More on knowing what the score is.

April 17, 2010 at 5:47 pm 28 comments

It’s right near the end of a football match. Richmond has the ball with this decision to make: if they are up 3 points they should try to play defensively and guard their lead. If they are down 3 points they should attack and try for a goal. The guy with the ball has to guess. The footballers, you see, aren’t allowed to know what the score is. Apparently this makes the game more legitimate, being in ignorance of the score.

So, do you all think that’s how football should be played? And what is so special about bridge that we shouldn’t be allowed to do the right thing when we should have the information in front of us to do so?

On the matter of not being allowed to know what the score is when you are making your decisions, I noticed this hand recently in a 2007 Bridge World:



In 6NT, Reese was playing a weakish team that he figured would also be in the slam. He had the choice between 3-3 hearts and DAx with the long clubs (diamond to the king and then duck one), so that in the fullness of time RHO would be squeezed in the reds. What should he do? How bizarre that the first thing he has to do is guess how the match is going. Let’s say that it was the last board. If he were 6 IMPs up, it would be clear that he should take the same line he thinks is being taken in the other room. If he were 6 IMPs down, then presumably he should take the other line, that being the all-things-are-equal odds best line. Yet we play a sport where we aren’t allowed to know what the score is and make the correct decision based on that.

A few days ago Phil left the comment: ‘Nearly all the time when you know the score the answer to the problem is going to be the same as when you didn’t know the score – knowing the score distorts your perception of the problem – why add a further level of complexity to an already complex game?’

Why add more complexity? That’s no argument, Phil. Dumb the game down??? But in any case, I can’t see that it does anything but simplify things, here turning an agonising guess into a straightforward clear-cut decision. It does the opposite of distorting perception, rather it clarifies it.

It is true that it won’t necessarily affect matters, but let the game decide that, just as in football the timing of the situation may well change the strategy or tactic appropriate at the time.


Entry filed under: thoughts on bridge.

Search and Planning Under Incomplete Information: A Study Using Bridge Card Play by Ian Frank Tomorrow…

28 Comments Add your own

  • 1. Richard  |  April 21, 2010 at 8:54 am

    The way I see it, your task is to do better than the pair at the other table. If you know the score, and they know the score, this may -may- affect your opinion of what the pair at the other table will do. But until you get down to the last few boards, I can’t see any real change in how you play. It’s pretty much common knowledge that the attempt to chase swings will rapidly put the match beyond hope about 99 times out of 100. The only situation where it could be justified is where there are few boards left and you know that without some big swings you are bound to lose. At that point, you have nothing to lose. But if you are behind after the first quarter, even quite a long way behind, the usual winning plan is to keep playing percentage bridge and wait for Lady Luck to even out. And the reason that strategy is favored is because it has been seen to work, many times.

    • 2. cathychua  |  April 21, 2010 at 9:21 am

      Certainly as in all sports, knowing the score will only sometimes be relevant!

  • 3. Jonathan Mestel  |  April 21, 2010 at 1:14 am

    Last time I was in a comparable position, we had to replay 3 boards of a K.O. match because they’d played them the wrong way at the other table. There were two fairly obviously flat boards and one which we played first and they played 3rd, which was critical. Certainly it would have been nice to know the score before the critical board, and also to know that the flat boards really were flat. Oppo had the advantage of knowing more about the score on the critical board.

    Were everything wired up, with two identical sets of boards, knowing the score could be arranged. If necessary, one could wait for the result at the other table on an earlier board before playing a card or selecting a call. But personally, I think it would add to the complexity and session length for little gain.

    The real problem with IMPs is the 26 IMPs riding on 50% slams, not not knowing the score.

    Perhaps we could also be told whether or not the contract was the same at the other table!?

    Do you have point-a-board- events in Oz?


    • 4. Bill Jacobs  |  April 21, 2010 at 12:20 pm

      There was a hilarious Bridge World article on this many years ago. 3 boards are fouled in a knockout match – the director determines they must be replayed. Team A is 5 imps ahead of Team B, going into those final 3 boards.

      The boards are played in the same order at both tables.

      The first two boards are totally flat.

      The third board is obvious to bid to a slam. You have to find a queen in a 7-card fit, in which the shape is 100% known that one player has 4 cards, the other has 2 cards.

      Both declarers can assume that the other declarer will be in the exact same position, and know all the above facts.

