Software for a slightly more involved statistical check of PBN files

[BudH]

Software such as DealComposer, Dealmaster Pro, and Dealer4 will show you high card point averages and total number of balanced hands, voids, singletons, and suits at least 7-cards long for a set of computer generated pre-dealt hands.

 

Occasionally I compare our local clubs pre-dealt hands (in PBN file format) with the following connected statistics:

 

High Card Points: 10.0000000000 per hand

Balanced (4333, 4432, 5332): 0.4760415243 average per hand

Voids: 0.0511637922 average per hand

Singletons: 0.3202474398 average per hand

7+ card suit: 0.0403212924 average per hand

 

But is there any other software that can examine a PBN data file for more than HCP, balanced hands, voids, singletons, and 7+ card suits? I would like to check some other distributional statistics other than these most common ones.

 

Bud H

[wyman]

Software such as DealComposer, Dealmaster Pro, and Dealer4 will show you high card point averages and total number of balanced hands, voids, singletons, and suits at least 7-cards long for a set of computer generated pre-dealt hands.

 

Occasionally I compare our local clubs pre-dealt hands (in PBN file format) with the following connected statistics:

 

High Card Points: 10.0000000000 per hand

Balanced (4333, 4432, 5332): 0.4760415243 average per hand

Voids: 0.0511637922 average per hand

Singletons: 0.3202474398 average per hand

7+ card suit: 0.0403212924 average per hand

 

But is there any other software that can examine a PBN data file for more than HCP, balanced hands, voids, singletons, and 7+ card suits? I would like to check some other distributional statistics other than these most common ones.

 

Bud H

 

http://xkcd.com/882/

 

Also you may wish to only compare one hand per deal (I assume you're not, since you average 10HCP/hand with such amazing precision). A 7+ bagger with north changes the likelihood of one being dealt to south.

 

Other than this, I'd recommend just writing your own software to do whatever analysis you wish on the PBNs.

[BunnyGo]

http://xkcd.com/882/

 

Also you may wish to only compare one hand per deal (I assume you're not, since you average 10HCP/hand with such amazing precision). A 7+ bagger with north changes the likelihood of one being dealt to south.

 

Other than this, I'd recommend just writing your own software to do whatever analysis you wish on the PBNs.

 

What a great link; I was trying to teach that to my students the other day.

[CarlRitner]

Check with Richard Pavlicek. His dealer program spits out all sorts of analyses, maybe it can be tweaked to read from PBN.

[hrothgar]

Bud, prior to moving to Akamai a few months back I was the technical marketing manager for MATLAB's statistics system.

I would be shocked if you were to find any software package that will do what you want out of the box.

Mass market software packages target large markets (and analyzing PBN bridge files is not a large market)

 

Your best bet is to get access to a statistical programming language and use this to custom code what you need.

RPy is probably your best bet. (MATLAB would work great, but its probably a lot more than you'd want to spend)

 

If you don't know how to program, you might be able to convince someone to throw together some code for you...

[mgoetze]

http://xkcd.com/882/

I was already thinking of this comic when reading Bud's previous thread, but couldn't be bothered to go look for the URL. ;)

[PeterAlan]

Software such as DealComposer, Dealmaster Pro, and Dealer4 will show you high card point averages and total number of balanced hands, voids, singletons, and suits at least 7-cards long for a set of computer generated pre-dealt hands.

 

Occasionally I compare our local clubs pre-dealt hands (in PBN file format) with the following connected statistics:

 

High Card Points: 10.0000000000 per hand

Balanced (4333, 4432, 5332): 0.4760415243 average per hand

Voids: 0.0511637922 average per hand

Singletons: 0.3202474398 average per hand

7+ card suit: 0.0403212924 average per hand

 

But is there any other software that can examine a PBN data file for more than HCP, balanced hands, voids, singletons, and 7+ card suits? I would like to check some other distributional statistics other than these most common ones.

