Rotating hands to balance strenght between NS-EW

[hrothgar]

in spain they cannot kick you for counting <_<, that's something I never understood from america.

 

My father played in the low limit tables, because the difference between the minimum and the maximum was greater there than on the other tables.

Rules vary by state

 

In Nevada the casinos can ban you from counting.

I don't think that they can in New Jersey

 

In general, casinos that allow players to count alter the Blackjack rules to increase the house edge.

[hrothgar]

thanks richard, those are the percentages I had in mind mroe or less.

 

now, try to apply them to bridge, and tell me what difference it makes to know aprtner has average 8 HCP after he passes in first sit, or when he opens the bidding.

Comment 1:

 

I don't know about you, but when I'm am doing any (serious) work on bidding methods I spend an awful lot of time studying exactly these sorts of questions.

 

Comment 2:

 

To continue with the Blackjack analogy:

 

Card counting "works" because the counter is able to identify relatively short periods of time when the game is stacked in his favor and adjust his betting or have the whale join the table or what have you.

 

I don't see the point in engaging in inane thought experiments in which you pose stupid questions and I waste time trying to derive answers. It should be perfectly obvious to anyone with half a brain that if you start adding state information to the game people are going to start altering their behaviour.

 

I don't know precisely how this will happen. I don't know what heuristic people are going to use to start "counting" the bridge session. (What is the bridge equivalent of "Wong Halves").

 

I am, however, quite sure that someone will come up with something clever...

[Fluffy]

you know, I enjoy your comments in this post, all of them, except when you compare me with people with half a brain and mad people like a white queen, I don't see the logic behind them, do you really need to make me feel insulted to support your arguments?

[hrothgar]

you know, I enjoy your comments in this post, all of them, except when you compare me with people with half a brain and mad people like a white queen, I don't see the logic behind them, do you really need to make me feel insulted to support your arguments?

Sorry

 

Things are a bit crazy at work right now. Unfortunately, I don't have the liberty to tell customers and coworkers what I think of some of their questions / comments and some of that frustration spills out onto the forums.

 

With this said and done, its oft been said that there is no such thing as a stupid question. I don't accept that. A lot of your postings in this thread contain basic logical errors are factually incorrect, and/or suggest that you really haven't thought things through.

 

Case in point:

 

tell me what difference it makes to know aprtner has average 8 HCP after he passes in first sit

 

Comment 1: This is a non sequitur. The question you pose isn't really related to the point that I was making.

 

Commment 2: The question itself is lazy... If you spent a couple minutes thinking about things you'd probably be able to come up with your own answer to this question and (probably) better questions of your own.

 

Conversations are a two way street...

If you aren't willing to invest the time or effort necessary to construct reasonable questions don't be surprised if people start to display some annoyance...

[Gerben42]

I've played with cards with an edge only when they are hand-shuffled or one time in a goulash tournament (but then we told people in advance and we had fun!).

 

Anything to change the probabilities is not bridge, sorry! I think trying something like that should mean you get your TD licence revoked.

 

Playing Blackjack or Poker, you play MANY hands and if you have a small edge even though the swings are huge, you will be ahead in the long run.

 

Although it is true that a good pair has a bigger edge on the field when they hold more HCP than average than when they have the weaker hands, this ALL EVENS OUT in the long run. In any kind of game. Yes even rubber bridge :)

[barmar]

Have any of you played the Money Bridge Tournaments on BBO, which are programmed to give the human player the most HCP on every hand? Knowing that none of the other players can have more HCP than you makes a big difference in bidding and figuring out card distributions.

 

This isn't quite the same thing as the statistical probabilities being discussed here, but it gives you an idea of how you can alter your behavior as a result of extra knowledge like this.

[jdonn]

Fluffy here is one way it could make a large and practical difference. You have some indifferent 16 count and they open a 3 level preempt on your right. If you "know" (or have strong reason to suspect) your side is supposed to have fewer than average points on either this hand or the group of hands, you can find a good pass since partner is likely to be broke. The table that played this hand first probably overcalled 3NT and went for a number.

 

I think as time went on and people thought about it more, that type of situation would come up all the time.

[barmar]

You know how some people like to put notes about each hand on their private score, like what the opening lead was or how the auction went? If players knew that the hands were cooked this way, I could easily imagine them keeping a running tally of their side's HCP.

