Theta is a secondary trump asking bid in Opener's main trump suit and asks exactly what holding Responder has in that suit along identical lines to those of Delta. Although Alpha is the primary trump asking bid, it is my experience that Theta (and Iota) are normally far more useful and used far more often than Alpha. In conjunction with a Low Beta, Opener gains much more exact information about Responder's level of controls and support for their trump suit, especially when Responder has exactly 3 Controls, since there is now no need for an expensive Beta using the weak scale.
When is a Bid Theta?
Theta is used in only two situations:
A simple new suit bid over the response to a low-level Beta (not in Responder's suit). eg: 1♣-1NT(Spade Positive)-2♣(Beta)-2♠(4 Controls)-3♦ is Theta in Diamonds.
A Repeat Alpha in the same suit is Theta...
...(unless Responder has shown a balanced hand in which case it is Iota).
(Note: A Repeat Alpha in a different suit is always Iota and never Theta).
If Responder shows a balanced positive with 1♠, then a bid which would otherwise be Theta is not Theta but alwaysIota, the collapsed version of Theta, because with a balanced hand the worst holding Responder can have is xx.
Responses to Theta
The responses to Theta are identical to those of Delta (in all cases, honour cards shown are generic rather than specific):
: - or x
: Q or xx
: Qx or xxx
: KQ or Qxx
: KQx or Qxxx
: xxxxx or xxxxxx
: Qxxxx or Qxxxxx
: KQxxx or KQxxxx
A 4-step response agrees the suit. Theta is always used with 5-card or longer suits
Repeat Theta Asks
In the same suit
Whatever Responder's initial response to Theta was, immediate Repeat Theta Asks in the same suit are available below game level and these ask for clarification of Responder's exact holding. Where Responder has shown two alternatives (ie: not a 5 or 7-step response) then the shorter holding is shown as the 1-step response to the repeat Theta Ask. Opener should not normally need to make a repeat Ask over a 5 or 7-step response to the initial Theta. If they do, however, then this is just asking about possession of the Jack in addition (and the 1-step response denies). A repeat Theta in the same suit always agrees the suit as trumps, whatever length Responder originally showed and whatever their response to the repeat Theta.
In a different suit
In the event of a response to Theta of less than 4-steps (ie: e negative response) immediate repeat Asks in a different suit are Iota and are uncondtionally forcing, even at game level.
The responses to Iota are similar to those for Theta except that steps 1 & 2 are combined into a 1-step response of "Less than Qx or xxx". If Responder made a positive response to Theta (ie: 4-step response or better), then the new suit bid is Epsilon, of course, because the Theta suit is now agreed as trumps.
In 4-card suits
There are times (eg: 24+ 4441 hands) where Opener may have to make Delta, Theta and/or Iota Asks in 4-card suits, but here Opener is presumed to be strong enough to deal with the consequences if they get a positive response showing HH or Hxx in the suit. Where a low-level Theta is used, however, and obtains a negative response, it will often be better for Opener to hand over the Captaincy with 2NT (or even 3NT) rather than making a Repeat Theta (Iota) in a second, 4-card, suit. Where this appears to be undesirable Opener must take care that the 3-step Iota Response that shows HH or Hxx does not take the bidding beyond 3NT, since that is quite possibly the last safe contract.
Handing over the Captaincy
Over a Minor Suit
If Opener rebids No Trumps immediately over Responder's response to Theta it is likely that this is at game level, natural, to play if the Theta suit is a Minor. If this is done at the level of 2NT however, it is handing over the Captaincy, perhaps suggesting that stops are bid upwards towards 3NT or simply showing a minimum semi-balanced 1♣ opener.
Over a Major Suit
If Opener takes this course when the Theta suit is a Major, however, it is definitely natural and to play or handing over the Captaincy if responder has made a 4-step response to Theta, suggesting that the combined holding in the Major makes 3NT a better proposition than 4 of the Major. If, however, Responder has shown a better holding than KQ or Qxx, then this is simply a device to invite cue-bids rather than using Asking Bids. As with any action that hands over the Captaincy it allows Responder to take the initiative in whatever way they see fit, but the most likely route is a cuebidding sequence which can be more efficient than Asking Bids, especally if Responder has shown lots of Controls and Opener has relatively few.
Theta is an incredibly useful bid combined with Low-level Betas. The reason that this route is much more popular than Alpha is because Alpha only tells you whether partner has a predefined measure of what constitutes Support (ie: Qxx or xxxx) or not. Theta, on the other hand, obtains a much more detailed picture of what partner has and Beta uses a smaller minimum range for Controls than Alpha (0-2 rather than 0-3) so there's less chance of getting a range response opposite an unpassed partner.
If Opener has AKQxxx in the suit, for example, the chances of Responder having xxxx is small, but xxx is quite sufficient in these circumstances. The Alpha user has to chance making a repeat Alpha in the same suit, hoping that Responder does indeed have a good tolerance whereas the Theta user getting a response of "Qx or xxx" knows immediately that this is the right suit and can make a repeat Theta to force agreement of the suit, knowing beforehand what the response will be. As stated in the pre-amble for Alpha Alpha is best
suited to big 2-suited hands where if Responder has no support for the first suit then there is a reasonable chance of support for the second suit. The other time when Alpha might be preferable is when Opener can tell that the response to the Low Beta may well take them to or just beyond their suit, necessitating an expensive Theta Ask at the next level.