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Maximal (Overcall) Double - When both sides have a suit agreement (Opponents Bid And Raise - OBAR in lower suit), a double invites game, while a suit bid is merely competitive.

Bid

Meaning

 

(1H) - 1S - (3H) - 3S

3S is merely a competitive bid to play with no interest in bidding game

(1H) - 1S - (3H) - X

X shows interest in game if partner has extra values

1S - (2D) - 2S - (3D);
3S

3S is merely a competitive bid to play with no interest in bidding game

1S - (2D) - 2S - (3D);
X

X shows interest in game if partner has extra values

(1D) - 1H - (2D) - 2H;
(3D) - P   - (P)    - X

X here is a cooperative (optional) Double, primarily interested in penalizing opponents since partner did not actively raise to 3H

(1C) - 1H - (2C) - P;
(P) -   2H - (3C) - X

X here is for penalty - no fit with partner in Hearts

Also see more Doubles and books on Doubles
 

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