What is 2/1 Game Force?
Two Over One Game Force (2/1) is a system of responses that allows a partnership to determine quickly where to place a contract. While most auctions won't involve 2/1 bidding, if neither player in opener's partnership has passed and opener's LHO passes after 1D, 1H, or 1S, 2/1 and a few accompanying bids can come into play. Strictly speaking, 2/1 bids are limited to 2-level bids by a responder who has not passed and that are in a lower denomination than opener's 1-level bid. This means that Pass—Pass—1H—Pass—2C is NOT 2/1 because responder has passed. Likewise, 1H—1S—2C is not 2/1 because an opponent bid between the 1H opener and the 2C response. In cases such as these, nothing changes from what you already know.
What kinds of bids can fall under a 2/1 system?
OK, now that we know basically why 2/1 exists and when it doesn't apply, let's look at the components of a relatively simple 2/1 system It will seem complex, but trust me, with a little practice it makes sense). The following conventions are useful in 2/1, and they cover almost every possible bid (the exception is so rare and easy to work around as to be inconsequential): Forcing 1NT, Bergen Raises, and Inverted Trump Swiss; we'll get into these and a couple others in a moment. There are many more conventions that are useful for competitive auctions, but 2/1 is designed for constructive bidding. (NB: 2/1 fits well with the Law of Total Tricks, so many of the more common conventions used by 2/1 players in competitive auctions reflect principles of the Law. It is not necessary to know the Law to play 2/1, but it does help.)
The core principles behind 2/1 are these: once a partnership knows it has the points for game in NT or a Major (or a 4-level contract in a Minor), it will pursue the bidding to a contract at that level; the earlier it can determine that it has (or, just as important, lacks) the strength for such a contract, the better. Furthermore, regardless of points, a contract is generally safe to a level at which the number of tricks required to fulfill the contract is equal to the number of trumps held between the partners' hands (this last point is a basic axiom derived from the Law). While this last point is a bit of an oversimplification in that many such contracts will be set, more often than not, when those contracts do go down, the defenders could make a contract worth more yet won't be doubling you for penalty.
To review, a 2/1 bid is defined as any response at the 2 level in a lower suit than opener's (2C/1H is a 2/1 bid). This may seems strange at first, but consider what this must now mean. Since a 2/1 bid guarantees points for any contract from 3NT to 4S, responder is promising 13 HCP (do not use total points in this calculation). Here is a list of all possible 2/1 bids: 2C/1D, 2C/1H, 2D/1H, 2C/1S, 2D/1S, 2H/1S. Obviously, though, these bids must say something more than, "I have 13 HCP." They are natural. A 2/1 bid in a minor shows the points, denies 4-card support in opener's suit, denies a 4-card or longer suit of a higher denomination, and promises at least four of the minor. The 2H/1S sequence works the same way except that it promises a 5-card hearts suit.
What about all of the supporting bids?
While what was outlined in the previous pargraph is really all there is to 2/1, other bids get used to make it a more well-rounded system. You may be wondering, for instance, how you can handle all of those situation in which you have fewer than 13 HCP. Let's first consider a situation in which you have Clubs and your partner opens Diamonds. If you lack a 4-card major and 4-card diamond support, you must have at least 4 clubs, so the worst hand you could have contains 4-3-3-3 distribution, and 1NT with 6-12 HCP seems fine, even if your partner passes. Either you will be safe with two flat hands or opponents are missing something bigger.
