Freaks

[jahol]

I used to play in the far best bridge club in my small (bridge country). Far best opponents, good competitions, nice atmosphere.. But there is one point, I have become a bit suspicious over years... random generator used for cards shuffling.

In general, I hate the idea of some average bridge players, that it is fine, when the card distributions are very unbalanced, with some portion of goulash, because the play in not very much interesting, when the boards are "normal". I think, in general, that bridge player should master just the "normal" boards to be good or best.

 

What do you think about the following statistics from yesterday competition in my club:

 

40 singletons

11 voids

 

1 x 8 cards in one suit hand

8 x 7 cards in one suit hand

22 x 6 cards in one suit hand

 

1 x 7-5 distribution

2 x 6-6 distribution

3 x 7-4 distribution

4 x 5-5 distribution

 

and all that in 28 boards!

 

In addition, the three most unbalanced freaks were real freaks also from other points of view

 

7-5 distribution:

AKQ8732---AKQ4---void---9

 

6-6 distribution No.1:

Q---AK7542---void---AKQJ53

 

6-6 distribution No.2:

void---AQJ1097---A---AK9876

 

I have been working for 25 years as mathematical statistician, but I am not sure what to think about this. Can the random generator get sick?

[matmat]

i would ask the director whether, perhaps, this wasn't a goulash tournament by accident.

[Free]

If you have a TRNG (true random number generator) it can't get sick. I've done some simulations and a TRNG works very well for statistical purposes.

 

A TRNG is not as easy to use (mine is slower than a PRNG), and many use a PRNG (pseudo RNG) based on a seed. These pass several statistical tests but not all. I've done some simulations with this as well (even with a 4096 bits PRNG), and I don't seem to have any problems. Ofcourse it's not easy to be conclusive because we're working with huge numbers. We can't do heavy simulations because the computers are too slow, and I'm not a mathematician that can calculate all the odds.

 

Even though the chance is very small to have a sequence like the one you describe, it is still possible. Is it sick because it produces one like this? No. But if this persists, then there might be something wrong indeed. It's like a plane falling on your roof: the chance is very small, but it happens. As long as it doesn't happen every week, there's not much to worry about.

 

Obviously you can tweak your RNG so it produces more extreme or more "normal" hands. If you discard every deal with 2 or more balanced hands, you'll get more distributional hands for sure.

[helene_t]

According to http://www.mathkb.com/Uwe/Forum.aspx/math/...ng-Bridge-Hands

in 28 boards you expect:

 

5.6 voids

17 6-cards

4.4 7-cards

 

So it seems that your statistic is somewhat weird.

 

If anything is wrong, I wouldn't attribute it to the fact the a pseudo random number generator is used. I would expect it to be a flaw in the bridge-specific part of the algorithm. The reason I say this is that pseudo-random number generators have been tested vary rigorously and for purposes where the accuracy is much more important than it is in bridge. Also, it is very easy to verify that serious pseudo-random number generators are good enough for this purpose. For example, the following R-script that deals 100,000 hands (25,000 deals) :

myhands = apply(as.array(1:100000),1,function(x)sample(52,13))

clubs=colSums(myhands<14)

diamonds=colSums(myhands<27)-clubs

hearts=colSums(myhands<40)-clubs-diamonds

spades=13-hearts-diamonds-clubs

sum(spades==0 | hearts==0 | diamonds==0 | clubs==0)

produced 5103 hands with at least one void, while the above reference says approximately 5100.

 

Still, you statistics are not so extreme as to rule out that it happened by chance. Could you post that statistics for the next couple of nights also? Then I am happy to make a formal statistical analysis, to see if the number of singletons, voids, 6-cards and 7-cards are excessive.