 

Bud H

Before you go looking for a solution, I suggest you could do with a clearer definition of your problem. What do you have in mind by "some other distributional statistics"? Do you want to be able to interact with this analysis software, or just to be given more details? Etc ...

[inquiry]

Bud you can do this yourself with microsoft excel (we will short cut here in this example).

 

Import the pbn file into excel. use the filter function to display only the lines that begin

[Deal " (include the space and the quote mark to avoid getting the [Dealer tag)

Copy all those lines and paste on a new worksheet, starting in cell A2

use find and replace and Delete [Deal "?"

Use the text to columns, fixed length, such that the four hands get a column, so that you ahve hands in column A, B, C, and D.

 

Now you can extract what you want. To extract HCP in each cell use the following equation (this if for cell A2).

 

=((LEN(A2)-LEN(SUBSTITUTE(A2,"A","")))*4)+((LEN(A2)-LEN(SUBSTITUTE(A2,"K","")))*3)+(LEN(A2)-LEN(SUBSTITUTE(A2,"Q","")))*2+LEN(A2)-LEN(SUBSTITUTE(A2,"J",""))

 

To extract spades for a cell, use the following equation, this finds the first "." in the string, and subtracts that period, giving you the length of spades. If there is a spade void, for instance, the first period is at position "1", so 1-1 = 0, or the void, etc....

=SEARCH(".",A2)-1

 

To find the number of hearts, you use the following, where in this example F2 is the number of spades...

=SEARCH(".",A2,(SEARCH(".",A2)-1)+2)-(SEARCH(".",A2)-1)-2

 

(note, that if you had the number of spades in a cell, say F2, that the equation for hearts could simplify to....

=SEARCH(".",A2,F2+2)-F2-2)

 

The minus "2" is to remove from the count the space taken up by the two periods (one after spades, one after hearts... you have to find the period to know where hearts end. The -F2 or the -(SEARCH(".",A2)-1) is to remove the count for the number of spades in the hand.

 

Here is the equation for diamonds, assuming the following, the number of spades is in cell F2, the number of hearts is in G3, and the hand being looked at is in A2.

=SEARCH(".",A2,F2+G2+3)-F2-G2-3

 

If you placed spades, hearts, and diamonds in columns F, G, and H, then clubs is easy,

=13-SUM(F2:H2)

 

You can use excel to extract anything else you like, including the nubmer of singleton ♦7's if you like.

 

The stats you want is then up to you.... you can recombine the suit lengths, for instance to get a format like 5=3=3=2, 4=4=4=1, etc. You can use pivot tables or plots, or histograms, etc to get whatever you like.

 

If you have any trouble with this, you can email me your PBN file, and I will get it all chopped up in the this format and email you an excel spreadsheet back, or you can tell me what you want to beat out of the data, and I will see if I can set up a spreadsheet to do it for you and email that to you.

 

 

[hrothgar]

Bud you can do this yourself with microsoft excel (we will short cut here in this example).

 

I don't think that Excel is a practical choice for the type of analysis that Bud wants to do.

 

Let's assume that we wanted to use a Chi Square test to test a given null hypothesis...

Most of these events are rare and as a rule of thumb I've never liked using a chi square test if the expect frequency is less than 5.

 

You're going to need a really big sample size before you expect to see 5 8+ card suits in a a set of hands.

The amount of manual manipulation necessary seems untenable.

[inquiry]

9

I don't think that Excel is a practical choice for the type of analysis that Bud wants to do.

 

Let's assume that we wanted to use a Chi Square test to test a given null hypothesis...

Most of these events are rare and as a rule of thumb I've never liked using a chi square test if the expect frequency is less than 5.

 

You're going to need a really big sample size before you expect to see 5 8+ card suits in a a set of hands.

The amount of manual manipulation necessary seems untenable.

 

Richard, I know you use to work for MATLAB, and I am aware of its power. But not everyone owns a copy, nor wants to go to the expense of purchasing it, much less learning the programming language to use it, and get the degree is stastics to know how to use it properly. Yet the majority of people who mess around on windows machines own a copy or can find a copy of excel.

