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; but, on balance, declarers scored up an extra trick for every ten
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
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
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
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