Sigma is a relatively new Asking Bid that occurs only immediately after a positive response to Alpha. One of the problems with a 3 or 4-step Response to Alpha is that there is sometimes a critical difference between Hxx and xxxx, but until we devised Sigma, there was no means (apart from a possibly using a tenuous process of elimination) whereby Opener could check exactly what Responder's support for the Alpha suit was. Sigma, therefore, is simply for the Alpha Bidder to check how good Responder's support in the trump suit is and there are 3 different scales, depending on how many steps the initial Alpha response went.
When is a Bid Sigma?
Sigma occurs only immediately after a positive response to an Alpha Ask. Which bid is Sigma depends on where the initial Alpha response "sits" in relation to the trump suit:
If the trump suit is the relay, or the next bid over that (normally after a 3 or 4-step Alpha Response)
A repeat Ask in the agreed trump suit below game level is Sigma, eg: 1♣-1♥-1♠-2♥-2♠ is Sigma in Spades. Similarly 1♣-2♦-3♣-3♠-4♣ is Sigma in Clubs.
If the agreed trump suit is not in the next 2 bids above the Alpha response (normally after a 5+-step Alpha Response)
Here a relay in the next bid up is Sigma (and Relay Beta, if required, is "bumped", eg: 1♣-1♥-1♠-2♠-2NT is Sigma in Spades, and similarly 1♣-2♦-3♣-4♦-4♥ is Sigma in Clubs.
There are no other situations where a bid can be Sigma
Also Note that Sigma (and Repeat Sigmas - see below) takes precedence over 4♣/4♦ Beta and a Relay Beta, but the Relay Beta is just displaced by one step, excluding the agreed trump suit and, if a Minor suit is agreed, excluding No Trumps. In practice there is not normally any conflict between Sigma and the Relay Beta unless the original Alpha Ask was "disturbed" (eg: 2NT=Alpha in Relay Suit or over interference). A Relay Beta is still available over the response to a Repeat Sigma.
Responses to Sigma
There are 3 different scales for Sigma depending on whether Responder has gone 3, 4, or 5+ Steps in response to the original Alpha Ask. This is because the minimum or maximum possible holdings are different for each. In practice, the 3 and 4-step scales are identical except that the higher responses to Sigma cannot occur over a 4-step response (because otherwise Responder would have gone 5+ steps in response to the original Alpha).
After a 3-step Alpha Response
After a 4-step Alpha Response
After a 5+-step Alpha Response
: Hxxxx * (See Notes below)
: HHxxx* (See Notes below)
Repeat Sigma Asks
If Responder shows no Top Honours or only 1 Top Honour in response to Sigma, then a relay in the immediate next suit up (taking precedence over a Relay Beta) is allowed to check for possession of the Jack.
is a repeat Sigma asking if Responder has the Jack of Spades. This might be a situation where Opener has K10xxx in Spades and wants to check further for trump solidity (ie: there is a big difference between Responder having Qxx and QJx, or Axx and AJx.
If we've agreed a Major suit and Sigma is used, then 3NT is potentially always available as a Repeat Sigma (if it's the Relay over the Sigma Response). If, however, we've agreed a Minor suit and Sigma has been used, then 3NT is only available for Repeat Sigma if (a) it's the Relay and (b) if Responder showed 1 top honour in response to Sigma. If Responder showed no top honours, then we reserve a Relay of 3NT as being "to play" and 4♣ becomes the Repeat Sigma.
The use of Sigma is always aiming for a slam contract. Where it is used and Responder's exact level of controls hasn't been definitely established then if a Repeat Sigma is possible but Opener has no space below game level for a Repeat Sigma, an apparent sign-off at game level is somewhat ambiguous. In these circumstances Responder has to take into account their actual level of controls and whether or not the Sigma response is likely to have been encouraging in deciding whether to treat the game sign-off as just that or as a Repeat Sigma. For example:
Now if Responder has No controls or only 1 control, probably best to treat this as a sign-off, but to respond as if it was a Repeat Sigma if they have 2 or 3 controls, or perhaps even with only 1 control but some other redeeming features, on the basis that Opener knows it's an ambiguous sequence, but Sigma is definitely interested in a slam.
