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February 05, 2005


Yeah, that's a lot of bells-and-whistles. That's actually fairly similar to what I used to play except I tended to run a weak 1NT opening (10-13 pts, IIRC) instead of a strong 1NT opening (15-17), saving 1C for the power bid of 15-17. Made life a little tricky for those 1-level contracts but it usually worked out pretty well if you were light on your feet.

I highly recommend Watson's "Play of the Hand" for learning, um, the play of the hand (that's what happens after the bidding is complete). It is put together very logically, starts from very basic principles, and builds up to some advanced techniques.

--Rick Taylor

From a chess-player's point of view, interesting questions are a) what about the time element? b) how strong are the computers? b1) why aren't these bidding systems more or less solved on a statistical basis?

I played a little contract in college so this doesn't completely dumfound me. However someone who has never played is going to wonder about the amount of information shared between partners that opponents won't understand. We used to have to state our bidding system before play began, which usually meant:"Stayman with a strong no-trump" :)

Do you hand your opponents a sheet a paper?

b1) why aren't these bidding systems more or less solved on a statistical basis?

Limited information, more or less: you're trying to encode a lot more information than the channel (i.e. the bidding system) can reasonably transmit, and to do so with a system that's meaningful enough to be executed by human players.

[There's also the problem of declarer but IMO that's of far less importance.]

Thanks for posting this! I'm thinking of taking up bridge because I love card games but haven't played in a long time because the ones I knew were too simple and the ones I don't know (bridge) seem too complicated.

But I like a challenge. Learning bridge will certainly be one :)

a) what about the time element? b) how strong are the computers? b1) why aren't these bidding systems more or less solved on a statistical basis?

A typical round will be three hands and about 7 minutes per hand. A typical session is a total of 24 or 27 total hands.

The computers are very good at the play of the hand, fairly good at defense and non-awful at bidding. Unlike GO you could probably learn quite well against computer opponents for quite a while.

On bidding and why there are multiple systems. Bidding is arranged hierarchically. The suits are ranked in ascending order clubs, diamonds, hearts, spades, no-trump. Once a particular bid has been made no one can make that bid or lower. For instance, once I bid 1NT (contracting for 6+1 tricks with no trumps) no one can bid 1C, 1D, 1H, or 1S. Bidding tops out at 7NT so there are only 35 basic bids. There is also Pass, Double, and Redouble for a total vocabulary of only 38 possible bids to describe an enormous number of possible permutations of 52 cards divided into 2 13 card hands (and that is ignoring the fact that the opponents often bid on their 13 card hands.) You can analyze it without knowing bridge by numbering the bids 1-35 (ignoring pass, double and redouble). Once you bid X all bids less than or equal to X are unavailable. So it is like having a vocabulary of 35 where every word you use cuts out lots of other words for the rest of the conversation. The major frequent bonuses are at the 'game' level. That is 3NT, 4S, 4H, 5D or 5C. As you can see, you have to contract for an extra trick in a suit (playing in a suit is usually worth an extra trick so that is fine), but you also have to contract for a further trick beyond that for game in diamonds or clubs. For that reason, bidding systems tend to favor finding games in spades or hearts (the majors) rather than clubs or diamonds (the minors). But there is a balance to be had because the slam bonuses are big at the 6 level and you get the bonus for 6 hearts, diamond, spades or clubs. (I'm still simplifying but it is close enough). But you can't really use the whole vocabulary because each time you go up a number you are contracting for an extra trick--the full vocabulary is only available to strong hands.

With a good pair, constructive auctions (bidding where the opponents are not bidding) are pretty refined. I would say that with a system much simpler than the one I have you can get to the right contract in a purely constructive auction at least 80% of the time. There are probably 5 major systems worldwide that will easily get you that. And any possible system will miss the right contract at least 2-3% of the time.

But, but, but.... the opponents don't just sit there like lumps. If you look at my system above, you will see a 'weak 2' in hearts and spades. This is defined as a fairly crappy hand (not many face cards) with 6 hearts or spades. The idea behind the weak 2 is that your partner typically has about 2 of your suit and a smattering of points so you can squeak home with the contract or down one, while your opponents have something but can't find the right contract. This happens because if I bid 2S, my opponents cannot bid 1C,1D,1H,1S,1NT,2C,2D,or 2H. And remember, it isn't just vocabulary, if they bid above me they are contracting at the 3 level for 6+3 tricks.

So different systems make different tradeoffs between preempting their opponents and having accurate constructive auctions. In the 1940s it was very common for 2H and 2S to mean "an excellent hand that is willing to play in 4H or 4S without at most one trick from partner". This allowed for very accurate slam investigation auctions, but were very infrequent. The also offered no preemptive value because if you were that strong, the opponents most likely have nothing. The preemptive hands are much more frequent, and much more annoying to play against.

The same thing plays out at the 3 level where almost everyone plays an opening 3 bid as 7 cards in the suit bid and a weak hand. There, even with 3C (the lowest ranking suit) you have shut out almost all of the easy to access low-level bids. In the 1980s preempts became almost ridiculously weak and less defined so they could be used more frequently. But the problem with that is when you partner is the one with the strong hand you have made it very difficult for your side to find the proper contract.

