Friday, June 26, 2015

Was Blackwood a One Trick Pony?

Easley Blackwood was a contemporary of Eli Culbertson, but not so well known or so rich. As an aside, in  the 1930’s contract bridge was such a social rage that Culbertson was able  to develop a commercial empire around it, and in the late 30’s was making $1,000,000 a year off of his bridge related enterprises. The name Blackwood conjures up the Ace Asking convention which bears his name. He developed that in the year in which I was born, but no need to go into that! Today his simple little convention has spawned all sorts of Ace and Key Card asking systems.
The most significant tribute I have heard about the Blackwood Convention was from expert and author Larry Cohen. In his top 10 bridge conventions of all time, he listed the Blackwood Convention as the one he would want if he could have only one. Blackwood was the executive director of the ACBL for a few years and also the author of several books on bridge, including my favorite, The Complete Book of Opening Leads (1983). Students of the game are still reading that today.

Wait, that’s not all! I was reading an e-mail recently that referenced a Bulletin from the Bedfordshire Bridge Association discussing “Blackwood’s Theory of Distribution.” Blackwood posited KJT32 opposite A874, the holding that made “8 ever, 9 never” famous in Bridge jargon, meaning that with 9 cards play for the drop of the Queen and with 8 cards finesse.
If you look at standard card distribution tables you will see that with 9 cards the 3-1  break is 50% and the 2-2 break is 40%, so that makes the 2-2 break appear to be an underdog. South starts out by playing the Ace and both East and West both play small cards. A small card is then led toward the King Jack and West produces another small card. What has happened is to change the odds is that two small cards have been played by West and one by East. Now the 4-0 and 0-4 probabilities have been eliminated and West has one less card in his hand than East. Thus East is marginally more likely to hold the Queen than West. The combination of these two factors makes East a 52% favorite to hold the Queen, so the drop is indicated. 

Confusing you say? Sure that’s why the someone invented the saying, probably back in the days when the English Lords were losing fortunes playing Whist. Even if you mix up the saying, it’s only a 2% difference so no big deal unless the finesse loses. 

A couple of things you may want to notice. First the saying is so well known that in any field 99% of the declarer’s are going to play for the drop. So for a 2% risk, you can make up for a bunch of match points that you let slip through your hands by earlier errant play. Of course that cuts both ways, if you are having  a good game, stick with the field to participate in an average board. The other thing to notice is you should take a page from the no “hold em” poker players. It is ethical to take into consideration any “tells” that may be inadvertently displayed by either opponent. If you see one gazing around the room, that guy probably has the Queen. Note however, that you act at your own risk. I know some players from whom I would draw just opposite conclusion. 

Now back to Easley. He realized that imperfect shuffles produced hands that do not lead to perfect mathematical solutions. Taking a page from Culbertson’s Law of Symmetry, he proposed what he called Blackwood’s Theory of Distribution and applied it to the 9 card holding. Blackwood’s Theory (at  least he had the grace not to call it a law) proposed that the location of the missing queen could be determined by declarer looking  at the length of his shortest suit (combining the hand and dummy).If the shortest holding is five or more cards or 4 cards breaking 2-2, then play for the drop. If the shortest holding is 4 cards not spitting 2-2 or fewer than four cards, take the finesse. While no mathematical proof was offered, the theory was tested over a large number of hands and produced excellent results. 

Will it fare as well against computer dealt cards? Probably not since the underpinnings were based on imperfect deals, but there are still several events that start with dealt cards. With computer deals I always imagine what combination of cards will serve to ruin my day and let that be my guide.