If, in (2) above, Teller responds to the Repeat Sigma, but initially made a 3-step response to Alpha, we assume they have 2 or 3 Controls rather than 0 or 1 (in which case they'd probably treat the Repeat Sigma as a sign-off), and now any subsequent Beta is using the Normal Scale rather than the Weak Scale, so save space. If the original Alpha response was 4-steps, we use the Strong Scale as normal, of course.
Sigma over Interference
The general rule for this is as follows:
If there is interference over a 3 or 4-step response to Alpha and a repeat in the trump suit below game level is possible (even if it's a level higher than it would have been otherwise), then that repeat of the trump suit remains Sigma and Pass over the interference remains Relay Beta.
If, however, a Sigma in the trump suit is not possible below game level because of the interference over a 3 or 4-step response to Alpha, then now Pass is Sigma (displacing Relay Beta), and Double becomes Relay Beta.
Over a 5-step or greater response to Alpha, Relay Beta is never required (because Responders controls known exactly), so over any interference, Pass is Sigma
Note: If, however, the interference over the Alpha response is of a pre-emptive nature jumping to a level beyond 3NT, now our Lebensohl-style Pass takes precedence over both Relay Beta and over Sigma, so now Pass demands a Double from Responder, and generally Double is Sigma and a Relay over the interference is Relay Beta, but if the Relay over the interference is the agreed trump suit, then we change things slightly (common-sense), so the Relay (ie: a bid of the trump suit) is Sigma, and Double is Relay Beta.
Here our ability to bid 3♠ as Sigma is unaffected (albeit one level higher than it would have been otherwise), so 3♠ remains Sigma and Pass is Relay Beta
Here the response to Alpha was 5 steps so Responder's controls are known exactly, no Relay Beta is ever required, and Pass is Sigma
Here the interference has prevented a 4♣ Sigma Ask, but Relay Beta is still "in the frame", so now Pass over 4♥ is Sigma and Double is Relay Beta
Here the interference is pre-emptive in nature and so Pass=Leb takes precedence over both Sigma and Relay Beta. Now, therefore, Pass demands a Double, Double is Sigma, and 4NT is Relay Beta.
* If it is impossible for Teller to have 5-card support for Asker's suit, then any Sigma Responses that unambiguously show a 5-card holding are omitted from the Sigma Scale. In practice this is only when
Teller has shown a balanced hand
We've agreed a Major suit via Alpha
Teller gave a 5-step or greater response to Alpha
So in the above circumstances the 2 and 4-step responses are removed from the scale used after a 5-step or greater response to Alpha. Responses in other Sigma scales that might be 4 or 5-card simply become unambiguously 4-card in such circumstances. Note that showing an initial positive in a Minor suit does not make it impossible for Teller to have a 5-card Major.
If the original Alpha Ask was made by bidding the trump suit itself and there has been no interference, then it is effectively always the case that Sigma will be a repeat of the trump suit after a 3 or 4-step Alpha Response, or a relay over a 5+-step response. When the original Alpha Ask was not made by bidding the suit itself (for any reason), then if the Alpha response sits just below the agreed trump suit or the suit below that, then a bid of the trump suit is Sigma, but otherwise a Relay is Sigma and Relay Beta (if required) gets "bumped" by one bid.
Sigma should be used sparingly as very often the bidding space is better used in other ways, and very often Responder's trump holding can be ascertained by a process of elimination by making Epsilon Asks elsewhere. The time when Sigma is normally found is when the Alpha-bidder has a relatively poor trump suit such as Hxxxx but otherwise a very strong solid hand not needing to ask many (or any) Epsilon Asks..
This Asking Bid is new as of August 2007 and the Responses and Scales are subject to change if we decide that alterations are merited after we've used the Ask for a while. One area that might be changed is whether to simplify the responses but to incorporate posession of the Jack into the original Sigma responses.
