Delta Club

Origin

In 2009 Ian Casselton asked me whether I thought a system based on the Delta idea could be successful. Delta – bunching all hands without a singleton or void into one bid while showing shortage rather length with shapely hands – was one of the many variants developed principally by Lukasz Slawinski and Stan Ruminski in Poland in the 1960s, 1970s and 1980s. It was little used for opening bids but became the basis of the response structure in Regres, one of the most popular weak opening systems.

We made a number of modifications to the original idea. One was to adapt the symmetric relay structure which was much more efficient than the one devised by Slawinski and Ruminski. Another was to change the shortages shown by the different openings: we thought it made much more sense to lump the minor-shortage hands together as all of these promised at least two cards in both majors, making it easier for responder to jump with major-suit length.

After a few years of tinkering I focused elsewhere; Ian continued to work on the idea, including making the relay structure very efficient. HITS shows the fruits of his efforts.

Why Delta Club?

I wanted to try Delta at the table in national events, had a partner willing to try anything (thanks Brad) and, following a successful second kidney transplant (my first had failed after 30 years), had both the time and energy to do the work to flesh out the system. Transforming an opening-bid structure into an effective system required filling in the gaps, especially how to develop auctions when there were not the values for game-forcing relays and ones where the opponents competed. This was a challenge as there was no information in English about how the Poles had handled such auctions, and few other system designers have started auctions by showing shortness rather than length.

I wanted to play a strong-club variant so as to test the effectiveness of the Delta idea without having the opponents distracted by a fert or a forcing pass.*

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* We could have played a forcing pass version in most national and state teams events in Australia; there are still one or two pairs who play forcing pass systems.

Australia’s system regulations, which are almost identical to those of the WBF, permit forcing pass and other HUM (highly unusual methods) systems under certain conditions. These include requirements about match length. They also prohibit the use of such systems in the early rounds of a Swiss (the format used for almost all major Australian teams events), or in the bottom part of a ranked field – typically the team needs to be in the top third of the field to be able to use a HUM.

Technically, Delta Club is a red system. Nonetheless, I asked the ABF Systems Committee to allow our opponents to use a written defence at the table given that our opponents would be unfamiliar with openings based on shortness. The Committee reasonably exercised their authority to designate the system yellow [a Highly Unusual Method].

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Delta Club in summary

1st- and 2nd-seat openings

1♣ = 15+, any shape
1♦ = 10-14 all BAL/semiBAL except 6/7M
1♥ = 10-14, 0-1C and/or 0-1D
1♠ = 10-14, 0-1H
1N = 10-14, 0-1S, 2-4H unless 0-5-4-4
2♣ = 10-14, 0-1S, 5+H except 0-5-4-4

The emphasis on showing shortness includes responses to 1♣: when we relay (when responder has a GF hand or, when opener has extra strength, a semi-positive hand) the first descriptive bid shows or denies shortness. And the responses are structured so that when responder has a (semi)BAL GF response opener will describe his unbalanced hand by showing shortness. (See Bells and Whistles below.) Showing shortness is also a feature of responses to the 1♦ opening when responder has GF values.

Note that the shortness-showing opening are ordered so as to place additional pressure on the opponents: with likely length in opener’s shortage the opponents must overcall at the two level.

Keen readers will have noticed that hands with 6M322, 7M222 or two shortages (so typically 6511 or 7411) are not covered by these openings (except hands with shortness in both minors). Delta Club uses 2♦ (5+S), 2♥ (6H322 or 2-7-2-2), 2N (6511 in hearts and a minor) and 3♣ (6511 in C and D) to show these hands.

In 3rd and 4th seats the opening bids are the same but with 1♣ now 17+. As a passed hand cannot relay to game opposite a non-1♣ opening we relax some of the shape requirements (e.g. allowing a 2N opening with 0-5-6-2).

Delta at the table

Alas, Covid restrictions in 2021 saw major events postponed or cancelled and prevented us from playing Delta Club at the table. However, we played it in a weekly online teams match where most players (but not me) have represented Australia. In these matches we have played the system on more than 600 boards. As well, we have bid thousands of deals in practice sessions.

