An SOS redouble is used after a penalty double, to request a different suit from the partner. It applies when * we have not agreed the doubled suit; * the contract is not bid by a one-suited hand (such as bidding the contract twice) * there are at least 2 unbid suits; * the auction is at a low level; It is commonly used after a penalty pass of a takeout double. The following redouble is obvious SOS: SOS redoubles are not used after a penalty double of 1NT, unless conventional runouts are used.
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