[billw55]

...

 

Although it is true that a good pair has a bigger edge on the field when they hold more HCP than average than when they have the weaker hands

 

...

I wonder about this. In a club game, or a lower level tournament event, I am used to this phenomena. When ops bid and make a perfectly normal game contract, our side frequently gets a little below average, because there always seems to be a knucklehead or two in the field who don't bid it, or otherwise screw it up. I would think that it would work the other way too, that a few pairs overbid to slam so we get a good score ... but for some reason, that seems to be much less common. Perhaps club level players bid fewer slams in general?

 

But ... is this also true in high level pairs events? Where every pair are experienced, strong players? I would think the field protection in such events would be adequte, that the "better cards equal better scores" phenomena should disappear. But does that actually happen in practice? And if not - why?

[Jboling]

You know how on some (all?) of the automatic deal softwares they have printouts that not only have the hands and DD contracts but also the point distributions, suit distributions, etc. While I doubt you'd wanna specifically rotate some hands, why not throw out the entire set after seeing X pts in one direction in point count and deal a new one (subtly and don't tell anyone)? I think that kind of control isn't quite so bad... It's more work for directors, but it's not really tampering anymore. Not to mention this software will sometimes deal more hands than will be played, which are then included in the total statistics. Of course, going exactly 20 on average each way is ridiculous since anyone with a pencil and paper can predict the HCP count for the last hand ;P but maybe throw out 24+ in one direction or something (or there could be built in software control for this).

 

Btw, where are the sim people who can tell us the chances of having one side average X HCP over 30 or so randomly dealt boards

If you cancel the whole set based on some statistic as the average number of hcp, you will introduce constraints on that statistic, and the set will become less random in that sense that you can predict something about the future deals based on the past deals. But if the constraints are loose enough, and even better the constraints would be unknown to everbody, I think it could become impossible for the players to predict the future.

 

I did some sims two years ago, it was more difficult than usual when you need to do statistics on statistics of sets of deals. My conclusion was that about three sigmas (standard deviations), was about possible without the limits becoming relevant almost ever, even in a case when the limits were known to players. This means accepting 99.7% of the deals (in case you have one constraint, for instance hcp for N-S, which automatically limits E-S as well). I used sets of 26 deals as an example, with the three sigma limits 17.3-22.7:

 

xxxx 10.0 16.0 20.0 23.0 24.0 25.0

--------------------------------------------

21.5: 20.0 20.0 20.0 20.0 20.0 20.0

22.0: 20.0 20.0 20.0 20.0 20.0 20.0

22.5: 20.0 19.9 19.8 19.7 19.6 19.6

23.0: 20.0 19.8 19.4 18.2 17.0 13.4

23.5: 19.9 19.5 18.5 15.5 12.2 2.4

 

In the table I have the expected average hcp of the remaining deals, above we have the played deals so far, and to the left the average so far. So if your average will stay under 22.5 (and over 17.5) you will practically have no information at all. For instance at 20 deals we have total bias of a 6*0.2=1.2, that is slightly more than a jack totally on the remaining deals. The average will stay between 17.5 and 22.5 99.4% of the time for 26 deals, and it will be less common for less deals. So I think most of you overestimate dramatically the impact of having hcp-limits on actual playing decisions.

 

I also did the same statistics for two sigmas, that is 18.2-21.8 limits, which probably is too tight limits:

 

xxxx 10.0 16.0 20.0 23.0 24.0 25.0

--------------------------------------------

21.5: 19.9 19.8 19.7 19.7 19.7 19.8

22.0: 19.8 19.5 19.1 18.1 17.1 14.4

22.5: 19.7 19.2 18.2 15.3 12.4 3.6

23.0: 19.6 18.7 16.9 11.9 6.8 -7.7

23.5: 19.5 18.1 15.5 8.3 1.2 -20.2

 

Here you could probably use information about the limits around 10% of the deal sets, but only at the end of the set.

 

I recall that only our old Unix machine with Solaris operating system had flexible enough command tools to do the above statistics. I think I needed the command flex to grep the relevant statistics from Staverens dealer, which can do the hcp-statistics for 26 deals. The Unix machine is unfortunately no longe with us, so unfortunately I cant easily do more statistics of the above type.