So bidding has to take a lot of things into consideration, and different systems trade them off in different ways. Which is why there isn't just one system. :)

From a chess-player's point of view, interesting questions are a) what about the time element? b) how strong are the computers? b1) why aren't these bidding systems more or less solved on a statistical basis?

The time element is a constant problem in bridge. Unlike chess, there is no time rule. It is essentially impossible to use a device like a chess clock, for a wide variety of reasons, so various methods have been used to deal with players who are exceptionally slow. None of them seem to work very well, and there are some legendarily slow players.

Sebastian is right that the system he describes is way more complex than what a beginner would use, but it is not particularly complex in the context of serious tournament competition. In fact much of it is commonplace, and the vast majority of serious players would be able to play this with him as a partner (as long as he kept quiet about the Social Security Trust Fund) with only a small amount of further discussion.

That doesn't directly answer your question about the statistics. The difficulty is partly the reasons anarch gives: the limits of human memory and the limits of the "information channel" - the available legal bids. There is also the desire not to give away unnecessary information to the opponents who are, as Bob Mcmanus says, fully entitled to know the meanings of your agreements.

It is also useless to develop a highly complex system which can be easily disrupted by the opponents' bidding. A standard defensive technique when facing such a system is to enter the bidding much more aggressively than usual, intending to disrupt the opposing bidding. This sort of "sand in the gears" strategy is common in any case, but more so against artificial systems.

So, the long way around is to say that bidding systems develop more by evolution than by analysis. When I took it up very little of what Sebastian describes was played at all, and much that was played was regarded as controversial. Over the years the success of certain methods has come to make them, if not universal, widely popular.

"However someone who has never played is going to wonder about the amount of information shared between partners that opponents won't understand."

In a tournament you fill out a convention card which outlines most of the above. When you partner makes an 'unnatural' call you are supposed to alert the opponents. If they want they may ask you what your partner's bid means after the alert. Your bidding system is not supposed to be a code which is impenetrable to the opponents, it is supposed to be a communication system which is disclosed to both sides. There are various rules in place to cover situations where you forget the system and misinform the opponents. But there is no way I'm going to get into describing the kind of refereeing that is involved in that.

Wow. My bidding system is CLEARLY out of date. I guess that shouldn't surprise me, seeing as I get it from my cranky old grandad in the Yukon. You want old-fashioned, go to Whitehorse. They still hoard gold nuggets up there, why should it really surprise me that much that the strong two bid has been found to be imprecise by later players?!

One question about the weak two, Sebastian. What's the point-count range?

The point count range is 5-10 though many prefer 6-11. When non vulnerable suit is no worse than QTxxxx vulnerable should be KJxxxx or better. Third seat can be 5 cards and depending on vulnerability can be complete junk if I'm sure they have a game somewhere. With partner passed and non-vul vs. vul. I will bid 2S on as little as KJTxx x Qxxx xxx in third seat. Makes it rather tough to find the heart game especially if partner has three spades and the bidding goes P-(P)-2S-(Double)-(3S)-??? If partner is broke they probably have a slam, and if he has a smattering of points I will go down 2 or 3 doubled for -300 or -500 instead of the -620 or -650 I would be getting. Every now and then I'll make for +490 and sometime they will get to 4H when my partner has four and they will go down.

This agressive style is facilitated by the fact that in first seat we will open almost any 11 count with shape so most of the time I have a hand that weak in third seat I can 'know' they have game.

Still don't understand why one can't take a database of 10**6 hands and run through them with say 100 different pairs of bidding systems on a fast machine or a network. Probably there are a lot of shortcuts in gameplay one could take a la the chess databases which have all the 6-piece endgames calculated out perfectly - i.e., for a particular hand, any defense that doesn't convey information blah will lose against best play x% of the time. Ok, maybe you'd have to iterate to chose the best counter-strategy against any given strategy. Here I'm assuming that limited-info strategy can be handled by either brute force or by the more rule-of-thumb chess methods.

There are about 5.3 x10^28 possible bridge hands. One of the problems is that there are multiple ways to bid each hand. The perfect system to bid hand X when my opponent passes is not always the perfect system to bid the same hand X if my opponent bids 2S or even 3S.

Play of the hand is probably a solveable problem, but it has so many variables that the human mind can't keep them all in. I don't think bidding is solveable, but it is almost certainly amenable to Darwinian style selection processes.

Also reducing a bidding system to programmable parts is tough. The rules I have outlined have lots of little nuances--some of them which people are rarely if ever totally aware of. At this point I think a good computer program could beat most above-average pairs, but probably not any world-class pair.


There are simulation programs that are used sometimes in the discussion of specific bidding problems. These problems are stated as "you hold the following hand, and the bidding proceeds thus and so and now it's your turn. What is the best bid?" (there are other relevant considerations but let's ignore them for now). Players considering such problems (at their leisure - not in actual play) can generate, say 100 deals consistent with the bidding and use them to address the problem. Unfortunately, this requires that each generated deal be analyzed manually.

