[hanp]

Is 0.95 almost exactly 1 these days?

[Fluffy]

depends whoom you ask han, was it in the watercooler where I red that nowdays 1$ is now 0.99$ because 1 cent goes to VISA or MASTERCARD?

[Fluffy]

jdonn, on Jan 21 2010, 08:59 PM, said:

Fluffy, why? No one would ever notice a difference. If they did then they would find a way to take advantage of it. So either you are wasting your time or changing the game, and in either case breaking the laws. I think you just have to accept there is very little support for something like this.

yes, I almost gave up when Richard said this, but then some insults and such brought me back to the topic and made me realise I was willing to pay the price in order to get the advantages.

Someone getting "unfair"* advantage is better than a full line having the problems of being helpless looking at what their opponents do.


* Also to note I don't like someone getting advantage because of it since its not part of the game, but if someone is smart enough to count all and take a decision that has become 1-2% better and win due to it, well, he at least deserves some credit and I am willing to pay him. I beleive that what actually will happen is that people will overreact to these feelings and rather than take an advantage they will lose.

My opinions now is, I have no clue, maybe it is a big disaster, can't ignore that many smart people is telling me a big fat NO. But I feel like it deserves a try.

My bet is that even if you activate it nobody will ever notice. But you will save someone's otherwise boring afternoon/evening.

Since richard stopped insulting me I think I can finally drop the topic (lets hope).

[hrothgar]

Fluffy, on Jan 22 2010, 01:06 AM, said:

Someone getting "unfair"* advantage is better than a full line having the problems of being helpless looking at what their opponents do.

Duplicate and team scoring were developed to eliminate this "unfair" advantage...

[Lobowolf]

Fluffy, on Jan 18 2010, 10:51 AM, said:

unfair is to sit down on a nearly yarborough 70% of the deals and depend on what opponents bid/play all the time having nothing to do about it.

The makings of a really good Water Cooler thread!

Fairness: Equality of Opportunity, or Equality of Outcome?!

[barmar]

billw55, on Jan 21 2010, 03:24 PM, said:

kayin801, on Jan 21 2010, 02:38 PM, said:

Does anyone else find it eerie that one standard deviation is almost exactly 1 HCP? (Granted this is only for 24 board tourneys) Or am I just being a geek? BTW, thanks for this sim Hotshot, it's exactly what I wanted to know.

Well there must be some number of boards for which sigma is 1 hcp, or very close to it. As it happens, it's pretty close for 24 boards. Maybe Hotshot ran sims for a few different set sizes, and presented the one with sigma closest to 1. Or maybe he just got lucky his first try

Maybe someone figured this out many years ago, and that's why club and tournament sessions are around 24 boards.

[matmat]

hotShot, on Jan 21 2010, 03:33 PM, said:

30 board tourneys:
The mean HCP NS: 20.00167601676

18 Board tourneys
The mean HCP NS: 20.00167601676

128 Boards
The mean HCP NS: 20.001689108103

isn't that a little odd?

edit -- these aren't independent trials, are they... just repackaging of the same hands into different tournament lengths, huh?

[hotShot]

matmat, on Jan 22 2010, 01:38 AM, said:

edit -- these aren't independent trials, are they... just repackaging of the same hands into different tournament lengths, huh?

You got it.

[helene_t]

Lobowolf, on Jan 22 2010, 12:09 AM, said:

The makings of a really good Water Cooler thread!

Fairness: Equality of Opportunity, or Equality of Outcome?!

Same thing, unless you insist on believing in free will

Sorry that's nonsense of course, just couldn't resist.

[billw55]

barmar, on Jan 21 2010, 07:27 PM, said:

Maybe someone figured this out many years ago, and that's why club and tournament sessions are around 24 boards.

I'm pretty sure the number of boards is related to the legth of the session (i.e. time). If sessions were much longer than maybe 30 boards or so, people would start to get hungry.

[blackshoe]

The tradition around here is that a session takes three hours. We used to play 24 boards exclusively. The ACBL recommends 7.5 minutes per board. 7.5x24=180 minutes=3 hours. People wanted more boards, so they got more boards. The TDs did that by lowering the time per board to about 6:20, and allowing about twenty seconds for people to move between rounds. We have more than one director who starts chivvying people to move even before the "three minutes to go" warning from the clock. OTOH, we also frequently have players who finish their round early, and start asking for boards before that same warning. Both are annoying.

[jdonn]

Now hijacking a little, but I have never for the life of me understood the distaste with people who finish early and want to start the next round early. When they have to wait they may finish the next round late and it would have been completely avoidable. It also keeps the pressure on everyone to keep things moving.

[gnasher]

jdonn, on Jan 22 2010, 06:44 PM, said:

Now hijacking a little, but I have never for the life of me understood the distaste with people who finish early and want to start the next round early.