It is now possible to draw some preliminary conclusions:

1. Shortness-showing (and shortness-denying) openings are intrinsically difficult to defend.

2. Showing shortness rather than length makes it harder for both sides to bid effectively but the balance of advantage seems to lie with opener and responder except when opener has a long one-suiter or a genuine two-suiter.

3. Showing and denying shortness leaks information to the opponents (although it is unclear whether it is more information than if we showed length or just different information) but, in general, responder is better able to utilise the information than the opponents.

4. Showing shortness makes it much harder to arrange for the hand that is describing itself in response to relays to be dummy.

Why are Delta’s one-level openings intrinsically difficult to defend?

Consider what happens when we open 2♣. The opponents know that we have at least five hearts and that hearts is very likely to be the longest suit in our hand. Yes, they have been pre-empted — no 1♠ or 1NT overcalls — but they know that they do not need to worry about playing in hearts, so only four strains (clubs, diamonds, spades and notrumps) are in play for them. Most importantly, they can agree that a double shows a takeout double of hearts*, the suit we are known to be long in.

As well as being able to show a hand with shortness in our known long suit the opponents can give a variety of meanings to their heart bids: a direct 2♥ could be Michaels, and advancer can bid hearts as a cue raise or transfer or to create a force or ask for a stopper or jump to show a splinter raise.

Now consider what happens when we open 1♦ through 1NT. Whether we open to show shortness or 1♦ to deny shortness there is no anchor suit, so our opponents need to cater for playing in all five strains. Over the opening bid they have no easy takeout double or cuebid, and when they overcall there is no cue raise or stopper-asking bid. Typically, our opponents’ defensive bidding is less precise than our teammates’ actions over a length-showing (or -suggesting) opening bid.

Openings that may or may not have length in the bid suit are not new to Delta Club. Consider the Precision 1♦, especially for those players who don’t use a special opening to show hands short in diamonds. For these players 1♦ is 0 to 8 cards (for some only zero to five as 2♦ shows hands with long diamonds). Against all these variants opponents have to decide how and when they will bid diamonds naturally. (1♦) 2♦? (1♦) X (P) 2♦? (1♦) X (bid) 2♦? (1♦) 1M (P) 2♦? The list of auctions pairs need to discuss is lengthy, and the answers not always obvious. And the defenders have to decide whether their defence to a 0+ 1♦ should be different to that when 1♦ shows 2+diamonds. One consolation is that diamonds is a minor suit and so matters less than if the opening were a major suit.

Another example of an intrinsically difficult to defend method is the Multi 2♦, showing a weak two in hearts or spades (possibly also one or more strong hands). Here too the defenders have to decide what their bids and doubles show. As over a Precision 1♦ opening there are lots of auctions to be discussed, including ones like (2♦) 2♠ (P) 3♥ where 2♠ is a natural overcall. Is 3♥ a cue raise or a natural bid?

It’s worth noting that the system regulations in jurisdictions such as Sweden recognise the importance of an anchor suit and the consequent ease of defending bids with one compared with bids that lack one.

For a helpful discussion of what constitutes a method that is intrinsically to defend see my post here and the subsequent discussion, as well as some of the discussion following my earlier post on Delta Club.

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*In my opinion, having a meta agreement that, unless the opponents are known to have more than 60% of the high cards (so 25+HCP), double is takeout of the suit the opponents have shown is the single-most valuable principle for countering transfers, switches or unfamiliar openings. Especially after transfers and switches, make the opponents pay for the extra space they create. This has lots of advantages, including that it typically offers a less-risky method of entering the auction. If the auction starts (1NT) P (4♥) and 4♥ is natural then fourth hand has to decide whether we are in or out of the auction, and typically partner has the last guess — bid or defend. However, if 4♥ is a transfer then fourth hand can double without forcing partner to act as the opponents are virtually certain to bid 4♠. There are a small number of auctions — like (1♣) P (1♥) where 1♥ is a transfer — where an alternative treatment might be best but they are rare.