To extend this to the evaluation of bidding systems is a hugely complex task. Let's take the simple and totally unrealistic case where the opponents promise to pass throughout the auction. You feed in a few billion deals, have various systems bid them, and see who does best. Voila!

Not so fast. First of all, bidding systems are not totally mechanistic. Often the player has a choice of bids. That, in fact, is why bidding problems of the type I described exist at all. The player must choose one from several options allowed by the system. One such choice is to place the contract based on the limited information available about partner's hand. Another is make a further bid which might give partner the needed information, or elicit further description, etc. So the decision rules are, at best, not easily described to a computer. There needs to be a whole meta-system for choosing among permissible bids. Note also that the choice may be influenced by the identity of partner or the opponents, or your standing in the tournament. Bridge has the tactical equivalent of the Hail Mary pass, clock-killing, stealing a base on a weak-armed catcher, etc.

But even removing those last two factors doesn't solve the problem. Bidding systems can be changed in very small ways. In fact, most regular partnerships are constantly tinkering, looking for small improvements, better ways to handle certain problem situations. Now any halfway decent system, including ones much simpler than Sebastian's, is going to get to the right contract in an uninterrupted auction the vast majority of the time. So, comparing two different systems the margin of victory willbe small. So we might find that a small tweak to the loser will make it the winner. Another way of saying this is that if we undertaketo describe systems mechanistically we will find that the number of possibilities ishuge. To illustrate, Sebastian describes his system in terms of possibly 30 characteristics. (I haven't counted). For most of these there are at least two choices, and often more. There are other things that could be included without being inconsistent. Are you getting the picture?

And remember, we haven't let the opponents bid yet.

I am reluctant to claim that the problem absolutely cannot be solved as you describe, but it wouldn't surprise me if that were the case. It is worth noting that bridge-playing programs bid badly. Sebastian says "non-awful," and I suspect he is being kind.

To give you a notion of the contrast between play and bidding, the developer of one program told me his software was clearly the best declarer in the world, and I consider this is a believable claim. Computer bidding is very far away from this standard. I doubt the best programs are comparatively anywhere near as good as commonly available chess programs.

Modified Roman, where 1 Club or Diamond is artificial, opening 1 Spade or Heart bid promises 5 with 10 to 13 points, opening 2 Clubs or Diamonds makes the same promise, weak majors and opening three in any suit is seeking game, 4 Clubs artificial seeking slam asking for Aces, 5 Clubs asking for Kings, other bells & whistles as appropriate. Responses all depends on the noise the other side makes.

Thanks for the thorough replies.

"Now any halfway decent system, including ones much simpler than Sebastian's, is going to get to the right contract in an uninterrupted auction the vast majority of the time. So, comparing two different systems the margin of victory will be small."

So I take it that (using the info from the post that skill will out) there's more variation in playing the hand? And if so it sounds like, having arrived at a good bidding system, a pair can concentrate on play - which contradicts the fiddling-with-details-of-bidding point.

Actually, I need to reread the above and see if I understand why the bidding systems don't uniquely specify good bids (otherwise computers could bid well trivially). Have there been studies of whether there is any (nonintentional) information passed by demeanor or tone of voice between human partners?

You said you learned to play over the internet. Did you join a membership site? How much did you pay if you did? Any recommendations or warnings?

I've been debating doing something like that, though Brad DeLong mentioned a long time ago that he played online backgammon with Iranians, which also seemed rather interesting.

"Have there been studies of whether there is any (nonintentional) information passed by demeanor or tone of voice between human partners?"

Heh, oh yeah. But that is a complicated area. It is eliminated at the highest levels by placing screens diagonally down the table so you can't see your partner--bids are placed as tiles in a box.

You are also misinterpreting what this means:

Now any halfway decent system, including ones much simpler than Sebastian's, is going to get to the right contract in an uninterrupted auction the vast majority of the time. So, comparing two different systems the margin of victory will be small.

By 'uninterrupted' Bernard means that the opponents are not interfering by throwing in annoying bids. As bridge has developed, people have come up with more and more ways of getting in the way without risking damage. The preemption discussion above covers a lot of the common situations. Even simple systems are rather good if the opponents shut up. The problem is that they don't. I'll give an example but it is going to be long because I'm going to have to explain a lot.

A shorthand (super-simplified) way of looking at hands involves 'points'. Generally aces are 4, kings 3, queens 2 (though edward and I are worth at least 6 points), jacks 1. In reality this undervalues aces and overvalues jacks but lets try to keep things simple. Most non aggressive players will open with 12 or more points. In most simple systems a one level bid in a suit has a huge potential point range. Usually 12-22. This means you require a few bids to clarify the contours of the hand. The 1NT bid in contrast is tightly defined. It is 15-17 points with a flat shape Normally 4432, 4333, or 5332 (notation showing for instance 4 of one suit, 4 of another, 3 of yet another and 2 of the last). This is rather strong, if your partner has more than 1/3 of the remaining points you should be able to make game (the bonus points). This narrow definition makes it very for the partner of the NT opener to place contract properly. In most people's system the NT portion covers all the major possibilities quite easily. With a good understanding of stayman (one of the first conventions learned) and transfers (maybe the third) you can hit about 90% accuracy. With more tricks than that you can get to probably 99% accuracy. In the 1970s and 1980s some experts decided that letting their opponents have a perfect auction wasn't getting them anything. In the old days since the 1NT bidder was strong, people were afraid to get into the auction without a long and strong suit because you had to enter at the 2 level and with a strong opponent you were setting yourself up for a penalty double. Later people discovered that it was safe to enter the auction with two-suited hands if properly described because it would both muck up the NT sides' bidding and usually your partner could help out in one of those two suits. Two suiters are not only safer, they are more frequent than one suiters. And now auctions instead of going something like (1NT)-P-(2D)-P-(2H)- all pass often go (1NT)-2S showing spades and either clubs or diamonds- ????

