Squeezing The Dummy

Friday, January 06, 2006

Fundamental Theorem

Often I would wonder what to do in tactical competitive situations that would arise. Do I want to risk pushing them into game/slam, do I want to psyche to throw out some confusion, do I want to walk to the dog? Taking things case-by-case just left me frustrated by every new situation that arose. I started thinking about basic principles, and then it came to me. The less room we give the opponents, the less likely they are to get to the right contract. That is the Fundamental Theorem of Competitive Bidding.

Ok, maybe that is not a groundbreaking realization. After all, that's why preempts exist. However in many situations even experts will out think themselves and make bids that violate the Fundamental Theorem. Here are a few example situations.

5 KQ9742 83 9632. White/Red, partner opens 3 and RHO bids 4 . What call do you make?

The opponents probably have a grand. How do we best stop them from bidding it? Well, we could try a 4N bid to cause some confusion. We may try a pass, hoping LHO will misjudge and pass not knowing that his opponents have a big fit. We could try a 6 bid hoping this pushes the opponents into bidding only 6 and not 7. We could just bid 7 and hope for the best. You would get support for each bid among experts, and probably even some more creative choices. However, I feel that your best chance of getting the opponents to go wrong is to bid 7 immediately. This is in accordance with the Fundamental Theorem; we are giving the opponents the least room possible and thus less of a chance to get to the best contract.

If we bid 4N, we give LHO a 5 cue. The opponents can then probe all they want before deciding what to do. If we pass, we give LHO keycard and cuebidding. If we bid 6 we allow LHO to pass and pull to 6 to suggest a grand. By bidding 7, we limit LHO's options to making a forcing pass, Xing, or bidding a grand. Some may suggest that this 7 bid will goad them into bidding a grand. The thing to remember is that that is not a bad thing. True, they will probably make, but what about when we hold 5 KQ9742 A3 9632 next time? If they are easily goaded into bidding grands, they may do it when we have this hand. Sometimes partner will produce a trick with a Qx, Kx, or even a side ace. With the opponent's options limited and you bidding 7 with hands that include a defensive tricks and ones that don't, they will simply be forced to get it wrong sometimes.

I took some heat for a bid I made in the nationals in Denver recently. I thought it was in accordance with the Fundamental Theorem, but I will let you decide. I held something like (I don't remember exactly) --- AKQ7432 AKT932 --- red/white at MP. It was 2 passes to RHO who opened 1. The trick on this hand is obviously to avoid your opponents bidding 7 whenever you decide to bid 7. I chose to bid 7 immediately. I thought this would put enormous pressure on LHO, who as a passed hand would probably not have 6+ spades. Bidding 7 on a 4-card suit would be impossible, so he would need to have a 5-card suit and just bid 7 without hearing support from his partner. However, if I start with 1 or 2N, LHO gets the opportunity to bid 3. Now his partner might get a chance to raise, and it will be easier to find the save.

A possible counter-argument is that I will never mix it up with a red/white 7 overcall. I will always have it made, or very close to having it made. However, I think this is true of all red/white 7 bids no matter when they are bid. They might be mild gambles, indeed on this hand I'm not necessarily cold for 7, and if the opponents always bid 7 they will be doing so some of the time that I am going to go down.

At the table my LHO did actually bid 7 on a 5-card suit. I felt ok with that since I feel that someone who bids 7 there will very likely do it if I overcall 2N and he bids 3 and hears a raise followed by me then bidding 7. I gave him the least possible chance to get it right, or so I think.

So whenever you feel stuck about what to do in situations like these, just remember the Fundamental Theorem. It will serve you well, and has a very sound basis.



  • I defended this same hand. Brian opened an ultralight 2 spades in front of the 7-6 monster. That hand doubled! I bounced to 4 spades and that hand balanced with the same 7H after about a 5 minute tank. We have a cheap sac; it brought up the negative slam double idea which we talk about every 2 or 3 years when the need for it comes up.