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Doesn’t showing shortness invite the opponents to contest the auction, especially when we are short in spades?

Yes, it does, but arranging defensive methods to take advantage of that is tricky (see Part 3 for possible ways to defend shortness-showing openings). As noted above, the shortness-showing openings are ordered so as to place additional pressure on the opponents: with likely length in opener’s shortage the opponents must overcall at the two level. And finding 4-4 fits can be tricky as often neither opponent has the correct shape for an initial action, and an overcall in another suit can make it difficult to find the secondary fit (see example below). Of course, sometimes the 4-4 fit is not as playable as bridgeplayers are used to because the opposing trumps are known to break 4-1 or 5-0.

Often the opponents have to rely on a delayed entry to the auction in order to compete. Frequently, they can do so knowing that we have a fit and limited values. However, bidding is much easier when the auction starts

(1♦) X

than when it starts

(1♠) P (2♦) P
(3♦)

where 1♠ shows a hand short in hearts; 2♦ shows 3+D, usually two places to play and 0-11 working points; and 3♦ shows 5+card support without significant extra values.

Who benefits more from opener showing or denying shortness?

What does happen some of the time after a shortness-showing opening is that we miss our best fit or are unable to determine our combined fit and compete to the appropriate level. These are clear losses for the method.

On the other hand, we derive much valuable information by knowing opener’s shortness. It’s much easier for responder to know how well the honours mesh and whether KQx is a valuable holding for offence or defence.

When the defenders make the first statement about length they can be at an advantage but we also have advantages. Most of the time a shortness-showing opener has at least three cards in every non-short suit (so 4441, 5440, 5431, 6430 or 5530 – even 7330). In effect, opener has made a takeout double, so responder is well-placed. If responder has five cards in a suit that opener is known not to be short in then we are able to compete with considerable safety. With six cards in one of opener’s suits we are able to bid slowly with interest beyond game or to jump pre-emptively. Opposite an opening that shows length in one suit but nothing about the distribution of the other suits responder needs extra values or extra length to be able to compete in a different suit, even if that is the partnership’s best fit.

Problems can arise playing Delta Club when opener has a long suit or a two-suiter (at least 55). Now we are often at a disadvantage compared with the other table where a length-showing opening is identifying a key feature that is not revealed by its shortness-showing counterpart.

Here is an example from our matches.

Responder’s 2♥ bid denied 3+D unless responder had two more hearts than diamonds. While the 2♥ response need only be three cards, the bypass of 2♦ makes it very likely responder has four or more hearts, hence opener’s pass. When the opponents belatedly found their spade fit neither opener nor responder could be sure of a nine-card fit to make competing at the three level right, especially given responder’s useful (for defending) spade holding.

(Note in passing the value to responder of knowing opener’s shortage: if responder held something like xxxx KJxxx QJx x he would have known all his cards were working offensively and bidding 3♦ [showing 5-3 or similar in the reds] would be clear at the vulnerability.)

Who benefits more when opener denies shortness?

Our 1♦ opening is very frequent: almost 24% of all hands we are dealt in 1st seat!

When opener starts with 1♦ we are also well positioned. Responder knows of 2+card support for all suits. This permits responder to jump pre-emptively with less-than-invitational hands with a 5+card major or a 6+card minor. Responder also knows that opener is likely to have relatively low ODR (offence to defence ratio). Knowing that opener is always balanced or semi-balanced also helps responder with hand evaluation and defence.

Of course, denying shortness is also informative for the opponents, both during the auction and the play. The evidence so far does not suggest that this equals or outweighs the value to responder.

This is notwithstanding that the wider-than-usual range of “balanced” hands opened 1♦ can make it harder for us to find some fits, including when opener has a five-card major.

What about uncontested auctions?

