This blog provides supplementary thoughts and ideas to the site. If you haven't seen the main site, there is a lot there including the Martel and Rodwell interviews, photos, and articles. This blog is focused on advancing bridge theory by discussing the application of new ideas. All original content is copyright 2009 Glen Ashton.

Wednesday, July 02, 2008

For a detailed look at the restricted choice principle, you can see the entry in Wikipedia, but even better check out Richard Pavlicek's entry on his popular site:

With 5432 opposite AJT76, you lead small to the T and it loses to the K or Q. Later back in the 5432 hand what do you do?

The key chart is his "four possible events" chart, breaking the restricted choice into (the player behind the AJT76):

KQ and plays K - 3.4%
KQ and plays Q - 3.4%
K singleton - 6.2%
Q singleton - 6.2%

(He did some rounding)

KQ is 6.8%, compared to K singleton or Q singleton, both at 6.2%. Since with KQ, the player can pick either, assuming they pick randomly, the 6.8% splits into two 3.4%s, and it is considerably better to play for the singleton honour than the player having KQ exactly.

Can these odds change? - certainly if the player has shown shortness in other suits, decreasing the chance of being singleton in this suit. In addition, you might know the player - some club players always play K from KQ (they love the look they give you when they "tricked" you into giving them the Q later), while others want to always play the proper card, and thus will always play the Q. Also, if you are playing against an expert, and you see him or her flip a coin before playing the K or the Q, you can assume they've taken this playing randomly idea too far.