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Support Double - The use of a double to show 3 or 4 card support for responder's major suit.  With 2 card major support for responder's suit, opener passes; with 3 card, responder doubles and with 4 card major support, opener bids 2 of the major suit.
 

1x - (P) - 1H - (1S);
P

Pass shows less than 3 Hearts

1x - (P) - 1H - (1S);
X

Double shows 3 card Heart support

1x - (P) - 1H - (1S);
2H

2H shows 4 card Heart support

 

Partnership agreements are needed for several situations, including the maximum Support Double threshold (many play on through opponent 2S bid):

1H - (P) - 1S - (2x);
P/X/2S

Many play "systems on" as above

1C - (1H) - X - (2H);
P/X/2S

While responder's double implies 4 Spades, most play "systems off" when Responder did not bid the major

1C - (P) - 1S - (1N);
P/X/2S

Opponent makes a Sandwich Notrump overcall, showing a weak hand with length in the unbid suits.  Many play "systems on"

1C - (P) - 1D - (1S);
P/X/2D

Most play "systems off" when responder bids a minor suit

1C - (1H) - 1S - (2H);
2S/X/P

Responder's 1S promises 5+ Spades.  Partnership agreement is needed regarding opener's Spade length.

Also see Support Redouble, Books on Doubles

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