Forcing 1NT
Things get different when your partner opens 1H or 1S, though. Good bidding practices demand that you respond with 6+ HCP, but you can't show a lower suit at the two level in a 2/1 system unless you have 13 HCP (1S/1H is the same here as in Standard American), so 1NT/1H and 1NT/1S are much more general than under other systems. When you open a Major at the one level and your partner bids 1NT with no interference, you must say "forcing" to inform your opponents that the bid forces you to bid again if there is no interference from your RHO (this is called Forcing 1NT, oddly enough). Such a bid denies 4-card support in opener's suit (it further denies a 4-card Spade suit after 1H), shows 6-12 HCP, and says nothing more about distribution. This is why opener must rebid; passing out in 1NT can lead to a disaster under far too many possible distributions. Opener must then find a new bid. With a 6-card major, he may rebid his original suit; otherwise, he must bid a new suit. The flattest hand he can have in this case is 5-3-3-2, and this is not uncommon. Don't worry about bidding a 3-card suit under these circumstances; your partner will know his own hand and make a suit preference bid if his holding is flat or bid a suit of five or more cards if he has one. Remember that with about half of the points, a 2-level contract is not bad, even in a 7-card fit, and if your opponents aren't entering the bidding, they may well be missing something better. All other bidding in these auctions should follow the guidelines you have learned for Standard American. (For those concerned about hitting a 6-card fit, consider the distribution required to cause problems and you'll see that you should have no trouble finding a good fit or escaping to NT.)
Bergen Raises
The conventions common under 2/1 are precise while conserving bidding space—a combination that Standard American rarely manages. Bergen Raises help tremendously here. First, let's consider direct support. 2H/1H and 2S/1S are almost identical to what you already know. Both show 6-9 HCP, but rather than promising 3-card or better trump support, they guarantee precisely 3-card support. These bids are alertable. Note that this puts the bidding at the two level with an 8-card fit, meeting the guideline of having one trump for each trick required by the contract. Responder is then through bidding unless trying to compete (here the Law is useful, though normally in opener's hands) or forced to bid on by opener. Three-of-a-major raises and four-of-a-major raises are both preemptive sign off bids showing 4- and 5-card trump support respectively (they can be longer in the case of a 4-level bid) and 0-6 HCP. Note that these are also alertable and follow the same principle of placing the bidding at the level matched to the number of trumps held between the two hands.
There are, of course, other Bergen Raises for handling more common situations. First, 3C shows 7-9 HCP and 4+ trumps. Similarly, 3D shows 10-12 HCP and 4+ trumps. The latter is a limit raise, though either may result in a game contract if opener has the right holding. Opener may simply sign off in a part score or game or begin showing additional features for game or slam tries. There is one more Bergen Raise, but because of it's nature, it is game forcing. With 13-15 HCP and an undeclared splinter (singleton or void in a side suit), bid 3S/1H or 3H/1S; either is game forcing and slam invitational, and if declarer is interested in looking for slam, he may bid 3NT and wait for responder to bid the splinter suit. After opener's 3NT, then, a bid by responder indicates the short suit. If the auction (ignoring opponents, who are not bidding) proceeds 1H—3S—3NT and responder has splintered to show a short spade holding, he can still keep the bidding slow by bidding 4H. In this case, he would have shown a splinter in Clubs or Diamonds if he had had it, and his points and his heart holding are known, so the only logical meaning for 4H is to show a Spade splinter. All splinters should be alerted. Note that while these bids (especially since they are alertable) give opponents a great deal of information about your hands, opponents are not normally in a position to compete; meanwhile, your partnership has more than enough information to know how far is can bid safely.
Filling in the cracks
If you look over everything so far, you'll see that 2S/1H is left unclaimed. You may make this anything you wish or simply leave it as a strong jump shift, which is not alertable; I recommend having it show 16+ HCP and 5-5 or better in the minors, though this is an alertable bid and there is no comparable response over 1S, it makes use of an otherwise unimportant hole in the bidding (everything that could be shown by a strong jump shift in Spades can be covered by other bids, and opener should not pass after 1S/1H under any version of Standard American, provided opponents don't compete). In this situation, your partner will know to bid a 3-card or better minor if he has one. You have the points for game in a minor and the fit in that case; otherwise, he may gamble on 3NT or show extra length in his first suit (the other major is all but ruled out by his opening and your maximum combined 3-card major suit holding). True, this exposes the stronger hand as dummy, but that will probably not be a factor since you and your partner will almost certainly have extra values. Finally, if you're wondering why you shouldn't just bid this 2C/1H, consider how much more information about both points and length you are providing.