 

Excel can handle a lot of pbn hands with breeze. As I test, I ran 20,000 PBN hands from ACBL tournaments (which don't use uploaded hands).

 

In those 20,000 hands there were 388 hands with an 8 card suit, 25 hands with a nine card suit, and 1 hand with a ten card suit. I could have just as easily looked at 100,000 hands if I had a PBN file with 100,000 hands in it.

 

There were 3,653 hands with at least one of the four players held at least one void

There were only 15 hands out of 20,000 where the distribition of all four hands was 4333.

 

You can beat a lot of data out... and you can summarize it in a lot of different ways, without much skill. For example, here is a breakdown of just North;s HCP over 20,000 hands, which averages 9.989 points per hand for North.... close enough for me without a stat package.

 

0 69 1 167 2 280 3 502 4 759 5 1028 6 1310 7 1667 8 1792 9 1862 10 1869 11 1740 12 1615 13 1366 14 1080 15 896 16 690 17 483 18 315 19 215 20 141 21 65 22 51 23 20 24 6 25 9 26 2 27 1

[hrothgar]

Richard, I know you use to work for MATLAB, and I am aware of its power. But not everyone owns a copy, nor wants to go to the expense of purchasing it, much less learning the programming language to use it, and get the degree is stastics to know how to use it properly. Yet the majority of people who mess around on windows machines own a copy or can find a copy of excel.

 

Comment 1: If you are going to bother running this type of analysis, at least do it correctly. There is a reason that hypothesis testing was developed. If you insist on doing this in Excel, you find plenty of references to running chi square tests in Excel on the web.

 

Comment 2: There are a lot of issues with Excel's numerics. You probably won't get burned on a simple analysis but I would never recommend using Excel for anything you care about.

 

Comment 3: If you look at my original post, you'll see that I recommended using a combination of R and Python based on cost

[inquiry]

Comment 1: If you are going to bother running this type of analysis, at least do it correctly. There is a reason that hypothesis testing was developed. If you insist on doing this in Excel, you find plenty of references to running chi square tests in Excel on the web.

 

Comment 2: There are a lot of issues with Excel's numerics. You probably won't get burned on a simple analysis but I would never recommend using Excel for anything you care about.

 

Comment 3: If you look at my original post, you'll see that I recommended using a combination of R and Python based on cost

 

Richard, I don't care to run chi-squared test on bridge data. I doubt that BudH (the op) does either. Did you read his post, which is key here? His level of interest does not appear to be statistical testing. From his other post on this type of thing, he seems interested in seeing if his dealing program at his club was giving normal hand patterns or not.

 

He is probably interested in just checking the hands for peace of mind... not make a federal case out of it. He problably wants something like the following, The theoretical data was copied from Richard Pavlicek;'s Against all odds webpage, the bbo hands were the first 20,000 deals in a custom BB0 acbl tournmanent datafile in a bridgebrowser database.