      The question posed is:
      1) how should the team leading play this suit?
      2) how should the team trailing play this suit?

      This looks directly equivalent to Cathy’s topic, and it is indeed a most fascinating question.

      • 5. Ben Thompson  |  April 21, 2010 at 3:53 pm

        If you are absolutely positively 100% lay down sure that team A is ahead by 5 and both teams are in the same contract, then the play is just guess and double-guess.

        The trailing team wants to play the suit the opposite way to the leading team, while the leading team wants to play it the same way (as the trailing team). If the play is different, whichever way it’s different, the swing is enough to swing the match.

        I ignore the odds and finesse the opponent I like less. Or maybe I don’t, just to double-cross the other declarer.

        • 6. cathychua  |  April 21, 2010 at 5:11 pm

          That’s not necessarily so, though is it? In the case of the example Reese gave, you could quite comfortably come to the conclusion that the other declarer will not think of the ‘right’ line.

          I’ve no issue with the idea that bridge is a game of imperfect information. But some of that need not be so and isn’t intrinsic to the game. It isn’t intrinsic to teams that you don’t know what the scores are.

      • 7. Chris Mulley  |  April 21, 2010 at 6:45 pm

        As Ben Thompson says, this is just another boring zero-sum game. Certainly nothing over which game-theorists might get excited. I think Cathy’s problem is better, because the uncertainty in the contract at the other table adds a layer of complexity in working out the optimal strategy … quite possibly an order of magnitude.

      • 8. Jonathan Mestel  |  April 21, 2010 at 11:16 pm

        It could be worse! We could have a choice of 3 lines, e.g.
        cashing out for down 1, playing an antipercentage line which may make but which ensures not going more than 2 down, or the best chance for the contract which loses control disastrously if it fails.
        IIt would be possible to invent a scenario where if team A chooses line 1, team B should choose line 2, if A chooses 2, B should choose 3 and if A chooses 3 B should choose 1. Then the best strategy for each team would be probabilistic, i.e. you should choose each line with a certain probability. If you are predictable, then your opponents can choose a strategy which beats you.

        How do you play QJ9 opposite A5432 for 5 tricks?
        Obviously you run the Q, but what do you on round 2 if it holds of if it’s covered?

        The crucial question is what a defender will do holding Kx.
        It can be argued that he should cover 1/3 of the time.

        How do you ensure that you cover 1/3 of the time? I recommend humming a waltz to yourself. If declarer leads the Q on the 1st beat of the bar you cover, otherwise duck.

        You heard it here first. But be warned: “Waltzing Matilda “is not in 3/4 time. However “And the band played Waltzing Matilda” is.

        I hope this insight is of use to someone… but I doubt it, somehow.. …J

      • 9. Bill Jacobs  |  April 22, 2010 at 2:31 pm

        Well the mathematical / game-theory answer is, for the team leading:

        Create a random experiment which produces result A two-thirds of the time and result B one-third of the time. For example, glance at your watch and get result A if the seconds hand is between 12 and 8, and result B if the seconds hand is between 8 and 12.

        For result A: finesse through the hand with 4 cards (making 2/3 of the time). For result B: finesse through the hand with 2 cards (making 1/3 of the time).

        You will win the match seven-ninths of the time, no matter what your counterpart does.

        All other strategies can lead to inferior results, or superior depending on your counterpart.

        For example, if you always finesse through the long hand, you will win only 2/3 of the time if your counterpart always finesses through the short hand. It’s even worse if you go the other way, and your counterpart decides to make the percentage play!

        OK, I am a sad loser by being fascinated by this situation – I knew that already. But it does seem to me that there are parallels with Cathy’s decision on what to do over 3S – where if she can guess the same or better than her counterpart, she will win the match.

  • 10. Bill Jacobs  |  April 20, 2010 at 2:17 pm

    I don’t really get it Cathy. You might be right in theory, or wrong in theory, or there may be no theory, but …

    Logistically, it can’t be done can it?

    Say I’m playing a round of 16 match in the NOT in Canberra. How is it organized that I know the score at all points?

    In 20 years time, we may all be playing on secured time-controlled computer networks to enable your concept, but wouldn’t that remove the desired human contact (both tactical and social) from the game? The game would be much poorer for it.