Computers are fine in the first situation. They aren't so good in the second situation.

Basically the intervening bid actively destroys possible information exchange in a system that is already taxed considering the number of hands the limited vocabulary can describe.

One thing to realize is that most contracts finish off at below 3NT, so the common vocabulary is fewer than 15 possible bids rather than the full 35.

Liberal Japonicus, I learned to play at MSN's Game Zone. You can play against robots there (though they are awful) and get a feel for the mechanics. Then you can sit down with real people and play later. You might initially want to play 'rubber' bridge which is not scored in duplicate fashion against other tables. There are multiple rooms--start in the beginning rooms and see what happens. I would really reccomend Dorthy Hayden Truscott's book "Bid Better, Play Better" The first couple of chapters explain the framework of bidding systems and can help quite a bit.

Thanks for the response about weak twos. I have another question about the response to the 1nt. What is is a "pupppet" 3C response? b

Well, no. Playing the hand itself, barring some egregious screw-up, is largely determined by the cards that are out there and the contract (or bet) being played for. Sure, you can play better or worse, but the wrong contract (bad suit or wrong number) can make the best play worthless.

To make it concrete: you have a strong hand, maybe 16 points, with a five or six card suit in hearts, two face cards. Your partner has a good hard, maybe ten points, but only one or two hearts. If you're ultra tradionalist in your bidding--as, looking at sebastian's conventions, I seem to be--you run into the following scenario. You open 1 heart. Your partner responds with two of some other suit. You consider your cards and decide to rebid your hearts. Maybe there's cross-talk. You end up in a game-contract for 4 hearts. (Here's where I suspect that Sebastian's bells and whistles, non-point-count bidding might help more than the traditional convention.)

At this point your partner lays his or her hand down, and you're confronted with the dummy hand. The thing about the dummy hand is that the player needs to be able to move between the dummy and his or her own hand in order to maximize trick-taking. Whether that's possible or not is immediately evident to the player. Yes, of course, there's a certain amount of chance involved when one tries to guess what missing cards are held by whom in what position, but the real mystery in bridge is what cards will be revealed to all when the dummy lays down that hand.

So, back to the example. If I held five hearts and my partner held two, I would be in a nasty position, as I'd have a bare majority of trump over my opponents. (Finding oneself in a minority is even nastier, and of course it does happen.) What would really swing the day is whether I could leverage that trump via "cross-ruffing" (or leading a suit in which one partner was void in order to trump) or whether taking out all trump could set up a profitable side suit.

While the dummy's laying down is always to some degree the revelation of a mystery, the bidding process has evolved to make it less of one. The conventions are supposed to allow a finer prognostication of what the eventual game play will yield.

"????" - ?

JFTR - I read a few beginner's books back in the early 80's, and I read a dozen or two of the bridge columns in the paper per year. The situation you describe wouldn't have been in the former and doesn't seem to inform the latter, perhaps for pedagogic purposes.

So I take it that in addition to the bidding system you have a complex of rules of thumb and experience etc. that guide you in dealing with the interfered-with situations, hence the problems computers have.

Are there annotated examples of master-level bidding? In chess at least you can find someone holding forth at length about everything that happens in well-known games. One thing chess programmers did was spend a lot of time turning "I did this because the knight is worth more than the bishop in this sort of pawn structure" into numeric valuations, and perhaps something similar could in theory be done for bridge.

Puppet stayman is a response to one solution of a currently running debate--do you open 1NT with a 5 card major? Traditionally the answer is no/never/don't even think it, but especially with hearts or even with a 5332 with spades this can create a huge number of bidding problems. With 16 points, 5 hearts and a flat shape you are setting up an ugly problem if the bidding begins 1H-1S. You could bid 1NT which would normally describe an 11-14 point hand or you could dramatically overstate the hand with a 2NT response (showing 18-19 points).

The way about half of modern experts deal with that is by opening NT with a five card major. But now you have traded problems. Normally you want to play with an eight card major fit (8 cards between the two hands) in that suit. Regular stayman is great at finding the 4-4 fit but if you are opening 1NT with a 5 card major it won't find the 5-3 fits.

So if the partner of the 1NT opener (the partner is called responder) has 10+ points and a three card major he bids 3C. This is game forcing. The classic responses by the opener are 3D-no five card major but at least one 4 card major, 3H-5 hearts, 3S-5 spades, 3NT-no four or five card major. If opener has responded 3D (showing at least one 4 card major) if the responder has no four card major there is no 8 card major fit available and he bids 3nt. If he has one, he bids 3 of the major he does NOT have (allowing the strong hand to be concealed and the weak hand to be tabled as dummy). If he has both he bids 4c (but with my agreements this typically will not happen unless forcing to slam.

