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Tweedledum and Tweedledee

ParadoX Advances

A paradox bid is a non-forcing call of the suit you don't hold when length in one of two suits has been shown or implied by partner's bid, generally when the partnership expects to subside in one of these suits. Let's start with an example, bid against me by an efficient looking Italian pair at the 1998 European Mixed in Aachen.

In this writeup suit-ambiguous bids are marked "¥" and ParadoX advances "¶"

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A deal from play: Advancing an ambiguous major overcall
WEST hand
S J3
H 9853
D AK1085
C Q8
Pairs both vul
dealer West
EAST hand
S 98
H AQ1074
D 974
C A106
West North East South notes
pass 1C* 1D¥ double 1C*=3+, 1D¥=either major, double=takeout
1S   1S=heart support!

Strange auction against unknown opponents! I assume this was part of a more general defence to phoney club. East's response of 1S paradoxically showed heart support, and the ability to play the two level. Had East bid 1H West (presumably) would have corrected with a spade hand.

I was North and actually held clubs with 4 spades for my 1C. I made a takeout double of their implied heart fit and we bid to a 3S contract, but that's another story. While this may look pretty trivial, this style of advance can be used in any situation where partner has implied length in one of two suits. It is also very efficient, generally freeing up an extra step. Try our 1D¥ example using an alternative (and cumbersome) 1H=relay sequence

West North East South
pass 1C* 1D¥ x
1H* 2S! ?  

Look what has happened. Opponennts have got in first and now it's you who has to guess.

Furthermore, using relays there is no room for you to play in hearts at the one level (unless you agree that you might pass the relay). Paradox advances always save one step, and always allow you to drop the auction at the existing level.

Do you get the idea? Here West has shown an undisclosed major. If East can raise one, she bids the other one. Therein lies the paradox!

You have overcalled ambiguously at the one level but can still subside safely in one of either major. You have messed up the phoney club, but opponents still don't know your actual suit. You can use the now spare 1S/1S (or double) systemically for other awkward interventions such as a Raptor 4/5+ hand. Cool!

As it happened my own partnership was already playing ParadoX in several situations ...


Extending a strong 2 clubs

paradox example ParadoX negative responses allow you to incorporate 8 trick major Acol Twos into otherwise game forcing 2C

The challenge is to open 2C as either 8 tricks in a major or a massive hand, yet still stop in a playable contract opposite partner's usual rubbish. The answer is to make 2D a semi positive relay and to make paradox negatives in a major on very poor cards. In this scheme

  • 2H is either nothing, or a trick for spades only
  • 2S is a trick for hearts only

In the examples partner has opened 2C which in our methods can be game forcing, a 16+ three-suiter, or 8-9 tricks in a major.

S J32 H 853 D 10852 C Q84

Nothing for either major. Bid 2H and pass 2S=(natural with 8-9 tricks)

S Q5 H 93 D 10763 C J9652

Trick for spades only - bid 2H (later you can raise spades)

S 3 H J853 D J9643 C 862

Your 2S call shows a single trick for hearts only. Partner will now place the contract.

S Q3 H 9853 D 85 C J7532

With a trick for either major you bid 2D=semi+ve

The gains from this seemingly devious style:

  • The weak positive 2D response has effectively become a relay promising "a trick for either major". Opener can always get a major in at the two level and his second suit at the three level. This is especially useful for hearts, and avoids confusion later.
    You can still subside in 3 of opener's major
  • Playing Acol methods the 2S/S openings are free for other bids. I like Multi, and two further layers of preempts!
  • A new 4 level suit is now always a cue.
  • you havetaken pressure off your 1 levl opening and can safely pass these with as much as 6 points

You will need some ageements to force game or make a slam tries. The full 2C responses are on my own two system page. If partner has a nine trick Acol major Two you will find the method also always works. We not infrequently get auctions:

2C - 2H;
2C - 2S

Much to our opponent's surprise!


ParadoX Tricks opposite the Multi 2 diamonds

paradox example I claim no originality for ParadoX advances which are an intrinsic part of the Multi. But even here partnerships tend to underuse the method. Let's start with "standard" responses Partner opens Multi 2D¥ showing a weak two in either major (commonly) or various stong hands (rarely)
S 5
H A853
D K104
C KJ732
You respond 2S

Usually you play there, but the message is that game is possible if partner has hearts.

However ParadoX allows similar bids at the three level - extending the preempt

S J54
H K853
D 9
C Q10732

This time game looks on for opponents and a rapid ParadoX preempt extension of 3S makes things hard for them. In practice it always seems safe. Play there, or in 4 hearts. I have often made the same bid on S Qx and four hearts and it works fine.

It would be nice to play similar ParadoX preempt extentions at the four level, but my view and experience is that this does not work. There will always be hands where you simply want to simply bid game in your own major when partner pre-empts. 4H and 4S should be natural responses.


ParadoX and lebensohl

paradox example The basic lebensohl situation is that one player has shown values via perhaps a no-trump bid or double and an opponent has made a bid at the 2 level. The lebensohl bid is then 2NT* commanding a 3C "puppet" reply which is either passed or converted to another suit "to play". Direct bids of a suit can then be played as forcing. Lebensohl and ParadoX advances are just made for each other ..