    • 11. cathychua  |  April 20, 2010 at 4:24 pm

      I think I have not made my point clear. One of the reasons Australians commonly gave for not playing Cayne was that it ‘wasn’t bridge’ knowing what the score is. In my opinion that is as ludicrous as the idea of playing any sport without knowing what the score is. Whether or not it is doable in practice at the moment is irrelevant to the principle.

      • 12. khokan  |  April 20, 2010 at 5:07 pm

        I think that BBO as you describe it is just a “different” game, e.g., like comparing teams to pairs. You can’t really compare bridge to sports like football etc., as there isn’t the equivalent of two tables. You might compare bridge to setting pole position for F1 racing, though – I assume that the latter racers know the times they need to beat.

  • 13. Tony  |  April 20, 2010 at 3:24 am

    Are you advocating that each board should be played simultaneously at both tables in a teams match? And after each board is played the quicker table is required to wait until the board is finished at the other table so it can be scored? If so, i would not find it much fun at all.

  • 14. Rainer Herrmann  |  April 19, 2010 at 7:15 pm

    I do not know what the opening lead was.
    But I will assume it was a spade.
    Otherwise if it was a heart or a club you can test hearts first before embarking on a red suit squeeze against RHO and even on a spade lead East might not go in with the queen if you play a diamond from the table after finding out that hearts.
    do not break.

    But let us assume a spade led and that East would go in with the queen if you lead a diamond from the table (did you not say this was a weakish team):
    Playing on hearts will win 35.5% of the time
    Playing LHO for Ax in diamonds and at most a doubleton heart will happen less than 3% of the time if my a priory calculations are correct.

    I would rather question my assumption that they are in a small slam in the other room before playing for such inferior odds.

    I wonder what your team mates will tell you when the diamond king looses to the ace while hearts broke and it turns out that they were in 3NT in the other room.

    Taking the state of the match into account is rarely profitable,
    playing Bridge is what counts.

    • 15. khokan  |  April 20, 2010 at 5:02 pm

      I don’t think that you can’t test hearts first, if you’re playing for a squeeze, as this destroys entries (assuming you end up by cashing clubs).

      I agree with the rest of the comments, though.

      • 16. Rainer Herrmann  |  April 21, 2010 at 10:02 pm

        You are right, I messed up the play.
        Sorry for that.

    • 17. Khokan  |  April 21, 2010 at 8:17 pm

      On a spade lead, you can run it to the SJ (or play SQ and overtake) and lead a diamond up to the DK – at least this way, you can also cater for stiff DQ, or DAQ tight, on your left. There’s no need to pull a diamond away from DK.

  • 18. Ben Thompson  |  April 19, 2010 at 3:28 pm

    We already know the score at various breaks (eg after every set of a long match). Why is it valid to know the score at 56 out of 64, but not at 63 out of 64? In isolation, there’s nothing special about board 56.

    That said, I think we have to be very careful with board-by-board live public score updates because of player issues, even though live updates could be done reasonably easily with current technology.

    If we have to wait for everybody to finish playing a board before updating scores and moving on to the next one, the game will become unbearably slow. Every board will take 15 minutes. The more tables, the worse it gets (even in swiss teams, I may want to know the score in other matches so that, for example, I can judge whether I have to go hard or play tight to get the tournament win). I’m not playing in that tournament.

    If we don’t wait, we can either (A) instantly update the public score as each result comes in, or (B) only update the public score after every result on a board come in.

    (A) needs special care because slow players may get useful information about the hand they are playing directly from the score updates. Too dangerous, shouldn’t be done.

    Even in case (B), there’s an information advantage just in knowing your relative position better, which will go to the slow pairs, creating a “race” to be slowest.

    Barometer scoring solves the race to be slow by placing the usual time limit on each round, and having the updated scores come out some unspecified time later. Importantly, score updates happen after all scores are in for all tables and every board played up to the update point.

    Barometer is a good hybrid between the technically right method of waiting for the all the scores to come in, and keeping the game in motion.

  • 19. Chris Mulley  |  April 19, 2010 at 2:43 pm

    Sorry – couldn’t get past the unrealistic first example: Richmond are within three points of the opposing team at the end of the game and then, as if that were not enough, they have the ball as well?

    • 20. cathychua  |  April 19, 2010 at 2:49 pm

      Yes, I wondered about that, Chris!!! I was expecting Ben to be the one who commented…being a Tiger.

  • 21. andrew webb  |  April 19, 2010 at 6:53 am

    I agree it simplifies the game. But bridge is a game, essentially, of imperfect information, and dealing with the consequences of it. I don’t see the necessity to change that in this respect.

