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Unusual distributions became the "norm" Cards distribution defies statistics

#41 User is offline   hrothgar 

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Posted 2019-December-14, 20:13

 mlbridge, on 2019-December-14, 19:56, said:

So after #4584, I played in order:

#4769 - 1 hand with a void

#5170 - 4 different hands with a void.

So in 36 boards, 8 different hands had a void and one hand had 2 voids.

Explain to me how that is random.


The basic problem here is that you fundamentally misunderstand basic concepts like sample sizes and the requirement that one formulates hypothesizes BEFORE looking at the data set rather than afterwards.

If you go and look at a small data sample, you'll almost inevitably be able to find some way in which the observed data does not match the expected.

Case in your original posting, you were complaining that there were too many singletons.

I believe the quote was

Quote

More startling is if one looks closer at the single suited hands. One have less than 1% of occurring and 2 have 1.3% chance. So of the 12 hands, N was dealt 3 hands were about a 1% chance of occurring.


Now, after looking at a new set of boards you are advancing the claim that the the hand generator is producing too many voids.

If you want folks to take you seriously, make a specific testable claim about the hands that BBO generates and we can test these against some future day's worth of tournament data.
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#42 User is offline   smerriman 

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Posted 2019-December-14, 20:22

 mlbridge, on 2019-December-14, 19:56, said:

So after #4584, I played in order:

#4769 - 1 hand with a void

#5170 - 4 different hands with a void.

So in 36 boards, 8 different hands had a void and one hand had 2 voids.

Explain to me how that is random.

You're making similar mistakes as last time.

The probability a *given player* (eg South) has a void is about 5%.

The probability at least one of the four players for a given deal has a void is about 20%.

Over 36 boards, the probabilities of seeing a total of x voids (approximately):

0: 0.1%
1: 0.5%
2: 1.8%
3: 4.2%
4: 7.8%
5: 11.4%
6: 13.9%
7: 14.8%
8: 13.6%
9: 11.0%
10: 8.2%
11: 5.5%
12: 3.4%
13: 1.9%
14: 1.0%
15: 0.4%

All of 5, 6, 7, 8 and 9 voids occur over 11% of the time, so aren't unusual in the slightest.
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#43 User is offline   mlbridge 

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Posted 2019-December-14, 22:30

So continuing on, next tourney I played in is #5170.

There were 4 boards with a least one void. One of the boards have both opp with a void.

By the way, I do not noticed such distributions when playing in our imps tournaments. Only these robot rebate tourneys.
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#44 User is offline   smerriman 

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Posted 2019-December-15, 00:32

Now you're just making things up. I checked #5170, and there wasn't a single board that had two voids.

You had a typo; you meant #5519.

4 voids is not uncommon; it happens on average about once every four tournaments, and you're finding it surprising.

Even 5 voids isn't strange; the chance you've seen a 5 void tournament over 4 tournaments is about 36%.

And you only need to play 3 tournaments to make it more likely that you've seen a deal with 2 voids than you haven't.

You're just making yourself look silly now.
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#45 User is offline   smerriman 

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Posted 2019-December-15, 01:21

To top things off, guess how many voids you saw in the two Robot Rebate tournaments before the two you started reporting?

1 and 1.

Below average.

Bet you didn't pay much attention to those.
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#46 User is offline   mlbridge 

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Posted 2019-December-15, 01:33

All I know is in 48 boards, 4 tourneys, I have 12 boards with voids. Two of them have 2 voids.

According to your math, I should have about 20% of 48 boards = 9.6. I think 12 is much greater than 9.6, especially on a percentage basis. And that's not including the extra 2 voids.

You also indicate that 4 voids happen about once in every 4 tournaments. In my case, it happened 3 out of 4.

My analysis also includes the tourney with just 1 void.

I am not sure how many here play in the robot rebate tourneys. My personal experience is that those hands are far more distributional than the regular tourneys.
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#47 User is offline   smerriman 

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Posted 2019-December-15, 02:12

 mlbridge, on 2019-December-15, 01:33, said:

According to your math, I should have about 20% of 48 boards = 9.6. I think 12 is much greater than 9.6, especially on a percentage basis.

This is completely incorrect statistically. With such a tiny sample, a standard 95% confidence interval would be [4.16,15.03]. You would only be able to claim - and of course, not prove, since it can still happen 5% of the time - there is evidence of non-randomess if your average fell outside this range. Anything inside the range fits the null hypothesis that there is no bias.

 mlbridge, on 2019-December-15, 01:33, said:

You also indicate that 4 voids happen about once in every 4 tournaments. In my case, it happened 3 out of 4.

