More on "Hillyard Doubles"

Recently, I've been playing again with my good friend as well as one of my favorite bridge partners: Bruce Downing (see for example The Downhill Notrump).  We spent some time working through what he calls, somewhat tongue-in-cheek, "Hillyard Doubles".  One of the things I've found as a boon in software development is the power of "peer programming."  In practice, this usually works as follows:

• me: Dilbert [or some other denizen of cubicle-land], could you help me find a bug?
• Dilbert: sure, what's the problem?
• me: well, it's like this [goes into long-drawn-out discussion of the design of the program and during said discourse, realizes what the bug is without any help from Dilbert] -- ah, I think I've figured it out.  Thanks so much for your help, Dilbert!
• Dilbert: sure -- no problem -- any time I can be of service...

You see what I mean.  Well, bridge theory is a little like that.  It often requires me to explain to some interested party the reasoning behind an aspect of the theory and during that explanation, I realize something I hadn't before.

Here's a case in point.  As I'm sure you know by now, all doubles in "my" system, are takeout, or at least cooperative, until some event triggers conversion to penalties.  The level, in and of itself, is irrelevant.  So, for instance, the following double is two-way (not penalty): 4♥ 4♠ 6♥ X.  It asks the spade overcaller "I'm not sure about this.  I do have some spade support and I've got quite a few points, shortness in hearts and support for both minors, what do you think is right?".  Now, the spade bidder can pass or pull according to his hand.  With ♠AQJxx ♥Axx ♦Kxx ♣Qx, you're going to pass obviously, converting the double to penalties, but with ♠AQJTxx ♥x ♦KQxx ♣Ax, you're going to bid 6♠ and with ♠AQJTxx ♥– ♦KQxxx ♣Ax, you'll probably bid 7♦.  Admittedly, these situations don't come up often.  Incidentally, given that we voluntarily bid game on this one, we can assume that partner's pass over 6♥ is "forcing".  In this we play the same as Meckstroth and Rodwell: the meanings of double and pass are reversed.

But, wait a moment, after an auction like 1♥ p 2NT* 4♠, pass is again forcing (because we have committed to game -- let's leave aside for now the possibility that defending 4♠, making may be the par result).  But, according to my trigger rules, double in this situation would be 100% penalty (because partner jumped, showing a 9-card fit).  So, now we don't play the Meckwell system.  How do we resolve this inconsistency?  Well, the answer is that the inverted style of forcing pass is particularly well-suited to auctions in which it is the opponents who have jumped, thus depriving us of bidding space.  The standard style of forcing pass is good when we have jumped, thus already communicating lots of distributional information.  This was the Eureka! moment I had when discussing it with Bruce.

Fortunately, I've now got quite a few gullible, oops I meant to say sensible, partners who are willing to play my doubles.  One of these is Brian Duran, whom I played with yesterday evening.  We actually hit our stride reasonably well this time, scoring 58.3% and losing first in our direction only by a fraction of a masterpoint.

There were actually two hands on which a two-way double would have been just the ticket, and as it happens they were sequential boards, although, as E/W, we didn't play them sequentially. On the first of these, with none vulnerable, I held the following hand: ♠Q52 ♥2 ♦QJ42 ♣K9762 in third seat.  I passed after two passes and LHO opened 1♥.  Partner came in with 1♠.  RHO bid 2♥ and I bid 2♠.  LHO now bid 3♥ and partner bid 3♠.  You see how this is going.  There were now two passes and LHO dug out the 4♥ card.  There were two passes to me.  We were not in a penalty double situation, so my double would have been two-way.  But do I have enough at equal vulnerability opposite a passed hand?  I decided to pass.  Unlucky.  LHO wrapped up his 10 tricks and we were booked for a 14% board.  Had I rustled up a double, partner would pull it (hopefully!) to 4♠ and we would take our 10 tricks and reverse the tables so to speak.  So, a missed opportunity.

Now take my partner's hand on the next one (red on white) ♠K3 ♥AT7542 ♦K5 ♣952: LHO opens 1♦ and partner overcalls 2♣.  RHO passes and we bid 2♥.  This goes pass, pass and now RHO comes in with 3♦.  It seems like it should be our hand, right?  We've got three-card support for partner and six-not so great hearts.  It's a tricky decision.  This is where the cooperative double comes in handy (although normally, double would show at least three-card support for the unbid suit).  Partner doubled and I left it in with 3-2-2-6 shape.  We actually only outgunned them in points 21-9 but it was enough.  We chalked up +300 and a top.

