Weak Two's

Bridge World Standard says:

"A first- or second-position weak two-bid that includes three of this list of characteristics is unacceptable:
• five cards in the bid suit;
• seven cards in the bid suit;
• flimsy (definition adjusted to suit the vulnerability) six cards in the bid suit;
• side void;
• side four-card or longer suit.

Otherwise, opener may use his judgment."

So, for example, you can open 2H with

• 5 Hearts and a side void (but not a 4+ card second suit)
• 7 Hearts and 4 Diamonds (but not a side void)
• a good 6 Hearts, a side void, and a 4-card side suit.

Larry Cohen says that it is okay to open a Weak Two despite the supposed "flaws":

• With a void in a hand like KJT9xx -- QJx 98xx, but not when a void makes the hand worth a 1-bid, such as KQJT98 -- Axxx xxx
• With a poor side 4-card major and a good 6-card suit like KQJT87 xxxx xx x, but not when the quality of the two suits is reversed, such as QJxxxx AQTx xx x. And don't give a side 4-card minor a second thought; bid the Weak Two.
• When lacking 2 of the top 3 honors but with good intermediates. Cohen says that QJT987 is a better Weak Two suit than AK5432, but don't take the idea to extremes such as T98xxx

Position:

In first seat, you can be as aggresive as you like since you have two opponents to obstruct while describing your hand to your partner. Your partner should allow for your Weak Twos being weak at unfavorable vulnerability and sound at favorable.

In 2nd seat, especially at unfavorable vulnerability, current (2018) theory calls for sound Weak Twos. Since RHO didn't open, the odds are that your side has more points, so you don't want to obstruct your partner's bidding.

In 3rd seat, you can open Weak Twos with almost anything -- suits of almost any quality ranging from 5 cards up. Partner has already passed, and the goal now is to obstruct LHO.

In 4th seat, a Weak Two is more a case of bidding what you think you can make while making it harder for the opponents to reenter the auction.

Normally, a Weak Two opener should not bid again unless required to by partner's bid, just as when making higher level preempts.

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Responses To Weak Twos

The following are options which should be discussed with your partner in a live game, but are the defaults in BidBase:

Bid 3N with 15-19 HCPs and a balanced hand with stoppers in the unbid suits.

Example hand in response to 2:    AT32-Q2-KQ3-AT82.

Bid game in partner's suit with 19-21 points and 2+ card support.

A raise to game can be done strong or weak. The opponents won't know which. Neither will partner, but he has to pass either way, so it doesn't matter.

Preemptive Raises:

Other than the game raise, all raises are weak and preemptive and based on total trumps. Add your trumps to the 6 promised by opener and that is how many tricks you can bid (non-vulnerable). For example, partner opens 2 and you have 3 for a total of 9 Hearts, so you can bid for 9 tricks by raising to 3. With 4 Hearts, you could raise to 4.

In situations where opener's Weak Two may be weak, he could have only 5 in his suit, but usually he will have 6, so if you are also weak, you have to play him for 6.

In theory, if you have a very weak hand, you could raise to 5 or even 6 or 7, depending on the number of trumps, but experts advise making a "gentle" raise to just the 4 level to keep from tipping off the opponents. Deprived of bidding space, they may settle into game on the 4 or 5 level.

New Suit Forcing:

A new suit bid by responder can be played as forcing or non-forcing.
The default in BidBase is forcing. It promises 16+ HCP and a 5+ card suit.

Standard responses by opener to a new suit:

When the new suit is on the two level:
1. Rebid original suit with a minimum
2. Raise to 3 level with 3 to the A,K, or Q.
3. Bid 2N (artificial raise) with 2 to the A, K, or Q or with xxx.
4. Bid a new suit with a feature (A or K) and a maximum.
5. Bid 3N with a solid suit and no outside features.

When the new suit is on the three level (e.g.: 2-3):

• Rebid original suit with a minimum.
• Bid 3x with a feature and a max, if possible (e.g.: 2-3, 3/).
• Bid 3N with a solid suit and no outside features.
• Raise to 4 level with a max, support, no outside features.

Feature-asking 2N:

When should responder bid 2N Feature-asking?

• When he wants to bid 3N and needs to know if opener has any stoppers or a running suit.
• When he has a hand which can make game opposite anything but a minimum - 16-18 points.
• When he has a hand which can make slam opposite anything but a minimum - 22+ points.

