When first invented by Harold Vanderbilt in 1925, the intended use of the Redouble was to quadruple the score. Over time, just as with doubles, the redouble was found to be more useful for purposes other than “business.” Today, most redoubles are used artificially. Due to the rarity of this call, the topic is difficult and often unexplored in bridge teaching and literature. Most of the information that follows is intended for experienced players.
The most common use of redouble is to send partner the message: “Anything but here.” This is commonly known as an SOS Redouble (“Save Our Ship”). Here is an example:
The opponents want to defend against 1 doubled. South's Redouble is SOS with something like:
He wants North to try something else.
The second-most common redouble is the strength-showing redouble such as;
South's Redouble is strength-showing--10+ HCP. Any time the opening bid is doubled, the responder's redouble is "business" -- showing that the hand belongs to his side. All subsequent doubles by either North or South would be for penalty. Note the difference in the 2 auctions shown. On the first one, the opponents left in the takeout double for penalty; they announced that they wanted to defend against the doubled contract. In the second auction, there is no indication that N-S are in trouble.
There are many other kinds of Redoubles, some actually for business! If your side voluntarily bids a game, a redouble of the opponent's penalty double suggests that they have made a mistake and that you want to play your contract redoubled.
In general, though assume a redouble (if not discussed) is for rescue/SOS.
Support Redoubles, Control-Showing Redoubles and Rosenkranz Redoubles are some of the other artificial Redoubles. All of this is covered in more details in Larry's book on Doubles and Redoubles.
Or Michael's Doubles Webinar which you can find HERE.