hand 
pattern              theoretical                  bbo hands
4=3=3=3          10.53613032               10.5275
4=4=3=2          21.55117565               21.51
4=4=4=1            2.99321884                 2.91375
5=3=3=2         15.51684646               15.38625
5=4=2=2         10.57966804               10.56125
5=4=3=1         12.93070539               13.075
5=4=4=0      1.243337056               1.2375
5=5=2=1           3.173900413               3.155
5=5=3=0           0.895202681               0.8975
6=3=2=2      5.642489623               5.60625
6=3=3=1           3.448188103               3.505
6=4=2=1           4.702074686               4.73
6=4=3=0           1.326226194               1.33
6=5=1=1      0.705311203               0.67625
6=5=2=0      0.651056495               0.67625
6=6=1=0      0.072339611               0.07125
7=2=2=2           0.512953602               0.54375
7=3=2=1           1.880829874               1.945
7=3=3=0      0.265245239               0.25625
7=4=1=1      0.391839557               0.40625
7=4=2=0           0.361698053               0.34875
7=5=1=0           0.108509416               0.09625
7=6=0=0      0.005564585               0.01125
8=2=2=1           0.192357601               0.225
8=3=1=1           0.117551867               0.12375
8=3=2=0      0.108509416               0.0975
8=4=1=0           0.045212257               0.05
8=5=0=0           0.003130079               0.005
9=2=1=1           0.017810889               0.01
9=2=2=0      0.00822041                 0.00875
9=3=1=0           0.010047168               0.01125
9-4-0-0                     0.000966074               0.00125
10-2-1-0            0.001096055               0
10-1-1-1       0.000395798               0
10-3-0-0            0.000154572               0
11-1-1-0            2.49103E-05               0
11-2-0-0            1.14971E-05               0
12-1-0-0       3.19363E-07               0
13-0-0-0            6.3E-10                       0

 

Or he might be interested in probing chance of a hand with no card higher than a ten, out of the 80,000 individual hands in 20,000 deals, there were 275 (0.344%, theoretical 0.364%) or hands with no card higher than a nine (41 out of 80,000, for 0.0513%, theoretical number 0.0547%).

 

Or how many hands have a suit headed by AKQJ? (647, or 1.06%).. there were 11 of those dealst where AKQJ occurred in two suits. I didn't break down if this was in the same hand or different hands. Stuff like this is easy to extract, which I think is what he wants, and there is no reason to limit to the search to 20,000, that is just the number I used to see if he was interested. I offered to give him the excel sheet or to probe his data if he wants to send it to me (if he is uncomfortable with excel). Maybe you could step up and offer to do the MATLAB for him if my solution doesn't fit his needs. Somehow, I think this is the kind of thing he wants to do, however. So I set up excel to solve what he I thought he wanted.

[hrothgar]

 

Richard, I don't care to run chi-squared test on bridge data. I doubt that BudH (the op) does either. Did you read his post, which is key here? His level of interest does not appear to be statistical testing. From his other post on this type of thing, he seems interested in seeing if his dealing program at his club was giving normal hand patterns or not.

 

 

Just to be clear, you want to determine whether your dealing program is generating "normal hand patterns" but not do "statistical testing"?

How, pray tell, are you going to determine what does / does not constitute an acceptable result?

 

The entire point behind statistical testing is to establish a standard methodology to answer this question. If you're just going to make a random assertion based on gut feel why bother to look at the data?

[Trinidad]

Richard,

 

Not all statistics are about testing dealer software. And let's face it: Yes, Mathlab will do a great job at the statistical testing, but you still need someone with a knowledge of statistics to interpret the results. (To most people, "chi squared test" sounds as alien as "Mitä kuuluu?".)

 

I could imagine that Bud wants to compare how he is scoring on different types of hands. Does he do well on distributional hands? Does he do well when his side has the majority of the HCPs?

 

Maybe in half a year he will get the idea that they don't do well on distributional hands where the opponents own the hand. He concludes that he should look into his preempting style. Ben's Excel code will be just fine for that.

 

Rik

[hrothgar]

Richard,

 

Not all statistics are about testing dealer software. And let's face it: Yes, Mathlab will do a great job at the statistical testing, but you still need someone with a knowledge of statistics to interpret the results. (To most people, "chi squared test" sounds as alien as "Mitä kuuluu?".)

 

I could imagine that Bud wants to compare how he is scoring on different types of hands. Does he do well on distributional hands? Does he do well when his side has the majority of the HCPs?

 

Maybe in half a year he will get the idea that they don't do well on distributional hands where the opponents own the hand. He concludes that he should look into his preempting style. Ben's Excel code will be just fine for that.

 

Rik

 

Comment 1: Bud specifically stated in an earlier version of the same thread that his goal was to validate that the dealer program his club is using is generating fair deals

 

Comment 2: I never recommended using MATLAB and pointed out that you can use Excel for a chi square test

[inquiry]

Richard,

 

First, you poo-poo excel.....