 

Helene mentioned that she would accept such limits only in holiday bridge. I think competitve bridge could benefit from such limits as well. As I mentioend earlier if you get less points your bridge skills will have less impact on your result. HAving hcp-constraints could be viewed as design of experiments, where you try to estimate the skills of participating players. And as some of might know, truly random experiments are not optimal when you make only a finite number of tests on your test subject. I'm not suggesting that adding hcp-constraints would make tournaments optimal tests, just slightly better than truly random deals, so you could get more accurate estimates of bridge skills using less deals

 

Somebody mentioned finesses in this context, it is safer to use constraints on the pairs than on the individual players, as the latter could have impact on making finesses, while the former have no impact on this. During play of the hand you know the sum of the opponents hcp exactly when you see the dummy.

[peachy]

Helene mentioned that she would accept such limits only in holiday bridge. I think competitve bridge could benefit from such limits as well.

Whether what you say is true or not (benefit in competitive bridge), any tampering with the deals is against the Laws of Duplicate Bridge. That particular part of the Law is likely to never get changed so IMO we should all drop our dreams of doing it in real competition. And if anyone has actually done it, I'm hoping it was done out of ignorance of the laws.

[Fluffy]

ok, I admit it can make a difference knowing your average on the run.

 

However when I look it from the point of view of a good pair sitting on a line with very few strenght, they can pick between:

 

-Passing around 18/26 boards and being prone to what the other players do, often this translate on an almost perfect season of 55% MPs.

 

-Playing more boards and risking the loss of 2 MPs because a certain pair developed the skill of counting their average HCP for the season and made a decision based on it.

 

 

If I had to pick between the 2 I would have no doubt.

 

 

And the pairs who spent their time developing the skill to be able to take advantage, hell it requires a lot of effort, if they are willing to do so I am happy they try that instead of developing a face-shoulder-elbow code of signaling (wich would be a ton more useful).

 

But I am talking too much hehe, I guess the best thing is to just try it and see what happens :)

[hotShot]

If you are a good pair among average pairs you can score a lot when you have the weaker (HCP) hands:

- because you're better in defending, leading and signaling

- because you'll know when to preempt or sacrifice (and when opps did not bid enough)

- because you'll make the most out of the few good hands you get

 

And it is more fun, because it's actually a challenge.

 

Everybody can cash the gifts of weak leads, poor defense skills holding strong hands.....

[khaggblo]

I used sets of 26 deals as an example, with the three sigma limits 17.3-22.7:

 

xxxx 10.0 16.0 20.0 23.0 24.0 25.0

--------------------------------------------

21.5: 20.0 20.0 20.0 20.0 20.0 20.0

22.0: 20.0 20.0 20.0 20.0 20.0 20.0

22.5: 20.0 19.9 19.8 19.7 19.6 19.6

23.0: 20.0 19.8 19.4 18.2 17.0 13.4

23.5: 19.9 19.5 18.5 15.5 12.2 2.4

 

In the table I have the expected average hcp of the remaining deals, above we have the played deals so far, and to the left the average so far.  So if your average will stay under 22.5 (and over 17.5) you will practically have no information at all. For instance at 20 deals we have total bias of a 6*0.2=1.2, that is slightly more than a jack totally on the remaining deals. The average will stay between 17.5 and 22.5 99.4% of the time for 26 deals, and it will be less common for less deals. So I think most of you overestimate dramatically the impact of having hcp-limits on actual playing decisions.

I think this analysis is flawed. With the given constraints, each side knows they will have in total 520 +-70 hcp in a 26 deal set. If the NS average is 22.5 after 20 deals, they have had 450 hcp. Thus, they know with certainty that they will have 70 +-70 hcp, i.e. between 0 and 140 hcp, in the remaining 6 deals. They know, for example, that they cannot have the points for game on all remaining deals. That is knowing a lot compared to random deals. And of course, the situation could become more extreme closer to the last deal.

 

Similarly, EW know they will have between 100 and 240 hcp in the remaining 6 deals. This means, for example, that balancing and competing for the part score will be pretty risk-free. EW know they will have some values and will not be unlucky in terms of hcp.

