This is the classic takeout double. Of course, as the auction becomes too high (4S X), these doubles tend to show points, I think, and if the auction is too high (6H X) they would be for penalty.
It is also takeout for the two unbid suits when a suit has been bid and there is a response of a suit.
We play negative doubles through 3D. We do not play negative doubles over natural NT, Michaels, or Unusual No Trump. From Bergen:
Through 3D. The classic response double is for the auction 1x - X - 2x or 3x - X. I think we also play that it is a responsive double when responder to the opener bids a new suit. 1x - X - 1/2/3y - X. These show the unbid suits and imply lack of a long suit.
These occur in immediate response to partner's overcall. We play them through 3D if the opponents bid the same suit and through 2S if they are bidding different suits. The double shows at least a 3-card fit but no honor (A, K, or Q). Then, simple support implies an honor. The jump to the 3 level is so valuable preemptively that it should be possible with four small trumps.
We play support doubles when we open, the next opponent either passes or bids, there is a major suit response to the opening bid, and the other opponent doubles or bids but does not jump. In other words, a double is a support double over 1C - P - 1H - 2H, but not over 1C - P - 1H - 2S. The support double shown 3 of partner's suit. A pass hence show less then 3-card support. (More precisely, without any ruffing value, one could and probably would not make a support double.) Conventionally, any bid other than double denies 3-card support, but we do not play this aspect of the convention. When the opponent is doubling instead of bidding a suit, support doubles are still on, and three-card support is shown with a redouble.
Conventionally, support doubles are off when there is an immediate overcall of the opening bid. However, in his recent article Lawrence has them as on when there is an immediate overcall or double. We play them as on in this situation too (assuming all the other requirements are met.) This makes good sense when responder's suit bid could be a 4-card suit (for example, 1C - 1D - 1H - 2D - X). When responder is already showing a 5-card suit (for example, 1C - 1H - 1S - 2H - X), the support double shows doubleton honor in support.
Responses to the support double almost what you would think, especially if you think of the situation as being like responding to a takeout double. The bids that sound weak are weak, but a new minor suit is weak too. The only game force is cuebidding the opponent's suit; other jumps and such are limit invitational, and double jumps are splinters. If the support double was in support of spades, a bid of 2H shows four hearts and is not forcing. Rebidding the major does not necessarily show a 5-card suit, because responder might be pressed for a bid.
We do not play doubles as support when responder has bid diamonds, except in the particular case of 1C - (P) - 1D - (X) - ?, where it shows 3-card diamond support.
We have been calling these support doubles, but they are not. They occur in the support double situation, and only then, but when responder has bid 1D instead of 1 of a major. Now the support double shows 4 spades and a heart stopper; the 1S bid shows 4 spades and no heart stopper. (I don't know about the auction 1C - P - 1D - X - XX).
1. Suit-bids at the 1 level. Never for penalty.
2. 1NT. Double of their 1NT is penalty if partner has bid. Double of opening no trump is equal strength. Otherwise (partner has not bid), the double is takeout.
3. Suit-bids at the 2 level. Doubles are for penalty only when:
4. Suit-bids at the 3 level. Usually for penalty, except when: