I am not going to attempt to cover all 'reverses': I am only going to deal with opener's reverse into the 2-level after a 1suit - 1suit start:
1♣ 1♥
2♦
or
1♦ 1♠
2♥ etc
So I am not dealing with related topics such as whether 1♦ 2♣ 2♥ is a reverse or whether 1♠ 2♥ 3♣ requires additional strength (the 'high level reverse).
The first question that any partnership must ask, in terms of reverses, is just how much strength does a reverse show?
It is common, to the point of being universal amongst good players, that the reverse is a one round force. While I have seen a post or two questionning why that is, I am not going to try to justify this : not because I can't, but because of space/time constraints and the fact that most players accept that it is. There are many excellent basic bidding texts that can address the issue, and I may even respond to individual questions if I have time. For now, we will treat it as a given that a reverse creates a 1 round force. But this still doesn't answer, completely, the question of just how strong it need be.
There are two schools of thought about the strength shown by opener. My preference is for what is known as the strong reverse approach: opener has a good 18 or more, altho even we strong reversers will upgrade 16 or 17 counts with a good 3 card holding in responder's suit. Thus after partner responds to my 1♦ with 1♠, I'll reverse to 2♥ with AQx AJxx KQ10xx x, but not with x AJxx KQ10xx AQx.
The other school requires less for the reverse: so they might well reverse with the second hand.. but not with anything less. Note that the quality of the high cards count: the 4321 point count undervalues As and Ks while overvaluing Qs and Js, so bear that in mind when deciding whether to reverse.
I am going to assume a 'strong reverse' approach: but, and this is important, what follows makes just as much sense in the 'weak, but still good, reverse' school. Just bear in mind that opposite my preferred approach, responder will be forcing to game on weaker hands than opposite potentially lighter reverses: if I hold a good 6 count, then I know that we have the playing equivalent of 24+ hcp and, with any degree of fit, I'm off to game. Whereas, if opener may have a good but non-fitting 16 count, I'm going to want 8 or 9 to create the gf....or sufficient fit and shape to compensate.
Ok, so partner has reversed. How does responder handle this?
It is useful for responder to be able to immediately convey the good news when he likes his hand in the context fo the reverse: when he is able to commit to game. In the thread that prompted this post, opener had reversed into 2♥ catching responder with AKxxxx Kxxxx void Qx. The consensus of the experienced players was that 3♥ was forcing, but several expressed doubt that partner would know this. We can all see, I trust, why 3♥ as forcing makes sense, on the actual hand. But what if responder were QJxxx Jxxx xx Qx? Now this hand has to show the ♥ support, but wants to do so while allowing an out for opener who may have Kx AKxx AQJxx Jx.
So, one might well argue, 3♥ should be a weakness bid, and responder has to bid around the hand by, for example, bidding 3♣ as artificial, fourth suit.
This approach, while having some logic, was soon seen to be inefficient. What if opener, over 3♣, bid 3N or 4♣..... now responder has to bid 4♥ to show the suit, and is that just a gf or is it a slam try? And so on.
So years ago, some bright player or two (most inventions are invented several times) hit upon a lebensohl-like approach: use 2N as an artificial bid, usually connoting weakness... this allows all 3 level bids to be game force and natural.
2N asks opener to bid 3♣ unless opener can't stand the thought of playing 3♣. So with Qxxx Jx x QJxxxx, I respond 1♠ to partner's 1♦ and feel ill when partner bids 2♥. I can't pass, and I wouldn't want to because the opps probably have more trump than we do. So I bid the artificial 2N, hoping to hear 3♣ which I will pass.
If I am opener with x AKxx AKJxx Axx, I am delighted to bid 3♣.
If I am opener with Ax AQJx AQJxxx x, I refuse to bid 3♣: I bid 3♦.
(At the risk of adding confusion to a complex topic, I should add that many experts (including me) open 1♦ and rebid 2♥ with 5=6 hands of more than minimal values but far less than the hcp needed for a 'strong reverse'. Thus I would cheerfully open 1♦ and rebid 2♥ on x AQxxx AQJxxx x. So that hand type would rebid 3♥ over responder's rebid after my reverse.)
Back to the mainstream: this lebensohl-like approach works quite well and a lot of players still use it. It allows responder to use immediate 3-level raises of either of opener's suits as forcing. With a non-forcing raise of (or preference to) opener's suit, bid 2N and then correct or pass.
So with Jxxxx xx QJx Qxx, after you respond 1♠ to partner's 1♣ and he reverses into 2♥, you really don't want to encourage partner at all: you bid 2N and pass 3♣.
With AJxxx xx QJx Qxx, and the same auction, you like your hand. It is certainly a gf and slam is possible if partner has extras such as Kx AKxx x AKJxxx, so you bid 3♣. This merely announces we are going to game and I have a fit for ♣s. It is not in itself a slam try, but may be based on a wide range of hand types up to and including hands with grand slam ambition: the point is it is gf.
One point that hasn't been addressed so far is when responder has a rebiddable major: say the auction has started 1♦ 1♠ 2♥ and responder has a rebiddable ♠ suit.
2♠ is a one round force, but it may be weak. This apparent paradox arises from the fact that the 2♥ was forcing, so responder has to bid, and using 2N as a weakness bid makes no sense when responder wants/needs to show long ♠s. So responder will rebid 2♠ without in any way limiting his hand. Opener can complete the description of his hand by, for example, rebidding 2N with 5431's short ♠s or 5422 with a good doubleton (AQ is an example) or rebidding a 6 card minor or 5 card major or the 4th suit to create yet another force. Of course, opener can also raise ♠s or bid 3N if certain that that is the right bid: x AJxx AKQJxx AQ.... I'd open that hand 1♦, rebid 2♥ and then, over 2♠, bid 3N... no guarantees but I'm not playing below game even opposite the types of hands I respond on.
All of this is fine, and works reasonably well, but for those interested in something even better: use Ingberman.
This convention is similar to the lebensohl-type 2N above: in fact, on many hands, it works exactly the same. Ingberman use the cheaper of 2N and 4th suit forcing as the ostensibly negative bid. As with the lebensohl-like 2N, use of the Ingberman bid is the only way that the partnership is allowed to stop short of game.
This is an improvement on 2N, when it happens, because it increases the chance of the strong hand declaring notrump. After all, a very common hand pattern for a reverse is 5431 with a stiff in responder's suit.
Say you hold x AQx KQxx AKJxx and partner responds to your 1♣ opening with 1♠. You reverse to 2♦. If partner were to have a weak hand, without rebiddable ♠s, he has to bid 2N and now you play 3 of a minor or 3N from the wrong side. By allowing him to use 4th suit 2♥ here as the artificial, usually negative response, you as opener get to bid 2N! From the right side.
Change your hand to AQx x KQxx AQJxx and have the same opening, response and reverse. If he has to bid 2N, you are torn between 3♣ and 3♠. If he has 5♠s, 3♠ is definitely best, but if he has 10xxx Kxx xxx Kxx, you want to play 3♣. How do you know?
Well, allow him to bid 2♥ and you bid 2♠: a perfect description of your 3=1=4=5 hand. Now you find the 5-3 ♠s (and find decent games when he'd have passed 3♣ over 2N) while allowing him to play 2♠ rather than 3, or allowing him to intelligently decide between playing ♠s and ♣s.
Also, responder can now comfortably bid 2N naturally when 4th suit would be available: establishing a gf, showing stopper(s) in the unbid suit and allowing opener free rein at the 3-level to further describe his hand.
For this reason, many experts and advancing players use Ingberman.
I appreciate that introduction of these devices might seem a bit much for this part of the forum. I do believe that Ingberman is not too tough for Intermediates... once you master the idea that reverses require big hands and are one round forces, then having no discussion about follow-ups is actually worse: the B/I player is led out into the middle of the raging current and left with no boat or bridge to safety: he or she has to wing it as to what various bids mean.
Learn Ingberman early, don't be afraid to tell your partners about it, and if partner says 'ok' then you are going to be able to handle reverses almost as well as an expert.
Now, is this practical for playing online with B/I players? Not in a casual pickup game, but if the partner is compatible, and you want to arrange other games, why not email or pm him or her and suggest trying Ingberman?
If you are dealing with a real life partner: someone you hope to play with on a regular basis, then certainly Ingberman is a gadget that you can add ahead of many other optional devices, such as complex methods over their 1N (Surely Ingberman is no more complex than Cappelletti, a dreadful (imho) method many non-expert players love?
If you recognize that you need to understand and use reverses, but are not willing to learn either the lebensohl-like or Ingberman, then probably you should use 4th suit forcing to establish the gf and use bids of opener's suit as weak preferences/raises. That approach, flawed though it is, is better than no agreement at all: as posters in the original thread noted, no one is passing 4th suit no matter whether they understand what you are doing.
I am going to close with a few comments on a typical beginner mistake: which is to yield to the temptaion to open, say, 1♦ and reverse into 2♥ on strong 5-5 red suit hands, in order 'to show strength'. In is a fundamental principle of bridge (outside of certain non-standard methods) that one bids long suits before short(er) suits. Any reverse absolutely, without any room for exception whatsoever, promises more length in the first suit than the second.
If you hold a good 5-5, your choices are open the higher suit and rebid the lower without jumping or open the higher and jump in the lower.
Now, 1♥ 1♠ 3♦ is gameforce. While the upper limit of the hand is the same as the upper limit of a reverse, the lower limit of a jumpshift is higher than that of a reverse. We have seen that advanced players and experts have ways to stop short of game after a reverse: no such way exists after a jumpshift.
That can lead to tough decisions: 1♥ 1♠ 2♦ is exceptionally wide range: from whatever your weakest opening 1 bid looks like to just short of an absolute gf...for me, 2♦ could be an 11 count 54 or a bad 18.
Another potential source of confusion, to those who watch or read about expert bridge, is that there are hands on which it is appropriate to reverse into a 3 card suit. Let's say we hold Axx x AKx AKJxxx. We open 1♣ and partner bids 1♠. What do we bid?
Now, there are players and partnerships who have gadgets for this. I do myself, in one partnership. But what if you don't? A jump to 3♣ is a huge underbid, given that the bid traditionally shows 15-17 hcp, and this hand is worth more than the 19 points we assign it using the 4321 scale: it has Aces and Kings rather than Queens and Jacks and we have Axx in partner's major. So 3♣ is wrong, and no raise of ♠ is right: imagine playing 4♠ opposite xxxx KQx Qxx Qxx.
So most experts would manufacture a reverse into 2♦. Sure it is a distortion, but it is the easiest distortion to recover from. I am not encouraging these fake reverses, but I hope I am showing you why they can be, on a very small number of hands, the better alternative to other choices.
Now, this post is extremely long and yet merely scratches the surface of an important area of standard bidding. I would be happy to answer questions either here or by email/pm, subject to the caveat that I have limited time: I already spend more time than I can really justify on this forum
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