Some people play 2C as puppet stayman, but I find that reveals too much about the shape of the closed hand to the defenders. I use regular stayman for all invitational hands, and for normal game forcing hands where the responder has both four card majors or one 4 card major and less than 3 in the other major. 5-4 major hands are handled by smolen.

Puppet stayman was originally invented for use over 2NT because the 20-21 point flat hands aren't normally opened at the one level because of the fear that partner will pass when you can make game.

But I play 5 card major 1NT openers even without puppet stayman. The convention makes things more accurate, but for me, the gain in not misdecribing the opening value count is good enough all by itself. Besides, there is nothing like opening 1NT, having everyone pass and watching someone lead into your five card major.

Rilkefan, there are indeed annoted bidding guides. There is an excellent series of computer programs by Larry Cohen which go through various days at the Life Master Pairs. He goes through every hand played and comments on them.

So I take it that (using the info from the post that skill will out) there's more variation in playing the hand? And if so it sounds like, having arrived at a good bidding system, a pair can concentrate on play - which contradicts the fiddling-with-details-of-bidding point.

If the best contract is at a low (part-score)level, or is a no trump or major suit game contract (3NT, 4H, 4S), then most of the time fairly competent players will reach it, or one which is not much worse. This is not automatic by any means, but it is not the source of most bidding problems. These arise first when the opponents intervene in the auction. Essentially, this intervention reduces the amount of information you can exchange with your partner. Remember too that information exchange is not free. It is no good giving your partner very precise information about your hand from which he can only conclude that the bidding is way too high and you are about to sustain a large penalty.

The other source of difficulty is slam bidding, when you contract for twelve or, rarely, all thirteen tricks. Unless your side has virtually all the high cards, it is very difficult to diagnose this possibiity in the bidding. This is because matters like small differences in distribution, the presence or absence of a particular queen or jack, or sometime even a lower card, can make the difference. Unsurprisingly, much of the tinkering is aimed at these areas. I have not changed my basic system - not unlike Sebastian's (but we have disagreements - Bergen raises, ugh) in many years, but have used lots of variations. And these are often the areas where matches between top-level teams are decided.

That is not to say that play, and particularly defense, are routine. The play can become quite subtle and complex. On a technical basis it does not compare with chess, but it has the elements of probability, uncertainty, deception, and bluff/double-bluff that arise in any card game, as well as the need for defenders to cooperate without seeing each others' hands.

Actually, I need to reread the above and see if I understand why the bidding systems don't uniquely specify good bids (otherwise computers could bid well trivially).

Recall the bidding problems I described earlier. One place these problem are posed is in bridge magazines, where expert players are invited to submit their answers and reasoning. Typically, the problems are stated in the framework of a specified system, sincce otherwise the discussion would be chaotic. The best known such forum is in Bridge World magazine, and panelists submitting answers can fairly be described as some of the best players in North America. Yet there is considerable disagreement as to the best bid. (obviously, since otherwise this wouldn't be a very interesting article)

Often these problems involve very simple auctions. Sometimes they only ask what the best opening bid is. Making these choices is a probabilistic exercise. That is, the choice that works out best will depend on the other players' hands, and their reactions.

Consider the question Sebastian discusses - whether to open 1NT with a 5-card major. You would be surprised at the strong feelings on either side of this question. suppose you wanted to test this question by comparing two identical systems, one which allowed this and one which didn't. There are still lots of issues. Will you use puppet Stayman? Will you automatically open 1NT when allowed, or are there features that would induce you to open in the major instead?

Maybe it would be possible to include a simulation module in your program that would assess the probabilities and make the optimum choice. But it would have to make allowance for personalities. One choice might be best if partner is an aggressive bidder, another if partner is conservative.

Have there been studies of whether there is any (nonintentional) information passed by demeanor or tone of voice between human partners?

No formal studies are needed. The answer is yes. Intonation problems have largely disappeared since silent bidding came into use some years ago. Instead of bidding orally, a player puts a card with a bid printed on it on the table. Demeanor, including long delays, remains a problem.

I played a lot at a local club during my last two years at UCLA, and not so much since then, except for computer programs and a brief period of online play a while back. I mostly stick to the basics (Standard American with weak two bids, 15-17 1NT, and Jacoby transfers over NT) when I do play, and have managed to produce decent results on the rare occasions that I wander into a bridge club these days.

There are some rather good books about the early days of contract bridge, when it was still in its embryonic stages and the legendary Ely Culbertson was trying to make his system the king of the bridge world in the face of opposition from just about every other bridge expert in the world. Interesting reading, if you can track down one of them ("The Golden Age Of Bridge" would be my first choice, but a Google search came up empty--it is probably long out of print).

LOL--joke's on me. I should have searched for "The Golden Age of Contract Bridge", of course. There are quite a few links for that, including here. The first reference to it on the Google search results goes to Snopes, and an entry regarding the famous Bennett Murder Case, which is worth reading to remind one that it *is* possible to take the game too seriously, even if one's partner is an atrocious bidder. :-)

Go fish!