 

I don't think that Excel is a practical choice for the type of analysis that Bud wants to do.

 

Let's assume that we wanted to use a Chi Square test to test a given null hypothesis...

Most of these events are rare and as a rule of thumb I've never liked using a chi square test if the expect frequency is less than 5.

 

You're going to need a really big sample size before you expect to see 5 8+ card suits in a a set of hands.

The amount of manual manipulation necessary seems untenable.

 

 

Then you defend your first choice, (R and python, assuming budH knows anything about either), and continue to poo-poo excel ("I would never recommend Excel for anything you care about).

 

Comment 1: If you are going to bother running this type of analysis, at least do it correctly. There is a reason that hypothesis testing was developed. If you insist on doing this in Excel, you find plenty of references to running chi square tests in Excel on the web.

 

Comment 2: There are a lot of issues with Excel's numerics. You probably won't get burned on a simple analysis but I would never recommend using Excel for anything you care about.

 

Comment 3: If you look at my original post, you'll see that I recommended using a combination of R and Python based on cost

 

Now you seem to be advocating you did mention you COULD use excel (but of course you would never recommend it, see above).

Comment 1: Bud specifically stated in an earlier version of the same thread that his goal was to validate that the dealer program his club is using is generating fair deals

 

Comment 2: I never recommended using MATLAB and pointed out that you can use Excel for a chi squaretest

 

For anyone interested, excel does have problem with Chi squared testing for some extreme chi squared distributions, which might have something to do with Richard reluctance to recommend it, even if it would allow people to probe the hand records just the way BudH was looking (did anyone see any chi squared or p-values in Bud's OP? He just wants more ways to probe his data, and with excel this is straight forward and relatively easy. Another example? Here is the number of hands with at least one singleton Ace=1611, and number of hands with at least one AK doubleton 697 (I didn't bother to write an equation to check for more than one singleton ace in one or more hands on a deal, just if at least one singleton Ace existed... same for AK).

 

Anyway, just for which Richard, here is the observed hand patterns (33 of the 39 possible ones) found in the 80,000 hands found in the 20,000 unique deals. Just looking at the numbers, it might appear that eight card suits are dealt too often (there were 401 combined 8 card suits, and only 373.4 were "expected"). However, the sample size is still fairly small relative to all possible deals, and if it matters, the chi squared test gave a p value of 0.738184, suggesting that the null hypothesis (there is no statistical difference between the observed distribution and the theoretical distribution) can not be rejected (p would have to be something like 0.05 or less). So the observed deviations appear to be due to random chance alone, rather than some problem with the dealing program. You might want to check a larger size, and of course, I didn't test budH's dealing program, this was random bbo hands (I guess you could say the bbo dealing program). Anyway, the data is below for people to throw darts at, or use their own statistical programs to detemine the chi squared value and p values.

 

And look... assuming Bud has excel, he doesn't need anything else.... which, after all, was my point. http://www.bridgebase.com/forums/public/style_emoticons/default/wink.gif

 

 

PATTERN	OBSERVED	THEORETICAL
4=3=3=3              8422      8428.9
4=4=3=2            17208    17240.9
4=4=4=1              2331      2394.6
5=3=3=2            12309    12413.5
5=4=2=2              8449      8463.7
5=4=3=1            10460    10344.6
5=4=4=0                990        994.7
5=5=2=1              2524      2539.1
5=5=3=0                718        716.2
6=3=2=2              4485      4514
6=3=3=1              2804      2758.6
6=4=2=1              3784      3761.7
6=4=3=0              1064      1061
6=5=1=1                541        564.2
6=5=2=0                541        520.8
6=6=1=0                  57          57.9
7=2=2=2                435        410.4
7=3=2=1              1556      1504.7
7=3=3=0                205        212.2
7=4=1=1                325        313.5
7=4=2=0               279        289.4
7=5=1=0                 77          86.8
7=6=0=0                   9            4.5
8=2=2=1               180         153.9
8=3=1=1                 99           94
8=3=2=0                 78          86.8
8=4=1=0                 40          36.2
8=5=0=0                   4            2.5
9=2=1=1                   8          14.2
9=2=2=0                   7            6.6
9=3=1=0                   9            8
9=4=0=0                   1            0.8
10=2=1=0                 1            0.9
                         80000     79999.8