Well, that depends on how they do it. If they politely ask dummy at the next table for a board without distracting anyone else, that's fine. If, on the other hand, they shout "Board please" at me when I'm trying to think, I'm likely to treat them with distaste.

[hotShot]

We'll perhaps you like it, if someone comes to the table and tries to get a board, while you are busy makeing/defending the 2nd board.

[jdonn]

gnasher, on Jan 22 2010, 02:33 PM, said:

If they politely ask dummy at the next table for a board without distracting anyone else, that's fine.  If, on the other hand, they shout "Board please" at me when I'm trying to think, I'm likely to treat them with distaste.

It sounds like the only distinction you are making is whispering versus shouting. I agree but it seems like a minor reason that people don't like others to get ahead. I feel like it's usually that directors are trying to keep the movement organized, but it's really not that hard to make sure you are at the right place playing the right boards against the right pair.

But of course no matter what the procedure it's good when people are polite and bad when they aren't. That just seems like a side issue.

hotShot, on Jan 22 2010, 02:41 PM, said:

We'll perhaps you like it, if someone comes to the table and tries to get a board, while you are busy makeing/defending the 2nd board.

I don't mind at all in fact if they quickly grab the one we aren't playing and leave.

[barmar]

Maybe some players think it's unfair that those people are getting more time in the next round. Although if that were the case, I think players would make a stink over players playing during the hospitality break, and I've never seen anyone complain about that.

I've rarely seen anyone complain about it in general, but maybe I play with more polite people than are typical (I think this may be true -- I only know a small number of players who exhibit the rudeness that's considered stereotypical of club bridge players). However, I also generally avoid asking for a board if I can see that the player who would have to pass it is deep in thought and the round hasn't been called. More generally, lots of players seem to consider it impolite to ask for a board before the 2-minute warning of the end of the round.

[TimG]

Fluffy, on Jan 21 2010, 11:35 AM, said:

I can try and give you some fight back, but I will be bored soon though, I hope it will be enough for you to feel smarter than me.

Most of us felt smarter than you the moment you suggested "computer rotating hands to equalice the strenght".

[Mbodell]

blackshoe, on Jan 22 2010, 07:44 AM, said:

The tradition around here is that a session takes three hours. We used to play 24 boards exclusively. The ACBL recommends 7.5 minutes per board. 7.5x24=180 minutes=3 hours. People wanted more boards, so they got more boards. The TDs did that by lowering the time per board to about 6:20, and allowing about twenty seconds for people to move between rounds. We have more than one director who starts chivvying people to move even before the "three minutes to go" warning from the clock. OTOH, we also frequently have players who finish their round early, and start asking for boards before that same warning. Both are annoying.

We have one local club where you get 21 minutes for a 3 board set but the TD often doesn't let people start the last board if there are 4 or less minutes on the clock. And you still only play 24 boards. I'd rather have a "normal" pace and have the game take somewhere between 3 and 3.5 hours but play 27 boards.

[Jboling]

I did one more calculation related to the original thread, trying to answer the following question: If we have the average 22.5 after 20 deals (a 1% chance, equally big chance for 17.5-), and the total constraint on the 26 deal set is 22.7, how does the likelihoods change for getting a certain number of hcp?

    hcp       orig. lh    new lh     new/orig
            0    0.0001    0.0001    1.0899
    1.0000    0.0005    0.0005    1.0897
    2.0000    0.0022    0.0024    1.0895
    3.0000    0.0062    0.0068    1.0893
    4.0000    0.0180    0.0196    1.0889
    5.0000    0.0431    0.0469    1.0884
    6.0000    0.0919    0.1000    1.0877
    7.0000    0.1821    0.1980    1.0869
    8.0000    0.3404    0.3697    1.0858
    9.0000    0.5900    0.6398    1.0844
   10.0000    0.9540    1.0328    1.0826
   11.0000    1.4648    1.5825    1.0804
   12.0000    2.1220    2.2866    1.0776
   13.0000    2.9397    3.1576    1.0741
   14.0000    3.8845    4.1561    1.0699
   15.0000    4.8966    5.2137    1.0647
   16.0000    5.9067    6.2525    1.0585
   17.0000    6.8372    7.1868    1.0511
   18.0000    7.5739    7.8947    1.0424
   19.0000    8.0400    8.2978    1.0321
   20.0000    8.2218    8.3869    1.0201
   21.0000    8.0568    8.1074    1.0063
   22.0000    7.5668    7.4950    0.9905
   23.0000    6.8095    6.6232    0.9726
   24.0000    5.9072    5.6270    0.9526
   25.0000    4.8920    4.5506    0.9302
   26.0000    3.8795    3.5131    0.9056
   27.0000    2.9510    2.5927    0.8786
   28.0000    2.1292    1.8085    0.8494
   29.0000    1.4635    1.1970    0.8179
   30.0000    0.9556    0.7496    0.7845
   31.0000    0.5865    0.4394    0.7491
   32.0000    0.3375    0.2404    0.7121
   33.0000    0.1846    0.1243    0.6737
   34.0000    0.0942    0.0597    0.6342
   35.0000    0.0435    0.0259    0.5940
   36.0000    0.0176    0.0097    0.5533
   37.0000    0.0067    0.0034    0.5125
   38.0000    0.0020    0.0009    0.4721
   39.0000    0.0005    0.0002    0.4322
   40.0000    0.0000    0.0000    0.3934