[Fluffy]

you are right khaggblo, I think it is obvious that if this is ever going to work, you cannot play the full set of deals but have some deals not played.

[hrothgar]

you are right khaggblo, I think it is obvious that if this is ever going to work, you cannot play the full set of deals but have some deals not played.

And this is different from altering sigma how?

[Fluffy]

really, why are you taking this thing personal?, did I really offend you?, was it because I said US is not the world?, sorry, but with my half brain I cannot understand your actitude towards me.

 

but I am answering, if you don't play all the boards you cannot be sure that you are suposed to pick 30 HCP on each of the boards you aren't playing. Thus avoids certainity.

 

I doubt the sigma thing does exactly the same, but if you say it does I guess I am just wrong. Maybe in your opinion that means that I am a mad crazy man with half a brain with no logic. So be it.

[Siegmund]

I think it is obvious that if this is ever going to work, you cannot play the full set of deals but have some deals not played.

 

Absolutely right.

 

Most of us have a strong preference to play 26 (well, I'd prefer 30 or 32) out of 53,644,737,765,488,792,839,237,440,000.

 

If you have us play 26 randomly selected deals out of 30 balanced ones, you'll have undone almost all the "good" you were trying to do by balancing them, and just slightly reduced the complaints about your dealing procedure.

[hrothgar]

really, why are you taking this thing personal?, did I really offend you?, was it because I said US is not the world?, sorry, but with my half brain I cannot understand your actitude towards me.

In this case, it was the use of the word "obvious"

 

 

but I am answering, if you don't play all the boards you cannot be sure that you are suposed to pick 30 HCP on each of the boards you aren't playing. Thus avoids certainity.

 

I doubt the sigma thing does exactly the same, but if you say it does I guess I am just wrong.

 

I suspect (though I don't have the energy to try to prove) that one can approximate some (deal 30, choose 24) scheme with sigma = X1 with a (Deal 24, choose 24) scheme with sigma = X2...

[Jboling]

I used sets of 26 deals as an example, with the three sigma limits 17.3-22.7:

 

xxxx 10.0 16.0 20.0 23.0 24.0 25.0

--------------------------------------------

21.5: 20.0 20.0 20.0 20.0 20.0 20.0

22.0: 20.0 20.0 20.0 20.0 20.0 20.0

22.5: 20.0 19.9 19.8 19.7 19.6 19.6

23.0: 20.0 19.8 19.4 18.2 17.0 13.4

23.5: 19.9 19.5 18.5 15.5 12.2 2.4

 

In the table I have the expected average hcp of the remaining deals, above we have the played deals so far, and to the left the average so far.  So if your average will stay under 22.5 (and over 17.5) you will practically have no information at all. For instance at 20 deals we have total bias of a 6*0.2=1.2, that is slightly more than a jack totally on the remaining deals. The average will stay between 17.5 and 22.5 99.4% of the time for 26 deals, and it will be less common for less deals. So I think most of you overestimate dramatically the impact of having hcp-limits on actual playing decisions.

I think this analysis is flawed. With the given constraints, each side knows they will have in total 520 +-70 hcp in a 26 deal set. If the NS average is 22.5 after 20 deals, they have had 450 hcp. Thus, they know with certainty that they will have 70 +-70 hcp, i.e. between 0 and 140 hcp, in the remaining 6 deals. They know, for example, that they cannot have the points for game on all remaining deals. That is knowing a lot compared to random deals. And of course, the situation could become more extreme closer to the last deal.

 

Similarly, EW know they will have between 100 and 240 hcp in the remaining 6 deals. This means, for example, that balancing and competing for the part score will be pretty risk-free. EW know they will have some values and will not be unlucky in terms of hcp.