(oops, sorry, wrong thread.)

My grandmother tried to teach us once but it devolved pretty quickly into a fight over who had to be the dummy. I like Napoleon, which IIRC is sort of bastard version of bridge for people who don't have the patience for the real thing.

Ahh yes, the Bennet Bridge Murder. My favorite quip about that was the person who noticed that after killing her husband for opening light and playing 4 Spades poorly Ms. Bennet was aquitted of murder yet had trouble finding a bridge partner in the future. I also note that while we don't actually know the hand, the hand which was circulating around as the light opening hand actually isn't ridiculously light by modern standards. Probably 30-35% of modern experts would be willing to open that hand 1S in first seat.

BTW, the hesitation problem is not as serious at the top levels with screens in a competitive auction because when the tray comes back from the other side of the screen, you can't be sure if the delay was your partner or your opponent.

But I had totally forgotten to mention bidding boxes. At tournaments you don't say bids, you pick a card out of box and put it in front of you.

Bridge was enormously popular in the thirties and forties, and even in the fifties it was more popular than it is today. This was partly due to Culbertson's genius as a promoter, and in the thirties at least to the fact that (non-gambling) card games are a very inexpensive form of recreation.

Culbertson's matches were widely covered in the press - think of Fischer-Spassky - and he made a fortune from the sale of books and other bridge items. At some point Charles Goren supplanted Culbertson as the nation's bridge teacher, and he brought a less colorful approach, perhaps more in keeping with the spirit of the fifties. For example, he discouraged his readers from playing for money. He was no less successful financially than Culbertson, however.

Yeah, Goren's the most recent bridge book I've read. Even sadder in light of the fact that I'm 27.

Thanks for the book references above, Sebastian, and of course for patiently explaining some conventions. (Some of the fancier proper-name conventions I'm just going to look up.)

Let me just add that the sorts of things that Sebastian plays are essentially confined to tournament bridge, where the competitors all play the same hands. To win at tournament is to bid or play a deal to a better result than everyone else. Ordinarily in tournament, you play as a partnership.

Some of us still play rubber bridge, where we cut for partners and deal the cards, and where this degree of artificiality would be gross overkill. I have trouble in the US because I learned ACOL, in which most bids are weaker than they would be in standard American, and I have to adjust to partners who don't understand it. Fortunately the US games I've found play for lower stakes.

Yes for rubber bridge in the US you will probably play a stripped down version of what you would play in tournaments--probably something akin to the now quite popular 5 card major system which goes by the name "Standard American Yellow Card" or SAYC.

"Consider the question Sebastian discusses - whether to open 1NT with a 5-card major. You would be surprised at the strong feelings on either side of this question. suppose you wanted to test this question by comparing two identical systems, one which allowed this and one which didn't. There are still lots of issues. Will you use puppet Stayman? Will you [...]"

This sounds like the situation in chess - no one knows what the best opening moves are, so one picks a system according to one's taste and sticks with it until too good a move is found for the other side. But that doesn't get me closer to the issue of why computers can't bid well - in chess the programmer selects a set of reasonable openings for the computer and that's that (to first order [and admittedly one wouldn't say computers play the opening well, and in fact I should admit that they probably don't handle the late opening transition to middle game well]). I see SH described part of his system as "1NT-- 15-17 (with judgment)" - so that's obviously not programmable as it stands - and I'm way too ignorant to know how much leeway say Smolen gives.

Anyway, this discussion makes me sad my fiancee doesn't like games involving having to read books.

But that doesn't get me closer to the issue of why computers can't bid well - in chess the programmer selects a set of reasonable openings for the computer and that's that...

Have you ever played Kriegspiel? That'd be the best chess analogy I can give.

I've played bughouse (a four-person variant) - and indeed I would guess it'd be hard to program.

Ah, ok. Imagine you're playing paired Kriegspiel then. [I don't remember the rules of bughouse but this oughtta do the trick.] The point here isn't just that you're playing against your opponent, you're somehow coordinating with your partner on the other board. If the two of you play in concert, the other side is toast; if you two don't combine forces, you're dead.

You have plenty of openings to pick; the problem is, so do your opponents. Even if you have preexisting agreements with your partner, the complexities preclude precise transfer of information until it's potentially too late. So, for example, you might open with the Ruy Lopez -- because you're of a classical persuasion ;) -- only to find out after fifteen moves that you should have opened with a Queen's Gambit in order to give your partner the support he needs. If that discovery doesn't occur until too late in the game, oops, game over.

Now, in bridge bidding, the mere act of communicating both decreases the size of the remaining channel and raises the stakes. [Continuing in my (bad) chess analogue, this equates to the fact that the longer it takes for you discover the state of your partner's board a) the less chance you have of "correcting" your opening to match with his, and b) the greater the danger your partner could be in.] As a result, you're trying to compress a huge quantity of information into a channel that, by design, simply isn't capable of holding it all without raising the stakes unacceptably high. This in turn makes bidding extremely difficult: how do you decide which things are worth encoding versus which things aren't and how do you distinguish between the various signals, all the while trying to ensure that by the time you've figured out everything you need to know you haven't raised the stakes higher than you can attain?