Initial responses when second hand passes are more like those in a canape system where responder wants to allow opener to show his long suit. Initially, I experimented with using step as an INV+ relay and step+1 as a catch-all response to allow opener to show his long suit. Testing showed that to be much less effective than using both step+1 and step+2 to show such hands and be semi-natural, i.e. after a 1♠ opening showing a shortage in hearts 1NT is an INV+relay and both 2♣ and 2♦ show less-than-invitational high card values, at least three cards in the bid suit and playable in at least two strains.

Even when the auction is uncontested opener can have difficulties showing a long one-suiter or a real two-suiter. We can also be in trouble finding our best when opener is (semi)three-suited. Consider an auction that starts

1♠ (P) 2♣ (P)

where 1♠ shows 0-1H and 2♣ shows 3+C, less-than-invitational values and typically at least two places to play. If opener has four clubs he will usually pass 2♣. Simulations suggest it’s right to do so with a hand like AKxxx x Qxx Axxx, even though responder will have three or four spades about 45% of the time. The risk of rebidding spades is that 18% of the time he will have zero or one spade (when opener is known to have exactly five spades). However, if responder has xxxx Qxxx Kx Kxx we’ve just missed a spade contract that has reasonable chances to take ten tricks in order to play a definitely not cold Moysian 2♣. Easy to lose 5IMPs, and if our opponents find their heart fit the loss may be 6 or 7 IMPs. And if responder held Qxxx xxxx KJ Kxx we have missed a game we would want to be in.

Right-siding / wrong-siding?

If using a consistent suit-showing order, it is much harder than usual with Symmetric relay to structure responses to minimise the likelihood that teller will be the first partner in a relay auction to bid the strain of the final contract. Showing shortness first rather than length initially randomises which partner will bid which strain first. However, there are some optimisations which can be made to mitigate this, at least partially.

Does playing Delta Club increase variance?

YES. In spades! Virtually all auctions where we open the bidding will be different from what occurs at the other table. Importantly, even when the contract is the same the information available to the opponents will be markedly different: whether declaring or defending, the opponents will often know how a suit is breaking (either because opener has shown or denied shortness in the suit). Of course that information is also available to us when we defend. Why look for a ruff in partner’s hand if you know he can’t be short in the suit?

As usual, if you expect to beat your opponents then playing a high-variance system increases the risk of losing (and of winning big).

What is the impact of the absence of experience?

What would you do with ♠KT ♥QT82 ♦8542 ♣T64 after partner opens 1♥ (showing 0-1C and/or 0-1D and 10-16HCP) in third seat at unfavourable vulnerability?

I didn’t know what was best so I passed on the basis that game was unlikely and partner was likely to have three or more hearts. The deal was

so, as the cards lay, my decision cost us because we have a comfortable spade partial. I was lucky the loss was only 4 IMPs when partner was one off and, at the other table, South opened 1♠, West doubled and East bid 1NT, which was also one off.

Was pass correct in the long run? I don’t know. I haven’t encountered that problem before. I was relying on my knowledge from simulations that South’s average number of hearts is more than three when I have a four-card suit. I suspect that passing was wrong because we were likely to find a guaranteed 7- or 8-card fit if I had responded 2♣, showing at least three clubs and at least two places to play (and denying as many as three spades).

Playing Delta Club Brad and I are constantly encountering problems for the first time. Even when they have come up previously in our practice, our sample size is very small. Often we are working from first principles or relying on simulations to give us frequency data that can help us make probability-influenced choices. Unlike players using standard, or even those playing “normal” strong-club methods, we can’t draw on decades of accumulated experience by many players including experts. Many problems are now routine for standard methods: the pros and cons of different options are relatively well understood. Not so for us.

The same is true for the defenders. Our opponents are often in auctions unlike anything they have ever encountered before, and trying to find “standard” analogies to draw on can be challenging.

I think how to respond to a shortness opening with less-than-INV values after a pass by RHO, and how to handle competitive auctions when opener has promised shortness are the areas where there is the greatest scope for innovation and improvement. Ian thinks we can do better with continuations after the very frequent 1♦ opening.