In a Weekly Bridge Quiz, opener held A-QJ7432-Q8643-3 and the question was what to bid. 
One response was "1H - Game could make opposite as little as xxxx-Kx-KJx-Axxx with which pard probably would not bid over 2H." 
Another said "2H - 4H usually makes opposite as little as: xxx Kxx Kxx Axxx. [2H-2NT, 3S-4H]." 
This raises the question of how strong a hand responder must have to bid 2N. Every reference on the Internet says at least opening strength, which would exclude the 2 hands above. Other sites say 2N bidder must have significantly more than opening strength.

Standard responses by opener are

• Rebid the same suit with a minimum
• Bid a new suit with a feature (A or K)
• Bid 3N with a solid suit.

Feature Asking in Competition

Little or no inforation is on the Web about this topic. A September 10, 2020, Weekly Bridge Quiz gives the hand 6-KJT976-K8753-J with bidding of 2H-2S-2N-3S-?? (vul. vs non-vul.) and the "answer" being 4 to show the feature. 
Fortuitiously, if Ogust is being used and 3 of the top 5 honors is considered a good suit, then 4 is also the bid to make if Ogust is used in competition. 
With a bad suit and bad hand, I would just pass and leave the contract up to partner, though at unfavorable vulnerability, one shouldn't open a Weak Two with such a hand.


Also see Ogust responses.

Defense Against Weak Twos:

Direct Calls over a Weak Two:

Non-jump overcall on the 2 level shows a good suit of 5+ length and 12-13 HCP. Each higher minimum level (e.g.: 1S-2H vs 1D-1H) requires an additional trump.

A jump overcall (e.g.: 1D-2H) shows a good suit and 14+ HCP.

A double then bidding a suit shows 17+ HCP; otherwise (not bidding again) shows 15-16 HCP and 3+ length in each unbid suit.

A 2N overcall shows 15-18 HCP and stopper(s) in the Weak Two suit. Systems are on.

A 3N overcall shows a solid minor of 6+ length and a good stopper in the Weak 2 suit.

A cue bid may be Michaels or Western Cue Bid, depending on partnership agreement.

Responses to Partner's Direct Overcalls:

Rule of 9 - Pass Partner's TOX?

If LHO preempts and partner doubles, add the level of the preempt to the number of your trumps and the number of your trump honors. If the total is 9+, consider passing for penalties.

It may be easier to remember this as the "Rule of 7" starting with a Weak Two. You need some combination of trump length and honors equal to 7 such as 4 trumps and 3 honors (counting the Ten) or 5 trumps and 2 honors, etc.

For every level up on the opening bid, subtract 1 from the 7, so a 3-level preempt only needs 4 trumps and 2 honors or 2-4, or 3-3, 6-1, etc. A 4-level preempt only needs 3 trumps and 1 honor, etc.

If Partner Overcalls...

He's described his hand. Bid accordingly except that with 3+ card support, raise rather than bid a new suit of fewer than 6 cards.

A new suit is constructive, meaning it encourages game+ but is not forcing.

A cue bid is game forcing.

If Partner Doubles...

Responses are the same idea as responding to a lower level TOX while a cue bid shows 12+ HCP.

If you typically use Lebensohl, here are the responses:

With 0-7 HCP, bid at the 2 level if you can; otherwise bid 2N which is a relay to 3.

With 8-11 HCP, you are able bid your suit at the 2 level, you can't do so because that would show 0-7 HCP, so bid 2N and then bid your suit next, which is invitational. If you cannot bid your suit at the 2 level, then bid it on the 3 level immediately showing 8-11 HCP since bidding 2N first would show 0-7 HCP. Lebensohl is off if RHO acts.

Doubler normally accepts the relay over 2N and bids 3 but may bid a new suit with a strong hand or bids game or cue bids with an even stronger hand.

With 12+ HCP, jump in your suit.

Bid NT or pass for penalties with the right kind of hand.

Players of Minimum Offshape Takeout Doubles can make responses one level up from TOX of a 1-level opener:

Bidding in Pass-Out/Balancing Seat:

After a Weak Two opening followed by P-P...

A TOX shows 10+ HCP and 3-card support for the unbid suits. Preference should be given to a TOX over bidding a suit since partner may have trap passed.

A non-jump bid can be weaker than in direct seat.

2N shows the same as in direct seat but can be made with a lesser stopper.

Leaping Michaels

After an opening 2, 4 shows a good hand with 5+ in the suit bid and 5 of the other major. Discuss with partner whether or not this is forcing to game.

A cue bid asks for a stop in opener's suit. Advancer should bid NT with a stop. If cue bidder pulls responder's 3N, it shows a very strong running 1-suiter and a hand too strong to have jumped to game in the first place.

After an opening 2 followed by 4, 4 by advancer asks for the major and 4 are to play.

A jump to 4N over a Weak Two shows the minors and opening strength.