[peachy]

Jari, on Jan 19 2010, 05:10 PM, said:

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]

Quote

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]

Fluffy, on Jan 20 2010, 03:29 AM, said:

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]

Quote

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]

Fluffy, on Jan 20 2010, 03:43 AM, said:

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"

Quote

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]

khaggblo, on Jan 19 2010, 07:03 PM, said:

Quote

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]

Jari, on Jan 19 2010, 11:10 PM, said:

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]

Jari, on Jan 20 2010, 05:01 AM, said:

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".

Jari, on Jan 20 2010, 05:01 AM, said:

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.

Jari, on Jan 20 2010, 05:01 AM, said:

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]

khaggblo, on Jan 20 2010, 06:54 AM, said:

Jari, on Jan 20 2010, 05:01 AM, said:

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]

hotShot, on Jan 20 2010, 04:04 PM, said:

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

[bluecalm]

Seriously guys, spend your energy elsewhere.
It's pain to watch this thread unfold. The idea is super dumb and if you actually provoke some td's to try it it will be great shame. Do you really want superstitious players say "I knew it! We had too many cards to have game once again" to the face of opponents fixed by their stupid bidding and ACTUALLY BEING RIGHT about it ?

The world is full of people not understanding randomness and not appreciating it. The last thing we should do is to conform to false expectations and unreasonable demands. The lesson cannot be understood by bankers and economists of this world, maybe bridge players should be one who can ?

[hotShot]

To finalize the topic
I simulated about 114 years of 7 24 board tourneys a week.

Number of tourneys: 41666
The mean HCP NS: 20,00165502648
The variance: 0,95194261701304
The standard deviation: 0,97567546705503
Minimum: 15,958333333333
Maximum: 24,458333333333

[helene_t]

Great comment, Bluecalm. Nuff said.

[khaggblo]

helene_t, on Jan 21 2010, 05:10 AM, said:

Great comment, Bluecalm. Nuff said.

I agree completely. On the other hand,

hotShot said:

Minimum: 15,958333333333
Maximum: 24,458333333333

how come the min and max are not integers? Furthermore, they should be symmetrical with respect to 20. If the NS max is 20+n, the EW min must be 20-n (why consider only one side?).

The same principle applies to the simulation of hcp distribution (see HotShot in a previous post). If there are N deals where NS have, say, 10 hcp in a given number of deals, there must be exactly N deals where EW have 30 hcp. In theory, 20-n hcp occurs exactly as often as 20+n hcp. One could thus improve the accuracy of simulations somewhat by using the mean value of the number of deals having 20-n and 20+n hcp for both 20-n and 20+n hcp deals.

[gwnn]

i wanna learn statistics