Does that help?

Yo, rilkefan: what's your rating? Mine is abysmal, since I just used to play when I was hanging out with friends of mine who were very good. Being an outsider at a chess tournament was fun for the anthropologist in me. It also came in handy when I got to the philosophy job market, which immediately made me think: oh, it's just like a very big, very serious chess tournament, with one crucial difference: no one ever actually wins a game decisively, so the discipline to one's ego provided by reality, and specifically by the possibility that you might actually lose, is completely absent.

Here's another analogy. Consider the following variant on Kriegspiel: you play as per normal against your opponent for some number of moves, say 20. At the critical turn you and your opponent hand the game over to your partners, who haven't seen any moves whatsoever. They're simply presented the board as it stands with no knowledge of how this position was arrived at.

Now, you are allowed to transmit to your partner one "chess-bit" of information: a combination of a piece and a position, e.g. Qe6. That's it. Nothing more. Maybe you're telling him a move he needs to make; maybe you're trying to warn him about a checkmate threat; maybe it's code for him to try a back-rank mate. Who knows? If you're clever you might be able to use this piece of information, coupled with the position of the board, to give your partner just enough information to win the game. But how on earth are you supposed to compress, into one simple little chess-bit, your entire probabilistic understanding of the opponent's position?

[For added fun -- though this doesn't quite translate into chess -- allow the transmission of an unlimited number of chess-bits but with the caveat that after transmitting each chess-bit to your partner, he must remove one of the pieces you mentioned. E.g. if you tell him Pd3, Qe6, he has to pull a pawn, then your queen, off the board. A clever enough system should be able to harness this extra power but damned if I know how.]

This is as far as I think I can take this analogy into the realms of chess but I hope it clarifies the pitfalls of the bidding process.

I haven't played a tournament game since before the Wall fell - guess I was in Paris at the time, and probably rated about 2000 and rising quickly but probably soon to hit a low ceiling.

My question is, not why is bidding hard, but why are computers bad at it. It sounds to me like the theory is evolving rather quickly, which would make modelling good play hard. But if people can bid well, and can describe what they are doing when they bid, and the process takes a few seconds, then I would guess that computers would be able to bid well. But of course I'm arguing from ignorance here.

p.s. I "learned" to count in a system whereby one has to devalue (low?) honors in one-or-two-card suits but short suits count a point or two for trump bids. The column in the paper seems to tend to refer to "high-card points" or "points" interchangeably - is that the modern view?


Let me try one more idea. Bidding ultimately is probabilistic. Let's look at a very basic problem. Your partnership wants to reach, say, 3NT, when there is a 40% or 50% chance of success, depending on conditions. (I'm assuming some familiarity with scoring and terminology. If I'm wrong I'll clarify what this means).

Say it's a 40% situation. Your partner opens the bidding 1NT. There are a great many hands he can have for this, or we might say a large number of hands are mapped onto this one bid. Now suppose you have a hand which will make 3NT a good proposition if partner is at the strong end, but a bad one if his hand is weak in the context of the bid. In a simple system you have two choices. You can pass, not taking the risk, or bid 2NT, inviting partner to proceed with a good hand.

How to choose? The human player will use "judgment." She will consider a number of fine points about the hand and decide to invite or not. These fine points are difficult to quantify and specify precisely. They would include things like the presence and location of spot cards (tens and nines vs deuces and treys), for example, whether the hand has a five-card suit, whether honors are in the long suits (good) or not (bad), etc.

So how might a computer deal with all this? My guess is that it would attempt to simulate possible hands for partner. Put a billion hands opposite this one and see how often 3NT makes. But that doesn't solve the problem. Not only must 3NT be a good proposition, partner must bid it. In other words, you should bid 2NT when 3NT is a 40% proposition conditional on partner bidding it. How will computer-partner decide? Simulation of course. It will generate a billion 2NT bids and put them opposite its own hand, and decide based on the results. So your simulation must simulate partner's simulation. And this is a simple problem, which most players would solve in a flash, and correctly the vast bulk of the time.

The short version, it seems to me, is that any sequence of bidding covers a variety of hands, and that the needed assessment of probabilities is quite difficult, all the more so since it often involves assessing partner's assessment.

One thing I think a hot player/programmer could do (again, arguing from ignorance) is assemble a list of features of hands, develop a valuation system as a function of those features and the bidding and game situation (tossing in whatever heuristics are available), then look at a few 100k master bids and adjust the values accordingly to get the first-order results right. Formally, make a neural net. This has been a successful way of (or at least part of a way of) approaching chess. Probabilistic analysis and branch point analysis (if partner has x [n% likely] then blah [which has a score of A], and if y [m%] then foo [B], and then take the best expectation value) don't seem that hard to program (see the starting caveat).

Maybe. But if you're looking for agreement from experts on 100,000 bids you're not going to get it. And of course the general approach to bidding has always been to develop a valuation system as a function of hand features, refine it as you gain experience, talk to better players, etc.