Pairs nv/nv - 1NT is weak or mini

S A5
H KQ83
D 1043
C K1032
Your weak/mini 1NT is overcalled 2S
partner makes a puppet/lebensohl 2NT which is doubled.

Partner has commanded a 3C call, and generally is going to convert to diamonds to play. But his suit is long and ambiguous, you have fit for clubs.

Tell him about that with a ParadoX 3D bid! (Which he will usually pass). If there is fit about they will bid on in spades and partner will be able to judge whether to compete the four level. With four cards in both minor the ParadoX bid is 3H!

Note that it is safe to force the 4 level should there be 9-10 card club fit. The LAW will protect you non vulnerable.

Tweedledum and Tweedeldee battle
S void
H K109754
D 842
C AJ63
Pairs nv/vul
2H pass 2NT* (double)
2H was Dutch style showing 5/4 hearts with minor side suit. Again you safely indicate clubs by bidding diamonds. Often this may not matter, but can prepare the ground for spectacular action should partner hold say
S Q983 H 6 D 10 C 10987542

A good example of what Paradox in competition is about. The call may make no difference to you, but facilitates your partner's bidding considerably.


ParadoX opposite 1NT defences

paradox example

Pairs nv/vul: Your left hand opponent open 1NT

S 85
H Q873
D K1043
C 732
Partner doubles "DONT", RHO redoubles

The "DONT" 1NT double and Cappitelli 2C overcall, showing an unspecified long suit have been around in ACBL territory for some time, but were only legalised un UK in 2005 (you can blame me).

"Long unspecified suit" you say! Of course ParadoX advances are on here. I'd call a cheeky 2S indicating that you are happy to play in the other suits at least at 3 level. "Good luck opponents".


Using a Multi bid after partner opens

paradox example While the Multi 2D evolved as preempt, there is no reason why you cannot apply the same principles show a weak long suit once partner has opened! This works best opposite shortish minors that may commonly be a balanced hand outside your 1NT range. Multi's 'built in' ParadoX advances make this audacious gambit quite safe.
  • 1C (pass) 2D! = multi: 6 card major, 4-7 pts
  • 1NT (pass) 3D!! = multi: 6 card major, weak (or invitational?)

My thanks to Belgium's Tom Huybrechts for sending these innovative extensions to me. He uses this style to allow weak jump shifts and fit jumps opposite a loose 1C opening

Putting more into semi constructive sequences

note I like to play a mini no trump, and with a six card suit opposite we will pre-empt to the three level guaranteed an 8-9 card fit. 1NT - 3C! - all pass on a combined 17 points scores just fine.

Playing all four 3 level suit bids as preempts does however put a lot of strain on your conventional two level sequences. This page isn't about 1NT bidding, but once again I like an ambiguous bid - 2S showing length in unspecified minor, and either game or slam invitational values. I could have used 2NT for this purpose, but we like 2NT as an uninformative game invitation.

Both of the hands below hands pose a problem opposite partner's 9-12 mini no trump. The first may scramble a thin game, but will be in trouble if the diamonds cannot be run. You need an honour. The old Blue Club approach of 3 of a minor inviting 3NT solved this, but with ParadoX you can handle both of these via a 2S 4-way bid. The key is opener's rebid showing what fit is available.

S Ax
H 83
D KQ9732
C 1092
1NT - 2S¥;   Opener may rebid ..
  • 3C = no club honour (diamonds still undefined) Opener may try 3NT over 3D on inference, or pass
  • 3D = club honour but nothing for diamonds On the left hand, this is passed and will usually make.
  • 2NT = top honour in both minors (establishes game force)
  • 3NT = fast arrival, top honours but slam unsuitable
H A53
D 5
C AK7642

Knowing the long suit will be fluid the first hand can bid a cheeky 3NT. Opponents still don't know our long suit! The perfect reply for the second hand is interestingly 3D. You can more or less bid slam immediately on super-fit.

As in the other examples you still subside in 3 of a minor if the suit is not running. Over 2NT positive for both minors responder bids 3NT with the first hand and shows his suit forcing/slammish with the second inviting a cue. The general method is perfectly playable opposite stonger no trump ranges, but you may have strong 3 level bids available and not need it.


Other applications

paradox example If you make bids where one or more of your suits is always there but undefined then you will have opportunities for ParadoX advances. Some that I have used or come across:
  • The polish Raptor 1NT overcall, showing unbid major and a longer unspecified minor
  • Wilkosz 2D opening - weak 5-5, but always with a major
    Wilkosz opening is illegal in UK, but I use it over strong club under "any defence allowed"
  • Ambiguous suit defences to strong 1C
  • Puppet Stayman after 2NT (implicit: responder bids the suit he doesn't support)

    .. and any more you might think of


I know what you're thinking about, said Tweedledum but it isn't so, nohow
  Contrariwise, continued Tweedledee, if it was so, it might be;
    and if it were so, it would be; but as it isn't, it ain't. That's logic
   Through the Looking Glass : Lewis Carroll

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