Monday, July 25, 2011

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 K85QJ3 ♣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 AKQJ5AJ3 ♣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).


  1. The controls thing means you are using a 6-4-2-1 scale for the high cards.

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