Note that in all cases the table only tells about the next deal. After that deal, the average so far and the expected future average will be different. What khaggblo probably is thinking about is that if you for example get 25 on the next 5 deals, you will then know that you cannot have more than 15 points on the last deal. But this is something different, it means that you have the average 23 after 25 deals, which is much less likely. For the average 22.5 after 25 deals you know that you cannot have more than 27 on the last deal, and the average 22 after 25 deals means the upper limit is 40 on the last deal, that is it is completely unbiased. But as I mentioned previously, problems appear especially on the last deal, and this can be most easily remedied by using a random limit, so that the exact limit is unknown to everybody, which adds up to a big uncertainty for the average calculating players especially on the last deal. Which actually is the same as having an extra deal or two, which nobody plays. If we have one extra deal, with the total upper limit of 22.7, would mean that actual upper limit on the first 26 would then be between 21.86 and 23.36. Which is already a quite a big uncertainty, in the above mentioned case we knew that we had 15 or less on te last deal, which will change to that you can have 32 or less. With two extra deals the upper limit will be between 21.1 and 23.9. Even better results you get if you add a truly normally distributed offset to the limit, when you get no known limits. Except that you have to check that the upper limit does not go too close to 20, but a known lower limit on the upper limit does not help anybody, as far as I can see.

 

Another issue is that my table is about mean values, it does not say anything about how the upper limit affects the variance, it might become more biased. Anybody want to make a try? I don't have the time at the moment.

[helene_t]

HAving hcp-constraints could be viewed as design of experiments, where you try to estimate the skills of participating players. And as some of might know, truly random experiments are not optimal when you make only a finite number of tests on your test subject.

That's true but even in clinical trials you try to avoid the situation in which 99 of the 100 subjects have recorded and 52 where told that they were in the control group so the clinicians know that patient #100 is not a control patient because the number of controls was limited to [48..52]. It sounds like a silly problem and maybe it is, but even so there is a whole industry dedicated to dealing with such problems.

 

In Bridge it is different. Maybe not in principle, but the relative importances of the different concerns are different:

- Even in the dubious case where one compares EW to NS in a Mitchell, it doesn't matter much if the EW hands happen to have fewer HCPs than the NS hands. Weak hands can have interesting decisions to make, too. Compare this to a clinical trial: 80 controls and 20 cases, (something which may have a likelihood comparable to NS getting 24 HCPs on average, just making this number up) would be devastating.

- Cooking the HCP statistics may not solve the issue. There could still be more preempts in the NS line, more difficult-to-bid hands in the NS line, more hands favoring 5-card majors in the NS line etc. Again, compare to the clinical trial. Cooking for case-mix solves most of the problem.

- In bridge it could easily be devastating if a player knew at the last hand of the tourney that his p must have at least x HCPs due to the cooking. Compare to the clinical trial: Even if it could be known by an examiner whether a particular patient was a case or a control (which it usually can't: a block design that solves the issue completely is often feasible), he may not bother to find out (he knows that he is not supposed to).

[khaggblo]

Note that in all cases the table only tells about the next deal. After that deal, the  average so far and the expected future average will be different. What khaggblo probably is thinking about is that if you for example get 25 on the next 5 deals, you will then know that you cannot have more than 15 points on the last deal.

Actually not, I am trying to say more than that. I think it should be clear from my previous post that I am considering all remaining deals after a certain deal, in this case deal nr 20. It is clear that the statistics of the remaining deals are different from random deals, and this difference is not negligible. In particular, the variance of the point distribution will be reduced. This, for example, means that various kinds of estimations and predictions concerning any of the remaining deals, even deal 21 when we start bidding it, can be made with greater accuracy than with random deals.

 

On the other hand, it seems that you are mainly concerned with problems of the last deal and that one of your solutions is not to play the "last deal".

But as I mentioned previously, problems appear especially on the last deal, and this can be most easily remedied by using a random limit, so that the exact limit is unknown to everybody, which adds up to a big uncertainty for the average calculating players especially on the last deal. Which actually is the same as having an extra deal or two, which nobody plays.

If we have one extra deal, with the total upper limit of 22.7, would mean that actual upper limit on the first 26 would then be between 21.86 and 23.36.

Are you implying that a limit of 22.7 on 27 deals is equivalent to any limit between 21.86 and 23.36 on 26 deals? A don't buy that. If the limit 21.86 is enforced on 26 deals, I think most of the discarded deal sets would be within the limit 22.7 on 27 deals. And a par with an average of 17 hcp allowed by the 23.36 limit would have every reason to be disappointed and angry since you have promised to deliver quality checked deal sets...

[hotShot]

Just to add a little facts:

1000000 random deals

average HCP NS 20.0017

std. deviation 4.77

 

Distribute as follows:

 

Comb.