One thought that occurs to me is this: bids come in different types. Some are purely descriptive - they tell partner about your hand. Some simply place the final contract, based on information available. Some are coded questions or coded answers to coded questions. Some are descriptive with the added feature that partner is not allowed to pass.

A bidding system does not necessarily prescribe which type of bid is appropriate for a given situation. It is (almost) always allowed, if not wise, to place the contract, for example. The choice of type, as opposed to the selection from bids of the same type, is a big part of bidding, and this is very difficult to mechanize. It does not really depend solely on the hand and the bidding thus far. It also depends on the system itself, among other things. The wisdom of making a bid that describes some feature of my hand depends on the use partner can make of this information, which may well depend on what further bidding tools are available.

In other words, the continually refined hand-evaluation method may not be a solution, no matter how powerful the computer.

Culbertson's matches were widely covered in the press - think of Fischer-Spassky - and he made a fortune from the sale of books and other bridge items.

The match between Culbertson and Sidney Lenz in 1931 was particularly important (and well-covered) by the media, as the two sides (Culbertson played with his wife Jo, and Lenz played with the legendary Oswald Jacoby, who was a master level player of contract bridge, poker, and several other games,and--at age 21--was the youngest person ever to be certified as an actuary) were staking the reputation of their opposing bidding systems in the 150 rubber match. Jacoby was prone to "psychic" (bluff) bids, and Lenz remonstrated with him about it, to the point where Jacoby walked out in the middle of the match, leaving Lenz to finish his losing effort with other partners. The Culbertsons won easily, and Ely Culbertson ruled the bridge world as far as cited experts went until Charles Goren came along.

Ely Culbertson was a brilliant promoter of the game, but I'm glad Goren came along--I'd rather count points than "honor tricks" any day of the week.

Consider the question Sebastian discusses - whether to open 1NT with a 5-card major.

Never, bidding conveys information on the shape (distribution) of one's hand and sets the table for future bids and responses.

Consider the question Sebastian discusses - whether to open 1NT with a 5-card major.

Never, bidding conveys information on the shape (distribution) of one's hand and sets the table for future bids and responses.

Well, I said there were strong feelings. My view is "no problem, usually." With a balanced hand in the appropriate range you describe it in one bid. There is some risk of missing a 5-3 major suit game, so I usually avoid it with a maximum, but that is compensated for in many ways.

The 5 card major NT question can't just be dismissed on shape grounds.

If you are 3-5-3-2 or 2-5-3-3 with 17 points and you open 1H you are screwed if the bidding begins 1H-1S--especially if you have a weak heart suit. Your main options is 1nt--dramatically understating the hand. Your partner is likely to not even consider moving with 8 points. Your next option is 2 of a 3 card minor--that won't be pretty if your partner has a weak hand with 1 heart and 2 or 3 or even 4 of the minor you bid--they will pass and you won't be happy. A jump to 2NT will propel you into bad slams and a jump shift into your 3 card minor is repulsive and likely to get you to many bad contracts. You can repeat the 5 card major and get bad games when your partner raises you with 2 or marginal part scores when they pass. But if you open 1nt you can miss good 5-3 fits in some cases-especially if you don't have good tools. It is a tradeoff, and it isn't super-clear how it ought to work.


That reflects my thinking pretty well. I will say that with a maximum I am willing to risk the rebid problems because the 5-3 game possibility is livelier. Over 1H-1S I just try 2N, usually, and hope partner doesn't get too carried away. I'm only a point light, after all. With 15-16 the major suit game is further off, so there's less risk there. Partner will usually come up with a bid if we have game. We may end up in 3N rather than the 5-3 major, but that is often OK or better (especially at IMP's - a commonly misunderstood point).

I'm surprised that this conversation brushed only lightly against one of the most interesting (to me) aspects of bridge: the fact that it is a game of incomplete information (as distinct from chess or Go). There has been a lot of discussion of the impact of this on bidding, but mostly from a technical point of view. I want to bring up the psychological aspect.

Now in any competitive game there's a certain amount of "playing the opponent" (versus just the game), but in a game like chess where the pieces are all in view often the better strategy is to focus just on the pieces and not on what the opponent has in mind. This is not an absolute, of course, since understanding one's opponent's strategy may help guide one's own thinking. Then there's the example of Bobby Fischer's antics as highlighting the psychological warfare aspect of playing a game. But in a way the pieces speak for themselves.

In contrast, much of the skill in bridge (both in the bidding and the play) lies in envisioning the location of the unseen cards, including evaluating the position in terms of probabilities. Often one selects a bid or a line of play based on a choice between alternatives that have different chances of success. Some calculation is involved here (and that is where computers shine), but the laws entitle you to draw inferences from the demeanor of your opponents (though never of your partner). This introduces many subtleties into the game, including the possibility of bluff.

There is a plenty of skill involved just in playing well technically and avoiding mistakes, but I think part of the attraction of bridge is that it has a greater level of reading one's opponents' intentions than other games.

I haven't played in a long time, though I am still an avid reader of Bridge World. Thanks for the trip down memory lane.

Dang, this was an interesting thread, at least to me. We should do this again some time.

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