The support double is a bridge convention used to distinguish between three-card and four-card support for partner's suit response to one's opening bid in the scenario where his response is either overcalled or doubled by the opponents. A call of two in partner's suit indicates four-card support and a call of double promises three-card support; if partner's suit bid is doubled instead of overcalled, a redouble serves the same meaning as double. The convention was invented by Eric Rodwell in 1974.
For example, after 1♦ - (Pass) - 1♥ - (1♠)
A support redouble applies when Right Hand Opponent makes a take-out double of the response of one of a major: 1♦ - (Pass) - 1♠ - (Double)
The convention came as result of the scenario where in competitive auctions, the opening bidder would like to show his minimal three-card support for partner's suit on the possibility that partner has five or more cards in it. However, there would be a risk of a 4-3 fit, known as a Moysian fit which does not play as well as eight-card fits. Since the need to distinguish between three- and four-card support occurs more frequently than those cases where the opening bidder would like to make a penalty double over the opponent's one-level overcall, the meaning of the double (and redouble) was modified to convey the conventional meaning of three-card support.
Take the following auction:
Playing support doubles, North, the opener, has shown three-card support for South's 1♥ call. This is important because South might only have four hearts. Based on the South no trump bid, it can be assumed that South doesn't have five or more hearts.
Hand in hand with the support double is the support redouble which also shows three card support. Examine this auction, which is similar to the one above.
North has shown three-card support for South's heart suit. South uses this information to form the next bid.
Support doubles are not used (except by special agreement) by partner of an overcaller.
The assumption is that the overcaller must surely have at least five cards in the suit he has bid. As such a simple raise is normally sufficient to show some points and support. In such a situation, a double by the partner of the overcaller would be treated as either a Rosenkranz double, a snapdragon double, a responsive double or a penalty double based on partnership agreement.