It's unlikely that the strong hand will ever make an Alpha in a suit that contains no top honours. You'll notice that the scheme of stepped responses to Sigma ignores the possibility of Responder ever having AKQ stiff in the trump suit (except AKQx(x) with a 5-step or greater response to Alpha). If you, as Responder do find yourself in that position, the suggestion is that you treat your hand as having HHxx (a) if Opener uses Alpha and you have that holding and 4+ controls, or (b) if Opener uses Alpha and then Sigma and you have that holding and 0-3 controls.
OCP System Change Log
Omitting 'Impossible' steps in Sigma responses (23-Mar-2017)
If Teller has showed a balanced hand (as Opener or Responder) or if, as Opener, they've made any intermediate Opening that denies possession of a 5-card Major (eg: 1♦ or 2♣), and we subsequently agree a Major by means of Alpha, then, if Asker uses Sigma, any response that would show a 5-card holding in the Major is omitted from the response scale (because Teller cannot, by definition, possess a 5-card Major if they've shown a balanced hand). Thus in the sequence 1♣-1♠-2♥-3♥-3♠(Sigma)-???, now the 2-step response to Sigma, showing Hxxxx and the 4-step response, showing HHxxx, are both removed from the scale, and the stepped responses show Hxxx, HHxx, and HHHx respectively.
Sigma after 2NT Alpha or after Interference (16-Mar-2017)
Clarification of when a bid is Sigma: The rationale behind whether Sigma is a Relay or a repeat of the trump suit is based solely on the cheapness of a repeat of the trump suit. After a 3 or 4-step response to a "normal" Alpha (made by bidding the trump suit itself), a repeat of the trump suit is cheap, but over a 5-step or greater response to Alpha, that is not necessarily the case. The fundamental rule for Sigma is that if a repeat of the trump suit is within 2 bids (ie: it's the relay or the next bid above that), then a repeat of the trump suit is Sigma. If, however, it is not within 2 bids of the Alpha response (or any interference over the Alpha response), then the cheapest possible action by Asker is Sigma (include a Pass over interference).
Thus is in the sequence 1♣-1NT-2NT(Alpha in ♣)-3♠-???, now 4♣ is within 2 bids of the Alpha response, so that is Sigma and, in this instance 4♦ would be Relay Beta (and 3NT Natural). Similarly in a sequence such as 1♣-(X)-1NT-2♠(Alpha)-3♥-(4♣)-???, now, because of the interference, a repeat in Spades is not within 2 bids, so now Pass would become Sigma (cheapest action), and Double would be Relay Beta.
Beta after a Repeat Sigma at Game Level (28-Nov-2016)
If Asker uses Sigma after a 3-step positive response to Alpha, and then makes a Repeat Sigma Ask, this will often be at game level rather than below, which means the bid is ambiguous (ie: Teller may treat it as a sign-off if poor for their bidding so far). If Teller responds to the ambiguous Repeat Sigma, they are suggesting they are good for their bidding to date, and therefore we assume they have 2-3 controls rather than 0 or 1. If Relay Beta follows the Repeat Sigma Response, therefore, we retain the Normal Beta scale rather than switching to the Weak Beta Scale (as would be normal given the initial Alpha response). So
2♥-3♣ =Alpha / Support with 0-3 Controls
3♥-4♦ =Sigma / Hxxx
4♥- 4NT =Repeat Sigma / Jack of Hearts held
5♣-5♥ = Relay Beta using Normal Scale / 3 Controls
If the original Alpha response was 4 steps, Teller will almost always treat the game-level Repeat Sigma as such, and any subsequent Beta will continue to use the Strong Scale, as normal.
Sigma was created in August 2007 to cater for enquiries about trump solidity after a positive response to Alpha. Up till that point, Asker had had no way to check on trump solodity after a positive response. (Paradoxically, they could find out exactly what Teller had after an initial negative to the Alpha Ask.