Source: wimpy-bridge by Jim Diebel 
One of the places I most often see confusion at the bridge table is in the use of the redouble. In its simplest application, it’s supposed to indicate that the bidder is betting that his side can indeed make a doubled contract, but nearly always it has a different conventional connotation. Precise use of the redouble will significantly improve your contracts and consequently your results.
Showing Strength
Most often, a redouble is a declaration of strength. It is a way for Responder to tell Opener that their side has the balance of power. When partner opens and RHO makes a takeout double, Responder should usually redouble with hands of approximately 10 or more high card points. This action should send an immediate message to partner: namely that the opponents may be in trouble, and to consider defending. LHO should generally bid his longest suit, and if partner has 4 of that strain he is expected to double. When he doesn’t have LHO’s suit, opener should usually pass to see what his partner wants to do. If instead, opener makes a minimum (non-jump) bid, he is warning Responder that he has opened a somewhat light distributional hand that is more suited to offense than to defense. Holding shortness in his RHO’s suit is not a sufficient cause for Opener to bid again. Opener’s pass is not an acknowledgement that he is willing to defend this contract doubled, but simply that he has full opening values without either two long suits or one very long one.
| West | North | East | South |
| 1 |
Dbl | Rdbl | |
| 1 |
Dbl |
North has 4 spades
| West | North | East | South |
| 1 |
Dbl | Rdbl | |
| 1 |
Dbl |
North has less than 4 spades, but a full opening hand
| West | North | East | South |
| 1 |
Dbl | Rdbl | |
| 1 |
2 |
North likely has at least 10 red cards. 2 is not forcing
| West | North | East | South |
| 1 |
Dbl | Rdbl | |
| 1 |
2 |
North has opened a light hand with at least 6 hearts. Holding 6 hearts in itself is not a reason to bid here. With solid opening values, North should pass and await developments.
| West | North | East | South |
| 1 |
Dbl | Rdbl | |
| 1 |
3 |
North has a full opening hand, but good and long hearts. This is game forcing.
When the opponents enter the auction with a double, most of the time your bids will have a different meaning than if your opponent had passed. For example, unless you and your partner have expressly agreed otherwise, conventions such as Bergen, Inverted Minors, Jacoby 2NT, Jacoby Transfers and Forcing NTs are no longer in effect. In fact, a 2-over-1 answer by Responder is not only not game forcing, it isn’t forcing at all! The interfering double has not taken up any bidding space, but it has changed the meaning of a great many responses while simultaneously only adding one new call (the Redouble). Responder must choose his action carefully.
| West | North | East | South |
| 1 |
Dbl | Rdbl |
South tends to deny a 5 card major
| West | North | East | South |
| 1 |
Dbl | 1 |
This bid is same as if there had been no double. It is unlimited and forcing one round.
| West | North | East | South |
| 1 |
Dbl | 1 |
This is natural and forcing one round. It does NOT deny a 4 card major!
| West | North | East | South |
| 1 |
Dbl | 2 |
This is natural and non-forcing, even if you are playing Inverted Minors
| West | North | East | South |
| 1 |
Dbl | 2 |
This is natural and non-forcing. Over a takeout double, jumps are natural and weak.
| West | North | East | South |
| 1 |
Dbl | 2 |
This is natural and non-forcing. Some play this is a conventional heart raise.
| West | North | East | South |
| 1 |
Dbl | Rdbl | |
| 1 |
pass | pass | 1 |
South has exactly 4 hearts. (He bids 1 directly with 5) This sequence is forcing one round but not yet game forcing.
| West | North | East | South |
| 1 |
Dbl | 2 |
Same as if there had been no double. This is not forcing.
| West | North | East | South |
| 1 |
Dbl | Rdbl | |
| 1 |
pass | pass | 2 |
South is showing a 3 card limit raise. This is not forcing.
| West | North | East | South |
| 1 |
Dbl | 2NT |
There is no reason for 2NT to be natural, (South would redouble) South is showing a 4 card limit raise or better. North can sign off in 3, or make a game try.
After a redouble, Responder’s next bid tends to be forcing but not game forcing. If Responder ever cue-bids the opponent’s suit, it creates a game force. Unless Opener has shown weakness, the redouble generally forces the partnership to at least 2NT.
| West | North | East | South |
| 1 |
Dbl | Rdbl | |
| 1 |
pass | pass | 2 |
South isn’t bidding diamonds. He would have doubled 1 holding that suit. South is establishing a game force. The partnership cannot pass below game.
| West | North | East | South |
| 1 |
Dbl | Rdbl | |
| 1 |
pass | pass | 2 |
South is showing a 3 card limit raise. This is not forcing.
| West | North | East | South |
| 1 |
Dbl | Rdbl | |
| 1 |
pass | pass | 2 |
This is forcing 1 round, but not yet game forcing. South likely has 5 diamonds, but possibly only 4. New suits by Responder continue to be forcing.