already got a tremendously good board if the contract is makable, the redouble going for all of 2 points more! And if it isn't makable, the redouble costs 50 points. Quite a disparity. The above heading points out that it's like betting 25 cents against a penny. Doesn't sound like a worthwhile wager, no matter how certain your are.
No, of course North can't know all this. But he can be pretty sure that will be the odds, roughly speaking, on any tenuous -- and doubled -- slam bid. With the double, you're already in for a pretty good score if you can make. You can't force the opponents to double, but if you feel confident of your slam, you should be happy that they have done so. And if you can't make? Well, the redouble is obviously ill-advised and can push you way down in the scoring, which here was down to zero, while you stood to gain crumbs for the redouble if you were right. Maybe 2%, 3%. It's just not worth it.

This is not to be confused with being doubled at the five level when you're -- confidently -- slambound. If you feel there's slam, you must redouble. Otherwise, you're going to let the opponents sucker you into an inferior contract. The redouble offers a better score than the slam along with offering a one-trick cushion the slam bidders don't have. Similarly with getting doubled in little slam when you were grand-slam bound. You need a redouble to beat the grand slam score. Here, in a doubled little slam I'd be far less eager to stick in the redouble. Unless you're awfully confident of the grand slam, you might do well to let the double go and take a score that beats a lot of confreres undoubled in little slam, not to mention those in a grand slam that doesn't make.
On the above hand a redouble of five clubs would be ill-advised, of course. In recommending redoubles of 5 level bids, I'm referring strictly to those where you had every expectation of going to little slam. An opponent who doubles often suckers the opposition into fearing bad luck and thus passing meekly for a bad board. Here, however, I don't see how anyone could be all that confident of a six-level bid, which is the stipulation I've offered for redoubling: not confidence of a 5-level bid, exactly, but the expectation of going on to six. If you were going to be comfortable with the five level, I'd forego the redouble on the grounds offered in the last few examples: if you make (without an overtrick), you've already got a good board, and if you don't make, the redouble only doubles your misery.