    - Phil

    By Anonymous Anonymous, at 1/6/06, 12:02 PM  

  • Do you also bid to the limit when you have 13 cards?

    By Blogger hatchett, at 1/6/06, 3:58 PM  

  • hehe meant to have 6 hearts in dummy, thanks I'll edit that.

    By Blogger Justin Lall, at 1/6/06, 4:45 PM  

  • As long as editing is occuring, the diamonds were AKJTxxx I believe. And I wasn't even there!

    By Anonymous Anonymous, at 1/6/06, 5:26 PM  

  • AKJTxx I mean.

    By Anonymous Anonymous, at 1/6/06, 5:26 PM  

  • justin, i'm blown away by your blog. i'm not sure if this is a compliment or an insult (probably both), but it's really good and at the same time made me think, "whoa, this is justin??"

    i like your fundamental theorem. i invoke it to prove that the correct solution to #1 on jdonn's bidding poll is to open 6H.

    By Blogger Joon, at 1/7/06, 1:33 AM  

  • Great idea, but I disagree that the fundamental theorem should be invoked at all times. It is like theoretically optimal strategy for roshambo (rock/paper/scissors). You can play random, which is unexploitable (similar to making the bid that consumes the most room). However, random also doesn't exploit -- if your opponent goes rock every time, the optimal exploitative strategy is to go paper every time.

    I also held this hand in Denver and _given my opponents_, who did not look like the toughest pair in the room, judged to bid 2S over a third-hand 1S. They jumped to 4S and then were done after partner doubled 4S (go partner!) and then we slowly bid up to the 7-level without interference, and played it, making. I felt that on this auction and hand, a direct 7H would have propelled them into 7S, but a slow one would let them "get their hand off their chest". I'll never know if a direct 7H would have induced 7S, but the slow approach worked against them.

    By Anonymous eugene hung, at 1/7/06, 1:51 PM  

  • I do not think the point about roshambo is analagous. You would not randomly bid 7H red/white. As I mentioned in my post regardless of when you bid your red/white 7H the opponents should know you think you will have a good chance of making it. That is inherent and exploitable. If you bid a direct 7H that does not mean you think you have more of a chance to make it than if you bid it slowly.

    That being said, under the Fundamental Theorem your best chance to get them to not bid 7S is to give them the least room possible to exchange information.

    BTW there is also a big difference in your auction and my auction, at your table they opened 1S. Relevant information (RHO has spades) has already been exchanged, so against weak opponents a psychological approach may well be more effective. At my table it was much more likely that they would find the save if I let them exchange information because they may find a spade fit that way. When my LHO bid 7S he had no assurance of a fit at all.

    Weaker vs stronger opponents is very interesting. I asked one top pro what he did on this board, and he told me the auction. Basically my hand walked the dog, and the pro saved. He knew exactly what was going on. Against him I have no doubt a faster approach would have been more likely to be successful.

    By Blogger Justin Lall, at 1/7/06, 2:51 PM  

  • I agree. I didn't say your bid was wrong, especially given the 1C start; I just said it is a bad idea to assume that it is right in every situation.

    By Anonymous eugene hung, at 1/7/06, 11:34 PM  

  • The problem with always bidding to the highest level that you are willing to go is that when you don't further the preempt, the opponents can guess at partner's length in your suit, which will often affect the minimum high card strength for their actions also. I suspect a mixed strategy is best. I agree that psyching blackwood or similar is ridiculous, that just gives them both bidding space and the info that you have a fit.

    By Anonymous Mike, at 1/8/06, 2:39 PM  

  • I do not agree that failing to further the preempt with a normal raise is a good strategy. You guys are basically saying the fact that the opponents can take inference from your actions is bad, but it is an inherent part of bridge. Do we raise on voids as part of a mixed strategy as well? They do not have solid inferences on the number of trumps you hold based on the amount that you raised, some hands with 3 trumps pass a 3H opener from pard and some bid 5H. Some might bid 7H!

    By Blogger Justin Lall, at 1/9/06, 10:00 AM  

Post a Comment

<< Home