a) Requirements

 - Partner must have made a positive bid (other than Pass)

 - The player who makes a penalty double should hold less than two cards in partner's suit, 1 to 2+ quick tricks, and good trumps in the opponents' suit, especially in low-level contracts

c) Strategy of doubling for penalty

 - It is seldom profitable to double for penalty an opponent's call made freely (without an obvious preemptive purpose)

 - When in doubt about partner's penalty double, it is preferable to bid on, especially with good support for partner's suit and lacking quick tricks

 - Never remove partner's takeout double of a notrump bid unless holding a very weak hand and a long 5 to 6 card suit

b) Exceptions to the rules of penalty doubles

 - The double of a natural notrump bid is always for penalty except for an opponent's first response in 1NT

 - The double of a game bid is always for penalty except for a preemptive opening

 - The double of a notrump opening is always for penalty

 - The double of an artificail bid is never for penalty; the double is used to indicate a favorable opening lead