Bells and whistles

Showing shortness enables partner to make a better judgment about how well the hands mesh. I decided to extend that to sequences where responder to a strong club has a (semi)BAL hand and opener is unbalanced. However, doing so over a 1♠ response (showing a (semi)BAL hand meant we were starting relays up three steps — too high for the method to be effective. At Ian’s suggestion I swapped the 1♥ + 1♠ responses with 1♦. So, in response to 1♣:

1♦ = a GF hand with any (semi)BAL shape or with shortness in S or H

1♥ = any semipos hand (5-8 HCP)

1♠ = any double negative (0-4).

The jury is still out on this. The 1♦ response is, in theory, more easily subject to competition and responder has said nothing definitive about his shape except to exclude D or C shortness. And while responder has a clearer idea of how the hands mesh when responder relays and opener shows his strength, responder has to deal with the larger number of permutations of honours, which can make relaying more challenging.

The 1♥ response can make life easier for both partners because responder has shown some values but it pre-empts opener. For example, we played in 2♠ after 1♣-1♥-2♠ (showing 15-18 with 6+S and at most 3H) when a normal strong-club auction would have been 1♣-1♦-1♠-2♥-4♥.

Further, the 1♠ response pre-empts everyone, opener as well as the opponents, on deals that are more likely to be competitive. What must be true, however, is that we are better off after 1♣ (P) 1♥/1♠ (overcall) than had responder instead bid a classic 1♦ negative.

So far we are plus at the table on this swap but this is heavily influenced by two deals. Both are instructive. One occurred when the opponents were uncertain about their general principles which meant they failed to act and missed their 4♠ while we made 3♥. The other was because of uncertainty about whether the methods used after a negative 1♦ response also applied after a game-forcing one which led to 1♠ doubled four off.

Despite the appeal of playing a 1NT response to our 1♦ opening as a GF relay (Ian’s initial preference) Brad and I decided to place a greater emphasis on using a mixture of natural and transfer responses that allow responder to describe shapely hands. (Semi)BAL hands with slam interest, and hands that want to take control can also relay — the 1♥ response allows relay continuations.

We also have a variety of relay breaks for opener. The most frequent is opener’s weak relay after responder shows GF values with a (semi)BAL hand (1♣-1♦-1♥-1♠). 1NT shows a hand with extra strength or a reason for taking control. 2♣ shows 15-17 (semi)BAL over which responder shows his shape with 15+HCP. This looks like a waste of space as the shape-showing is up two steps but we actually gain space as responder’s minimum number of RP (Relay Points: A = 3, K = 2, Q = 1, kingleton = 1, singleton Q = 0) is 9 instead of the usual 4 for a positive response, i.e. responder’s shape and strength is shown two steps lower than usual.

With less strength responder bids 2♦ and we can avoid leaking unnecessary information and allow a choice of which hand declares if we play 3NT. Another useful relay break is when relayer shows shortness. I missed the opportunity to reach this well-fitting slam using such a break.

When partner opened 1N (0-1S, 2-4H unless 0-5-4-4) I knew the hands meshed well, so I relayed with 2♣ (invitational or GF). Brad showed a maximum with long clubs or a three-suiter (2♥) and then a two-suiter with secondary diamonds (2NT). I relayed normally (3♣), finding he had 1-3-4-5 (3♦) and, when he bid 3N, 8RP (Relay Points: A = 3, K = 2, Q = 1, kingleton = 1, singleton Q = 0).

My second mistake was to fail to realise that I couldn’t distinguish between good, bad and no-play hands below game, so I relayed with 4♣ then signed off in 5♣ when Brad showed 0 or 2 honours in clubs. This proved costly as the other table played 4♥. Both contracts made 12 tricks and the opponents won 2 IMPs in a match we lost by 1 IMP!

My first mistake was not to break with 3♦ over 2NT. This would have shown a D shortage and asked partner to ignore the DK and DQ when counting his RP. If I knew he had 8RP excluding those honours 6♣ is easy to bid.

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