The original likelihoods (denoted lh above) for low and high hcp are inaccurate, as they are obtained through simulation. In the 10 million deal set there were for example 7 deals with 0 points and 3 deals with 40 points. Fortunately these extreme values have little impact on the relative change in the likelihoods, which were obtained as follows:
1. Assume hcp between 0 and 40 for deal 21
2. Calculate the upper limit on the average for the remainng 5 deals (trivial)
3. Calculate the likelihood for that 5 random hands will be under that limit (obtained by numerical integration of the pdf, with the sigma = 2.13 for sets of 5 deals).
4. Repeat 1-3 for all hcp
5. This gives a multiplicative modifier on the likelihood for each hcp. The final likelihoods are obtained by normalization so that the total likelihood will be 100%.

So the likelihood for getting 25 points is reduced by a factor of 0.93, and likelihood that the oppos have 25 is increased by a factor 1.06. And having soft constraints shouldn't change these much. It is a bit more than I expected, but still I'm not sure if it would affect my bidding. When I preempt I do it under the assumption that the opponents have game anyway (I use the 4-3-2-rule). And the likelihood for our side having 20+ points is still almost 52%.

But anyway I agree with the others about that such constraints will probably never be accepted, for the reasons already mentioned.

PS. For those who teaches probabalities and statistics: The frequency table for sum of north and south hcp, which hotshot published, is a nice illustration of the central limit theorem. The hcp frequency table for each player is not that normally distributed, but the hcp sum of two players is very close to normally distributed. And the hcp averages of sets of more than one deal become even more normally distributed. So my above given numbers, which were calculated assuming normal distribution, should be quite accurate.

Edit: Forgot that the above likelihoods are a priori likelihoods, that is before looking at your hand. Typically you do that before you start bidding. The current hcp has of course a big impact on this, for instance if you have 9hcp instead of the expected 10 the unbiased expected value for the total hcp will be 19.33. And so on, a totally different situation for each current hcp-value. The above relative numbers could still be quite close to the truth. More accurate numbers could be calculated, but I'm not doing it.

[khaggblo]

Jari, on Jan 23 2010, 07:12 PM, said:

I did one more calculation related to the original thread, trying to answer the following question: If we have the average 22.5 after 20 deals (a 1% chance, equally big chance for 17.5-), and the total constraint on the 26 deal set is 22.7, how does the likelihoods change for getting a certain number of hcp?
.
.
The original likelihoods (denoted lh above) for low and high hcp are inaccurate, as they are obtained through simulation. In the 10 million deal set there were for example 7 deals with 0 points and 3 deals with 40 points. Fortunately these extreme values have little impact on the relative change in the likelihoods, which were obtained as follows:
1. Assume hcp between 0 and 40 for deal 21
2. Calculate the upper limit on the average for the remainng 5 deals (trivial)
3. Calculate the likelihood for that 5 random hands will be under that limit (obtained by numerical integration of the pdf, with the sigma = 2.13 for sets of 5 deals).
4. Repeat 1-3 for all hcp
5. This gives a multiplicative modifier on the likelihood for each hcp. The final likelihoods are obtained by normalization so that the total likelihood will be 100%.

Edit: Forgot that the above likelihoods are a priori likelihoods, that is before looking at your hand. Typically you do that before you start bidding. The current hcp has of course a big impact on this, for instance if you have 9hcp instead of the expected 10 the unbiased expected value for the total hcp will be 19.33. And so on, a totally different situation for each current hcp-value. The above relative numbers could still be quite close to the truth. More accurate numbers could be calculated, but I'm not doing it.

Given that you have the 10 million deals used to generate the initial hcp distribution, I think there is a mucher easier way to obtain the statistics without using any "advanced" mathematics.

1. Arrange all deals into 6 deal sets (e.g. by putting every 6th deal into a new set).
2. Discard the sets that violate the desired constraints for the 6 last deals.
3. Use all remaining deals to calculate the new hcp distribution for deal nr 21 (all because any deal in any set could be the next one).
4. If you really want to delve into this, you can select other 6 deal sets (there is a HUGE number of possibilities) from the original data and repeat steps 1-3. By combining these results, you can obtain more reliable estimates and even some confidence bounds on the expected hcp distribution.