Zar points

Most players are familiar with Marty Bergen's "rule of 20", amended slightly by Mel Colchamiro to be the rule of "22".  In Bergen's original, you count the lengths of your two longest suits, add your high card points and if the total comes to 20, you have an opening hand.  Colchamiro says fine, but you should still have two quick tricks.  Neither rule adjusts for poor texture – a concentration of honors in short suits and hence no honors supporting each other in the long suits.  Still, that should go without saying.

Zar Petrov's rule for opening hands is a little more technical than the simplicity of the rule of 20 but almost as easy to apply at the table.  Petrov developed his method of hand evaluation for bidding games and slams based on analysis of thousands (millions?) of actual results.  His original posting on the web was lost for a while, but I see that the Bridge Guys have re-posted it here.  I therefore don't plan to go into too much detail.  The method is summarized on Wikipedia, though the discussion is not good IMO (also the wiki people don't think so).

You might call it the "rule of 26".  Again you add the lengths of your two longest suits.  To that you add your high card points (A=4, K=3, Q=2, J=1).  Sound familiar?.  Now you add the difference between the longest and shortest suit.  Finally, you add the count of your "controls" (A=2, K=1).  If the total comes to 26, you're in business!  While the rule suggests opening some distributional hands that you might think extreme, it also suggests passing with some balanced, quacky hands that you might otherwise open without much thought.  For an example of the latter situation, let's say you pick up this beauty: ♠QJ4 ♥K85 ♦QJ3 ♣QJ62.  You might think this is an automatic 1C opening (I wouldn't).  But it is woefully inadequate using Zar points: distribution comes to 7 + 1 (the lowest possible) and hcp = 12.  You have one control (the HK) so that's 21 only.  It could have been worse if your twelve points were all quacks!

Here's an example of me applying Zar points to an opening at the recent Sturbridge tournament with Bruce Downing as my partner.  Playing one of the best pairs in the district, I picked up this hand as dealer (all vulnerable): ♠AT7653 ♥– ♦2  ♣KT9542.  Note that this hand doesn't qualify by the rule of 20 (or 22).  But it qualifies on Zar points (rule of 26) with a couple of points to spare!  12 + 6 + 7 + 3.  What happened, you ask?  I opened 1♠, and partner (with 19 hcp and a solid six-card heart suit) forced to game with 2♥.  At this point, things weren't looking so good.  Once we got to 4♥, I surprised partner a little by passing.  Result: down 1 (-100) which was good for a 75% board because most people overbid (or underplayed) and were down more.

Zar's main proposal is that the strength of a hand (for offensive purposes) is more or less equally based on distribution and high cards.  Since Zar adds these together we get a number which is approximately double the "Goren" number: 26 points to open, 16 to respond, 52 for game, 62 for a small slam, 67 for a grand. 

Personally, I use a formula which divides the Zar points by two because that comes much closer to the numbers we all know and love.  However, I do hate halves (just as I think it's totally weird that in the USA we halve matchpoints so that we have to add a special symbol "-" to the 10 digits).  Really, we should all start using Zars and get used to the numbers being approximately double.  While I'm on this particular rant, there's nothing magic about the Goren counts (based on the Work 4321 method).  All other things being equal and in the play of relatively balanced hands, each 2 Goren points is worth approximately one trick (a Queen you have is one that they don't have).  This assertion, by the way, is based on the analysis (by Matthew Ginsberg, developer of GIB) of thousands of hands playing at notrump.  See Extending the Law of Total Tricks for details. In the Zar point scale, each extra 2.7 points is about one trick.

But the main point about the Zar method of evaluation is that it takes distribution and fit into account in a logical and mathematically sound way.  The downside of Zar points is that we are encouraged to open light distributional hands and that when partner trots out the old penalty double or goes searching for a slam without a good fit, we don't always have the goods.

Referring back to my previous article Confessions of a heart suit repressionist, you may recall that on the first board, we had ♠KQ63 ♥T9876 ♦–  ♣AT97 opposite ♠94 ♥AKQJ5 ♦AJ3 ♣KQ6.  On the Zar scale, the first hand evaluates to 13 (high cards) + 14 (distribution points) = 27 (and is therefore an opening hand) while the second hand evaluates to 26 + 11 = 38 as an opening hand, possibly with some adjustments but these tend to cancel out.  The adjustments to take care of fit/misfit are quite complex, however.  But even without adding for the big fit, these two hands add to 65 which is almost enough for a grand (but not quite).

When third hand couldn't show attitude

Here's a thorny problem that I've been thinking about recently since it actually came up a couple of months ago.  I'm only going to give you one suit and no auction.  Yes, I know many of you are going to complain!