[TimG]

These observed and theoretical numbers don't do much to help Bud out. The skeptic at his club will just say: there are supposed to be 1505 7321 shapes and there were actually 1556, I told you the dealer program does funny things. Bud needs to know whether the 1556 observed hands is within the expected range of results with some sort of % confidence. It's been a long time since my statistics classes, I don't know if what he needs are confidence intervals or chi square tests or something else, but Bud definitely needs some sort of statistical testing rather than just showing raw numbers.

[inquiry]

These observed and theoretical numbers don't do much to help Bud out. The skeptic at his club will just say: there are supposed to be 1505 7321 shapes and there were actually 1556, I told you the dealer program does funny things. Bud needs to know whether the 1556 observed hands is within the expected range of results with some sort of % confidence. It's been a long time since my statistics classes, I don't know if what he needs are confidence intervals or chi square tests or something else, but Bud definitely needs some sort of statistical testing rather than just showing raw numbers.

 

well, these numbers even with stats are not going to help bud out, as these were not generated using "HIS" hands. And there is absolutely no reason to limit the test ot 20,000 deals. He should use 250,000 deals (giving a million unique hands)... or maybe even more. Still, the data presented above easily passes the Chi-Square goodness-of-fit test with unequal expected frequencies, he could even quote the p values (of course, not his deals).... The people at his club will not understand or accept that kind of validation either.

[Trinidad]

You need to know Russian to understand Russian. You need to know statistics to understand statistics.

 

Seems obvious to me, isn't obvious to everyone.

 

Rik

[TimG]

well, these numbers even with stats are not going to help bud out, as these were not generated using "HIS" hands. And there is absolutely no reason to limit the test ot 20,000 deals. He should use 250,000 deals (giving a million unique hands)... or maybe even more. Still, the data presented above easily passes the Chi-Square goodness-of-fit test with unequal expected frequencies, he could even quote the p values (of course, not his deals).... The people at his club will not understand or accept that kind of validation either.

They may not understand, but they're more likely to accept. But, it's not enough to say "they easily pass the Chi-Square goodness-of-fit test". He needs to show his work or give p values (and explain what those mean).

 

I think Bud wants to do two things: test the actual hands played for a month, then two months, etc which will obviously be a small sample; and test the hand generator on a larger sample.

[hrothgar]

well, these numbers even with stats are not going to help bud out, as these were not generated using "HIS" hands. And there is absolutely no reason to limit the test ot 20,000 deals. He should use 250,000 deals (giving a million unique hands)... or maybe even more. Still, the data presented above easily passes the Chi-Square goodness-of-fit test with unequal expected frequencies, he could even quote the p values (of course, not his deals).... The people at his club will not understand or accept that kind of validation either.

 

On the 20,000 versus 250,000 front: There is this handy little principal in stats known as asymptotic convergence. You don't need a quarter million hands. As I mentioned earlier in this thread, in the case of a chi square goodness of fit test, you want the expected number of observations to be at least 5.

 

http://www.talkstats.com/showthread.php/22609-Sample-Size-for-Chi-Square-test

 

(BTW, one of the limitations with Excel is that it still works very poorly if the number of rows increases beyond 65,536)

 

Personally, I refuse to accept that whether the people at the club with understand or accept the results of the analysis has anything to do with the choice to run the Chi square test.

 

1. If you genuinely believe that you're dealing with people to are immune to logic and reasoning then you should be blowing them off from day one. When they bitch about the deals do your best to ignore them.