HCP

NS   count

 1       5

 2      14

 3      66

 4     200

 5     424

 6     862

 7    1812

 8    3446

 9    5837

10    9494

11  14744

12  21488

13  29799

14  38694

15  49086

16  58605

17  68200

18  75410

19  80372

20  81950

21  80357

22  75905

23  68310

24  59259

25  49104

26  39165

27  29382

28  21065

29  14607

30    9471

31    5893

32    3430

33    1887

34     930

35     450

36     198

37      52

38      21

39      5

40      1

[Jboling]

If we have one extra deal, with the total upper limit of 22.7, would mean that actual upper limit on the first 26 would then be between 21.86 and 23.36.

Are you implying that a limit of 22.7 on 27 deals is equivalent to any limit between 21.86 and 23.36 on 26 deals? A don't buy that. If the limit 21.86 is enforced on 26 deals, I think most of the discarded deal sets would be within the limit 22.7 on 27 deals. And a par with an average of 17 hcp allowed by the 23.36 limit would have every reason to be disappointed and angry since you have promised to deliver quality checked deal sets...

What I meant is that you could aswell genereate the extra deal first (it makes absolutely no difference if you do it last), and calculate the hcp for N-S, which will be random number between 0 and 40. And then you can use this number to modify the upper and lower hcp limits for the set of deals to used in the competition. In the discussed case the upper limits will then be between (22.7*26)/27=21.86 and (22.7*26+40)/27=23.34. This limit will be close to normal distributed, with the mean (22.7*26+20)/27=22.6 (for the upper limit)and 4.77/27=1.8 as standard deviation (thanks to hotShot for a well timed calculation). So that would give that in 52% of the cases the limit is 22.7 or lower, and in the remaing 48% it is higher.

 

Still no time to study variance. Another interesting calculation would be how much does the likelihood for getting for example 25+ or 30+ hcp in the next deal decrease due to the limits.

[hrothgar]

Just to add a little facts:

1000000 random deals

average HCP NS 20.0017

std. deviation      4.77

 

Thanks for providing the results of the simulation.

 

I did a quick sanity check and 68.5% of the observations fall within 15 and 25.

 

Earlier, someone asked what the odds were that NS would get dealt at least "X" HCPs on each and every board in a tournament.

 

Let's assume that the tournament is 24 boards (a popular length). Furthermore, lets assume that we're interested in the odds that NS had at least 26 HCPs on each and every hand.

 

If we use the table that HotShot provided, there were 126,557 deals where NS had at least 26 HCPs. North - South will have at least 26 HCPs ~12.7% of the time. Conversely, N-S will have 25 or less HCPs 87.3% of the time.

 

Next, let's calculate the chance that N-S are deal 26+ HCPs on boards 1+2. Furthermore, lets assume that the number of HCPs on board 1 and the number of HCPs on board 2 are independent events. The odds of this happening is

 

(The percentage chance that N-S gets 26+ HCPs on board 1) X (The percentage chance that N-S gets 26+ HCPs on board 2) = 12.7% x 12.7% = 1.6129%

 

In a similar fashion, the odds that NS would get 26+ HCP on each and every board in a 24 round tournament is (12.7%)^24 = 3.0995e-022

 

Here's another interesting factoid...

Once again, we'll use HotShot's table.

 

The odds that NS are dealt 21+ HCPs (an above average hand) on any one board is about 46%

The odds that NS are dealt 21+ HCPs on each and every board of a 24 board tournament is 8.0573e-009

 

For kicks and giggles - and because I have MATLAB sitting on my desk - I generated a Bernouli distribution to show the percentage chance that NS would get dealt an above average hand X times times during a 24 board tournament.

 

x = 0:24;

y = binopdf(x,24,0.46);

 

Distribution =

 

# of Occurances    Frequency

0  3.7796e-007

1  7.7273e-006

2  7.5699e-005

3  0.00047288

4  0.0021148

5  0.0072061

6  0.019439

7  0.04258

8  0.077078

9  0.11673

10  0.14915

11  0.16171

12  0.14923

13  0.11734

14  0.078538

15  0.044602

16  0.021372

17  0.0085673

18  0.0028382

19  0.00076348

20  0.00016259

21  2.6382e-005

22  3.0646e-006

23  2.27e-007

24  8.0573e-009