Again, completely inconsequential statistically.

 mlbridge, on 2019-December-15, 01:33, said:

My analysis also includes the tourney with just 1 void.

I was referring to the two prior to all of the ones you've listed. As of course, you only started measuring voids because you suddenly noticed a lot of them in one tournament; before that you were focusing on something unrelated (and also incorrect). Choosing when to start measuring heavily biases the results.
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#48 User is offline   hrothgar 

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Posted 2019-December-15, 02:53

Not sure why I'm bothering, but...

For kicks and giggles, I ran the following command in R

> 1 - pbinom(3, size=12, prob=.051*4)
[1] 0.2161656

In English, this tells me the probability that I will see 4+ voids in a tournament of 12 boards.
I am calculating this by looking at the probability that I will generate 0, 1, 2, or 3 voids and then subtracting this from 1

Note, I am fudging things by assuming that the probability that you have a void on a board is 4 X (the probability that you have a void in one hand which isn't quite true
Like smerriman says, this is slightly more than 20%

Next, I ran the following command

> rbinom(1000, 1, .2161656)

This command simulates 1000 virtual tournaments and codes a 0 if you had between 0-3 voids and a 1 if you observed 4+ voids.

Note how frequently you see cases where three out of four tournaments have 4+ voids.
There was even one case in which 5 tournaments in a row had 4+ voids.
Weird ***** happens all the time

[1] 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0
[38] 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0
[75] 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0
[112] 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0
[149] 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0
[186] 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
[223] 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 1 0 0 1 0 0
[260] 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1
[297] 0 0 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1
[334] 1 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0
[371] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 0 0 1 0 1 0 0 0
[408] 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0
[445] 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 1 0 1 1 1
[482] 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
[519] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
[556] 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0
[593] 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0
[630] 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0
[667] 0 1 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0
[704] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1
[741] 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0
[778] 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
[815] 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0
[852] 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1
[889] 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0 1
[926] 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0
[963] 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 0 0 0 1 1 1 0 0 0 1 1 0
[1000] 0
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#49 User is offline   barmar 

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Posted 2019-December-16, 10:37

I just checked the last 90 days of mlbridge's hands in the database used by myhands (so it doesn't include daylongs and challenges).

There were 4055 hands. South had 176 voids, West had 199 voids, and North had 205 voids. We don't store East's hand in the database, software that displays hands calculates it from the other 3 hands, so I couldn't easily get the number of voids there. 37 of the hands had voids in multiple seats.

The best-hand feature is almost certainly the reason why South has fewer voids than the other seats, since a void contributes 0 HCP (BH doesn't add anything for distribution).

Someone with better statistics knowledge can tell us how far off this is from expectations.

#50 User is offline   smerriman 

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Posted 2019-December-16, 18:30

Taking best hand into account, my calculations for 95% confidence are:

South: (174.1,228.3)
Other seats: (182.1,237.4)
Multiple voids amongst South/West/North only: (28.7,53.8)

All those numbers lie in these ranges (if anything slightly below average, but not significantly enough).
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#51 User is offline   steve2005 

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Posted 2019-December-18, 17:38

 pink flag, on 2019-December-09, 16:31, said:

I won't do that, cos i arranged my game with the diss distributions. I talked to approximate 10 players, who feel exactly the same as me (all are very good players). If anyone believes this ok, if not, ok. But the way Mihai Buta is attacked here by some members is simply disgusting. Belive in what you want, but don't blame someone for an opinion.
Ok, lets say somehow your correct despite evidence to the contrary.
Then you have a big advantage versus us plebs who are expecting mundane distribution.
Just play for offside Queens!
Play for bad splits.
Bid conservatively as you know your getting bad splits.
Since your right you should get over 70% results easy.
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#52 User is offline   steve2005 

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Posted 2019-December-18, 17:48

 mlbridge, on 2019-December-10, 10:47, said:

I may not be a stat whiz. But if someone tells me that the probability of one quarter of the hands (with odds close to 1%) dealt to one player is somewhat normal, I would certainly question that.
simple math.
you see a hand that has a 1% probability. Think that is wierd..
but there are actually more than 6 different hand type all of which have 1% probability.
If any of these other hands shows up you would be just as surprised
but the probability of any 1% hand showing up is substantially higher.
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