 

2. However, if you are going to go to the time and bother of analyzing the data, then you should do so to the best of your abilities. To quote Hunter S. Thompson, "If a thing like this is worth doing at all, it's worth doing right".

 

FWIW, I wouldn't get all bent out of shape if someone went off and analyzed the data and didn't present me with a formal hypothesis test provided that they didn't know any better. As you folks have noted, not everyone has taken a real course in statistics. If someone doesn't know any better, so be it. Use it as a learning opportunity.

 

I might even prefer if the basic version of the presentation didn't consider these issues. (When I present to our senior management, I don't have confidence intervals in the PowerPoint deck. However, I make damn sure that I have performed a legitimate analysis and have back up slides available because if I don't and I get called on it I'm going to look like I don't know what I'm talking about)

 

I find your attitude baffling: You're willing to do 99% of the work, including the real heavy lifting. However, some perverted sense of stubbornness is preventing you from actually crossing the finishing line and performing a legitimate / useful analysis.

[mikestar13]

No point in doing any math if the goal is to convince skeptics among average club players. An example from my own experience as bridge director at a senior center. One Christmas season, we were having a special holiday game -- a two section Michell. As a treat for the players, I pre-duplicated the boards for both sections so that the players didn't have to do any dealing, and the two sections could play the same boards. The only response I got for my efforts was 24 boards of bitching about "these damned computer dealt hands", which I had lovingly prepared and hand dealt. Don't ever waste your chi-squares on club players!

[blackshoe]

If it were me, I'd just want to do one thing — and that's tell the skeptic to just STFU. :P

[BudH]

Thanks for the responses. I'm in San Francisco and just finished playing the finals of the Nail Life Master Pairs. (Unfortuntatly, a slightly below average evening session took me out of the running for a high finish.)

 

I might give the Excel method a try. Tim G is correct in that it will be difficult to convince the skeptics at my club that there isn't any funny business going on.

 

That being said, there were two days in the first few weeks where there were 12 and 14 voids in a session when there would normally be less than 7 voids expected. And looking over the hand records for those two days, I can seen why someone would think something wacky had occurred. But all the other days were somewhat close to normal.

 

So far, for the first 424 deals at our club,

 

Number Expected

 

Balanced 807 806.4

Voids 98 86.8

Singletons 534 542.4

7+ card suit 72 68.4

 

Although the voids are greater than expected, the number of splinters (voids plus singletons) is close to predicted.

 

After trying to defend "computer hands" recently, I was amused when the first hand in the qualifying sessions for the Nail Life Master Pairs had me bid 2S preemptive white vs. white with K876xxx and I found AQJ95 behind me with both black suits splitting 5-0!

 

Bud

[hrothgar]

Tim G is correct in that it will be difficult to convince the skeptics at my club that there isn't any funny business going on.

 

That being said, there were two days in the first few weeks where there were 12 and 14 voids in a session when there would normally be less than 7 voids expected. And looking over the hand records for those two days, I can seen why someone would think something wacky had occurred. But all the other days were somewhat close to normal.

 

Here's the rub...

 

Folks won't ever remember the 3,048 different ways that the hands don't look fishy. They'll simply fixate on the fact that there happened to be too many voids.

 

If you look at enough sessions, you're going to find something that looks "weird".

If you don't, that's a near certain sign that something is wrong with your dealing program.

 

I'm going to attach a well known example from statistics. Which of the following two images looks more random?

 

http://telescoper.files.wordpress.com/2009/04/pointb.jpg?w=450&h=401

http://telescoper.files.wordpress.com/2009/04/pointa.jpg?w=450&h=393

 

Check out the following for an explanation http://blogs.discovermagazine.com/cosmicvariance/2009/04/06/perceiving-randomness/

 

or jump to http://telescoper.wordpress.com/2009/04/04/points-and-poisson-davril/ for a more detailed treatment