The Extra-Trick Factor

Peter Cheung has analyzed nearly 400,000 hands from actual play on the OKbridge website.  His data show, among other things, that declarers of all skill levels won an average of 0.1 trick more than the double-dummy expectations.  Naturally, at the table both sides blew tricks in the play; yet on balance, declarers scored up an extra trick for every ten contracts.

That declarers would come out ahead over defenders is not surprising; I would have guessed the number to be even higher.  Whatever it may be, that factor greatly influences the results of "What if?" simulations.  That occasional trick, for example, might mean an extra 500 points for scoring up a vulnerable game, or even more for a slam.

Although few players would be so inclined, it would benefit them to calculate their their own extra-trick factor (henceforth designated as ETF).  If a player routinely raked in, say, 0.2 extra tricks per hand, then he would score better in the long term by lowering his requirements for various forcing and invitational bids — especially at total-point scoring such as in the Swiss Teams.

Admittedly, a truly accurate assessment of one's ETF would be possible only if one desired to know, could remember all four hands, and had access to double-dummy-solver software.  Less-dedicated types could choose to limit their studies to tournaments which provide handrecords that include double-dummy analyses.

I, for one, am curious enough to make the effort.  I am logging every personal declaration into a spreadsheet, which enables later analyses.  Thus far in 2007, I have declared some 700 contracts — at local clubs or sectionals, and my ETF is 0.41.  (Perhaps that rating will go down after incurring some higher-level competition.)  Your own ETF might be either higher or lower than mine; it doesn't matter.  The point is simply that being aware of your own declarer expectation level is a valid consideration toward formulating a bidding system, or at least toward making close decisions at the table.  Many of you already make some such adjustments, albeit probably without thinking about them in purely numeric terms.

In the next article you will see just how important the ETF really can be when applied to a decision as to whether to invite a game.

You may visit Peter Cheung's website at: http://crystalwebsite.tripod.com