Are All Choices Restricted?
Over Christmas break, I managed to put aside my studies for a little while and sneak off to New York for the annual end of year Edgar Kaplan Regional. My original plans were to play in the Bridge Pro Tour individual, but due to a scheduling conflict with a job interview, I could not play in that event.
Luckily, the people at the partnership desk were extremely nice and I picked up a team for the Bracket 1 Knockouts that just happened to consist of most of the players defending from last year. We ended up losing in the semifinals with some unlucky results. In the main event, the two-day Open Board-A-Match, my team finished 5th overall in a very strong field. Some of the more fancied teams didn't even qualify to the second day. In all, it was a most enjoyable and successful tournament even though I didn't win an event.
Here was an interesting hand from the knockout event (the exact cards in the non-relevant suits may be wrong) :
I opened 1
on the South hand and partner responded 1
. RHO overcalled 2
and I bid 2. With a weak hand I prefer to emphasize my six card suit first. Partner put me into game and I played on the lead of a small club.
The contract is cold, losing just 1 club and 2 diamonds as I can ruff the third diamond on the board. However, there's no point giving up the chance for an overtrick for no reason, even at IMPs. There are two basic ways to consider throwing East in. One is to play a diamond to the 
A early, and hope that RHO doesn't unblock a doubleton K or Q. This line will be needed if RHO is 4-1-2-6 for his overcall. However, as this will also require RHO not unblocking, I decided to play for the legitimate line where RHO is 3-1-3-6.
I started by winning the first trick in hand with the A and playing a spade to the A and ruffing a spade. I then played two rounds of trumps ending in dummy and ruffed another spade in my hand. The K played by RHO was a welcome sight. Now I exited with my J and RHO was in. He played back the Q and I won in the dummy with the A and led another diamond towards my hand. I finessed the 8 and won an IMP on this board in a match we won by 30 IMPs.
The reason that I chose the finesse was quite complicated. I decided that had RHO exited with a small diamond, my percentage play was clearly to run it to my 9 as there were twice as many cases of KT and QT as there were of KQ. I assumed that RHO knew my correct percentage play in this situation, so his only choice from his actual holding was the play the Q. I assumed that with both the K and the Q he might have taken his chances and played low.
Later that night, I was talking with a friend and we discussed this hand. His conclusion was different from mine, as he said that he would have gone up with the J. His reasoning was that if RHO was looking at QTx, then his only legitimate play might have been to play the T, hoping to smother my J, and playing for his partner to have the 8. So when RHO doesn't play the T, my friend assumes that he doesn't have it.
The next day I ran into my RHO in the playing area and he had yet another line of reasoning on how to play the suit combination. First, he said that he did not consider returning the T, because he believed that if I didn't have the 8, I was likely to have just played off the A early and played for the missed unblock. Then, he said that the play of the 8 was called for because it was a variation of restricted choice. I understood what he was talking about immediately. In this example, the restricted choice is that if he had KQx, he might have chosen to exit with either the K or the Q, whereas with a specific holding of QTx he had to choose the Q if he wanted to lead an honor (if RHO held Hxx it didn't matter). He then pointed out that there was a recent article in the Bridge World that talked about less well-known situations where restricted choice is useful.
I have not read the article yet, but I can understand when some of these less well-known situations might come up. The useful thing about applying restricted choice is that you will be using base probability information in your decision rather than game theoretic information such as guessing what your opponent would have played if he held different combinations. While my original reasoning was based on the latter of these two, I can see how restricted choice came in early in the decision when I considered that KT and QT combinations were twice as likely as KQ combinations. So perhaps many or even all of the choices in play we make and percentages we calculate can be based on a variation of restricted choice. I know I will definitely be on the lookout for new situations to apply restricted choice in the future.