    I have won a match because my team mates did well at predicting the state of the match. I have lost a match because my partner did poorly. I see such prediction as a legitimate skill within the game.

    • 22. cathychua  |  April 19, 2010 at 12:51 pm

      There would still be lots of imperfect information! Refusing to decrease it, though, sounds a bit to me like the arguments against scientific bidding. It should be like the old days where everybody guessed and the better guesser won…

  • 23. Tony Tee  |  April 18, 2010 at 1:14 pm

    Bridge is a game of incomplete information, so knowing the score does not change one’s perception of the problem – it changes the problem. What was “what is best to do, given my assessment of the score?” becomes “what is best to do, knowing the score?”. The information is incomplete is both cases but slightly less so in the latter.

    Does this matter, in the context of the game in its broadest sense? Being allowed to know more changes the game but does not necessarily make it better – depending on how we agree to define “better”.

    Duplicate bridge has always, at least until relatively recently, had to played in ignorance of the up-to-the-moment score, principally on the practical grounds of not being able to collect raw scores and calculate and communicate the resultant MP or IMP scores in a complete and timely way.

    Electronic scoring and results dissemination and, at least in major tournaments, all tables able to play the, let us say, 16 pre-duplicated boards in the same order means that up-to-the-second scoring is potentially available. However, what happens when at my table I come to play board 16 and am faced with TR’s slam play problem, only to find that the other table of our key match is still playing board 14?

    Do I proceed on the basis of the incomplete (missing boards 14, 15) information? Depending on the results for those boards at our table I may be little better off than I am now under the current procedures, so little has been gained / lost. And what of my opposite number? When s/he come to play board 16 how much score information is s/he given??

    Or must the two tables play all boards in parallel, not starting a new board until both tables have completed the prior one? I can see some time-keeping / slow-play issues looming!

    • 24. cathychua  |  April 19, 2010 at 12:53 pm

      Tony, it would certainly slow things down, but this is hardly a new idea. In the 1930s one board was played at a time and the score was always known – in Australia, at least. Technology will have sped it up since then…On BBO it doesn’t seem to cause issues, but this is an informal venue.

    • 25. phil markey  |  April 19, 2010 at 2:12 pm

      “Bridge is a game of incomplete information, so knowing the score does not change one’s perception of the problem”

      out of curiousity i sent cathys hand posted 12/4/10 to 4 mates of mine all of whom played open bridge for australia – i left out the bit where you knew the score and asked only what to bid over 3 spades

      i’m surprised to report that one of them actually bid 4 diamonds – personally i think thats because they couldnt believe that it was right to do the obvious thing – the other 3 passed

      of those who gave an answer to cathys problem other than me the tally was 4 votes for 4 diamonds – none for pass

      of the 3 i polled who passed i got some interesting comments about the merits of biddding 4 diamonds including;

      “it is not worth taking wild risks at teams”

      “even the law of total tricks is with me on this one”

      “i would regard 4 diamonds as highly invitational”

      it could be that bidding 4 diamonds is better when you know your 2 imps up but i never really saw an argument that expalined why that would be – or it could be that knowing the score changed people’s perception of the problem such that they felt obliged to use the additional information they were given to find a special answer

      • 26. Chris Mulley  |  April 21, 2010 at 10:05 am

        I did try to explain why I thought I would bid 4D when not vulnerable knowing the score, but I’m not sure that even I am convinced by my arguments.

      • 27. Khokan  |  April 21, 2010 at 7:57 pm

        I think you’re wrong, Phil.

        Furthermore, I reckon that if you presented this problem to the Master Solvers Club on Bridge World, a plurality would vote for 4D. Your polled comments seem extreme. The comment re total trick doesn’t make sense to me, for the reasons Bill Jacobs outlined earlier.

  • 28. phil markey  |  April 18, 2010 at 10:33 am

    i’m still chuckling at the people who want to bid 4 diamonds in the original hand you gave – HELLO – worlds easiest pass of 3 spades

    as predicted in my reply the whole world got a severe case of fancy play syndrome

    i get that in theory knowing the score enables you to make better decisions some of the time – in practice though knowing the score is going to be about pressure not so much about classical bridge ability

    i love a game about pressure – bridge has plenty of pressure – but if i want some more high octane pressure then i find myself playing poker


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