Higher-level NT responses
With 1NT/1-of-a-major accounted for and 4NT/1-of-a-major taken up with Blackwood, the only reasonably NT responses left are 2NT and 3NT. Both 2NT/1H and 2NT/1S show 16+ HCP and 4-card or better trump support. This is an alertable artificial bid, and it is both game-forcing and slam-invitational. Even with a minimum opening hand that lacks extra features, opener can sign off in a solid game with a likely overtrick. Furthermore, if opponents try to compete, you can be certain, with your 9-card or longer trump fit and 28+ HCP, that a 5-level contract is not wrong (though doubling their competitive bid may be better—you need to evaluate that on a case-by-case basis). After such a 2NT response, opener and responder can trade cue bids to show specific aces or voids; even in the worst situations, this won't drive the bidding too high, and it will allow one or the other to see slam potential with more precision than standard ace-asking bids.
The next bid is one that you may see once a year, if you play practically every day. Both 3NT/1H and 3NT/1S show 13-15 HCP and a 4-4-3-2 hand in which opener's suit is your 2-card suit. While this bid may work as a mild slam invitation, it is generally a signoff bid in game. With a 6-card or longer suit, opener may, if he wishes bid game in his suit, but he should note the problems that may come up with duplication of values because of responder's flat distribution and thus only attempt this switch if he has distribution that provides ruffing potential or is holding more than minimum opening points. This bid is not alertable as both the holding and the intent of responder are fairly clear.
Inverted Trump Swiss
Finally, Inverted Trump Swiss takes care of responder's minor-suit bids at the four level over one-of-a-major openings. All such bids—4C/1H, 4D/1H, 4C/1S, 4D/1S—are alertable and game forcing. First of all, the "inverted" part of the name refers to the manner in which 4C is stronger than the higher 4D bid. This change from Trump Swiss leaves more room, if only a single bid, for slam investigation after a strong response than after a weak one —even the single 4D bid this preserves may allow opener to provide valuable information. All Inverted Trump Swiss bids show 13-15 HCP, and 4- to 7-card trump support (more on this in a moment). The difference comes in the specific trump suit holdings. If responder has two of the top three honors in the trump suit (or as little as one of the top two with a 5-card or longer holding), he will bid 4C. If he lacks such strong holdings in opener's Major (while meeting the other requirements of these bids), he will bid 4D. Why 4-7 trumps? The bid also explicitly denies singletons and voids in side suits (remember those 3-of-the-other-major splinter bids?). The benefit here is that opener now knows where responders points are, more or less, and how much strength he needs in side suits if he wants to pursue slam. You'll note that one upshot of using these bids is that you rely on Blackwood less frequently when investingating slam because you can use cue bids and other information to find out just where to place the contract. Sure, if you have a tremendous hand you don't want it passed out too low, but then you will use some form of game-going bid, right? This is why it is called 2/1 Game Force. Your partner must keep bidding, so he has no need for jump bids that waste space if you respond using one of these conventions.
There is one gap in all of this, however. What do you bid with 13-15 HCP and precisely 3-card support for partner's 1S opening? OK, first of all, this is even less common than that 3NT response because your partner must first open 1S in either first or second seat, your RHO must pass, and you must have precisely 13-15 HCP and be holding 4-3-3-3 distribution (less common than the 4-4-3-2 distribution in the 3NT response) with hearts as the 4-card suit. Considering the distribution, bid 1NT with 13 HCP, dropping one point for your flat hand. It's a Forcing 1NT, so you can always correct to game in your partner's suit later. With a poor holding in your partner's suit, either bid 1NT or fudge a little to make it fit into 3NT, from which opener may correct to game in his suit if he has extra length. You aren't going to miss slam since your partner will bid on with extra values, and you aren't in terrible shape in 3NT and weak Spade support since your points must be somewhere else.