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!

The Downhill Notrump

A few months ago Bruce Downing asked me if I'd be available to play at the Sturbridge regional.  I said I would, with great enthusiasm, and here I am.

The last time we played must have been three or four years ago but we still had a card and were pretty much compatible with most of our system.  What to do about notrump openings, though?  During a pub lunch on Wednesday, we put together a system which we thought we'd like to try.  Later, Bruce came up with the name "The Downhill" notrump -- I expect you can see whence the name derives.

Here are the basics: 2/1 with a (slightly) variable notrump:

This is how we show balanced hands below 18 hcp:

Vulnerable versus not:

• 15-17: 1NT with the usual systems, including four-suit transfers, Lebensohl, etc.;
• 12-14: as standard (one of a suit with a rebid of 1NT)

All other situations:

• 10-11: 1NT with the following responses:

• 2-level bids are all to play (yes, including 2♣);
• 3-level bids are forcing and natural;
• 2NT is a modified form of "Muppet" (3♣ both majors, 3♦ one major, 3♥ no four-or-five card major, 3♠ five spades, 3NT five hearts)
• 4-level bids are Gerber, Texas and Jabbour (a kind of minor-suit-Stayman).

• 12-14: 1♦ followed by a rebid of 1NT
• 15-17: 1♣ followed by a rebid of 1NT.

Now, you should realize that we aren't suggesting that this system is the perfect way of playing bridge.  But it was simple and easy and fitted our way of thinking.  We expected some fireworks and we got them!

Here's an example from the pairs we entered to get the kinks out: you pick up ♠9842 ♥AJ83 ♦KT3 ♣Q6 as dealer with none vulnerable.  You open 1NT and after two passes, RHO decides to double.  LHO bids 2♣ and partner now doubles showing values.  RHO bids 2♥ and you double.  It turns out that we can make 4♥ on a Moyesian fit with 22 hcp -- but of course nobody is in it.  We don't take our ten tricks on defense, but we do take eight which is enough for a top (500). 

The second hand of the set is not so good.  At that point, we hadn't talked about the dreaded red on white situation, which is especially bad when in third seat.  This time our hand is ♠754 ♥6543 ♦KT5 ♣T42.  When RHO pulls out the red card, I have nowhere to go and the result is a bottom (-500).  Since then, we have decided to play normal strong notrumps when  red on white!

But, that one hand has been our only disaster.  On every other hand when we got to open 1NT, we have either ended up with the normal result, or we have ended up with a good pickup.

It's all downhill from here.

A lost opportunity

In fourth seat at favorable vulnerability, I picked up the following collection: ♠QT743 ♥JT842 ♦93 ♣8.  Partner opened 1♣ in second seat and RHO bid 6♦!  I passed, as did LHO, and partner doubled.  We play that such a double is cooperative, so I can take it out if I think it's right.  On the plus side, I have two five card majors, and partner should have at least one four-card major on this auction.  On the other hand, if partner has the ♣A I can likely get a ruff for down one at least.  I decided to leave it in.  In an auction like this, partner's double can't mean don't lead clubs as well as suggesting a takeout.  Therefore I felt that the obvious lead was the ♣8.  Unfortunately (but perhaps not surprisingly) declarer had the ♣A and moreover was able to get to dummy in diamonds (with the 8) to pitch the losing spade on the ♥A, which was the only card that dummy provided.  Once I don't lead a spade, the contract is always making, losing us a bushel of IMPs since most RHO's didn't bid 6 with their 1075 shape (with solid diamonds). 

Bidding 6♠ would have improved our score to only -500 which would have actually given us few IMPs on the plus side.  But best of all would be for me to lead a spade and set the contract for a gain of almost 12 imps.

The lesson here I suppose is that if you develop a system of unlimited cooperative doubles, you should at least try to use it!

Applying the Martin Defense to Interference over a weak NT

I recently became convinced to play the Martin Defense to interference over a weak NT.  I've always been a fan of negative doubles after a 1NT opener (of any range except 10-12 when I think penalty is probably more prudent).  But in the Martin defense, double shows exactly two cards in the suit bid by the interferer (regardless of the meaning of the bid).  It also shows sufficient cards to be reasonably sure they're going down, a good 9 to a good 12.  Anything more and we should probably try for game and anything less and it's better not to double them.  Given the generally balanced nature of the hand (opener has a balanced hand and if we have a reasonably balanced hand), then it's reasonable to assume that the entire hand is balanced -- not guaranteed of course.  Thus the number of total tricks is likely in the 15-16 range rather than anything more.

The first time we played it, it didn't come up and tonight it looked like it wouldn't again until the last round.  I opened board 1 with 1NT (12-14) as North (none vulnerable obviously) holding ♠A97 ♥76 ♦AKJT ♣JT53.  LHO bid 2♠ and partner doubled, showing precisely two spades.  RHO bid 3♠.  Well, this was an easy one.  They were contracting for 9 tricks on an eight card fit, while we have the balance of the high card points.  I doubled therefore, hoping for 100 our way (better than making 1NT) or even 300 if we were lucky.  Before the opening lead, we were told that 2♠ actually showed spades and a minor (Cappelletti/Hamilton), but it wouldn't have made any difference to our methods.  Partner led ♣4 and dummy came down with ♠J52 ♥KQ942 ♦53 ♣982, a reasonably good dummy from our point of view in that probably the hearts wouldn't be worth very much being most probably opposite shortness and with dummy being short of entries.  Partner came up with KT of trumps and we managed to get the contract down 3 (+500) for a top.  The best we could do unaided was 120 with our 23 hcp.  As predicted, the number of total tricks on the deal was on the low side: 15 (9 our way in diamonds and 6 their way in spades).

I guess you can count me a convert!

Rebidding after a double

Let's look at a few auctions that involve rebids after a takeout double:

1. (1S) x (p) 2D (p) 2H
2. (1S) x (p) 3D (p) 3H
3. (1S) x (p) 2D (p) 3H

Which of these show a good one-suited hand?  I think it's clear that #3 must show a good hand with very good hearts.  What about the other hands?  If you play that doubles can be two-suited, as opposed to three-suited, that's to say an extension of the principle of equal-level conversion, then #1 simply shows a hand that wants partner to choose between hearts and clubs.  Clearly, this is not a minimum hand because we might be forcing a Yarborough to declare at the three level.  But it's a different hand from that in auction #3. 

However, it seems to me that in auction #2, where partner has shown substantial values, 3H would simply confirm four hearts and a relatively minimum double.  Presumably, in order for partner to bid 3D, he's either got sufficient values to play 4D if he has no heart support, or 3NT, or 4H if he has four hearts.

But I admit this is an area I'm not sure about.  And I doubt if there's anything in the books about this.

Comments?