You are on lead to 1NT (let's assume for the sake of argument that it went 1NT all pass).  Here's your holding in the suit in question:  QJ52.  You decide to lead the 2 and dummy's holding in the suit is T7.  Declarer calls for the T and partner produces the K which is headed by declarer's A.  Notice that partner hasn't been able to show attitude -- he simply was trying to win the trick.  

A couple of tricks later in the hand you are on lead again (partner hasn't had the lead yet) and you decide to cash the Q of this suit.  Dummy plays the 7 perforce, partner's card is the 6, and declarer plays the 8.  How do you continue?  Yes I know you want to know the rest of the hand but please bear with me.

There are three unseen cards: 9, 4 and 3.  Here are partner's seven possible holdings:

1. K9643
2. K964
3. K963
4. K643
5. K96
6. K64
7. K63

If partner is showing (present) count from #6 or #7, then declarer started with A984 or A983 in which case if you continue with the J, you will actually give a trick to declarer. 

We can probably rule out #4 because playing the 6 would be confusing to partner (and this doesn't look like a situation where it would be helpful to confuse declarer).


What about #1, #2 and #3?  Could partner be showing attitude?  Wouldn't he play the 9 then?  Well, yes, he would with #2 or #3 because he can afford to play the 9 to show attitude.  But where partner has all three of the missing cards (#1), he cannot play the 9 because the suit will then block!  Partner may have no outside entry.

There's one more possibility: #5 -- partner is simply playing his lowest card.


The bottom line is this: with #1 (attitude) we want to continue with our J and then the 5.  With #5 (attitude, kind of), we should continue with our 5 to partner's 9.  With #6 or #7 (count) we must not continue at all.  #2, #3 and #4 are impossible (according to our logic above).


Can we actually tell what to do?  Is partner showing attitude or count?  The books are silent on this issue.  Kantar and Bird don't cover it.  Neither does anyone else that I've found.  But according to the logic that, in following suit, partner shows attitude first, then count, then suit preference, it seems to me that partner should be showing attitude because he didn't get a chance when we led the suit before.  It would be different if partner got the lead and returned this suit: by convention, he shows present count by returning his original fourth best card (or high from an original holding of Kxx).  


So what happened in practice?  Partner started with holding #1 (K9643) and opening leader never played the J.  So, from a suit where we should have taken four tricks, we actually took one!  Not a good result :)

Pseudo-balancing

There are two schools of thought with regard to balancing.  The fearless regard it as safe to overcall in a pre-balancing situation after responder has raised opener.  So, for example, 1♥ p 2♥ 2♠.  This style is known as OBAR BIDS (Opponents Bid And Raise - Balance In Direct Seat).  I'm not a strong advocate of this style myself.  The majority are content to balance when the raise has been passed by opener and a pass would otherwise end the auction.  The theory of course is that the opponents have about half the deck and a fit.  Therefore, we have half the deck and a fit.  Most of the time, this works out fine but you can still come a cropper when all of the hands are balanced and the suits are not pure (translation: a relatively low number of total tricks). 

But there also times when both opponents have made signoff bids though one is not in the true balancing situation.  What theory is there on this situation?  I've never seen it mentioned, but I think it could be called pseudo-balancing.

Here's an example:  love all and your hand is ♠Q9542 ♥KQ85 ♦J8 ♣Q7.  You pass as dealer, LHO opens 1♦, partner passes, RHO bids 1♥, you pass again and LHO bids 2♣.  Partner passes again and RHO now comes in with 2♦, natural and to play.  While LHO's 2♣ isn't perhaps as limited as a 1NT rebid would be, you can still be 95% confident that LHO will be passing.  So, unlike the situation where the bidding has gone, say, 1♥ p 2♥ where LHO might easily be planning to bid game (and may double your interference), your chances here of being doubled for a painful penalty are almost nil. 

So, the question is: with the given hand, would you bid 2♠?  Or will you leave it up to partner to act?  I'm interested to hear your comments.  I think I would bid 2♠ but my partner on this occasion did not. We got a 17% board for -90. 

You're no doubt wondering what my hand was, the one that was truly in the pass-out seat.  This was it: ♠J763 ♥AT7 ♦QT3 ♣K82.  I decided not to come in on the following grounds: 1) I have a horrible, balanced 10-count with a lousy spade suit (remember, they've bid the other three suits); 2) my partner who was in the pseudo-balancing seat could not act [see above]; 3) we might get a decent board simply defending 2D when other declarers are in notrump; 4) my diamonds are actually quite good defensively but not offensively; 5) whereas opponents with a major suit fit will start thinking about game with about 22 hcp, opponents with a minor suit fit might have around 24 hcp before they start thinking seriously about game.  Trying to make a two-level contract without a great fit and with only 16 hcp might not be a barrel of laughs!