[mlbridge]

In tourney #9779, played on 12/09/2019, the hands were closer to probability as 6 were balanced, 4 were two suited and 2 were single suited. However, what is startling is again the percentage of being dealt a certain distribution. On hands #2 & #6, N was dealt hands with about 1% chance of occurring. So in my two combined tourneys, on 24 hands, N was dealt 5 hands with about 1% chance.

If one examines closer, on hands #9 and #11, W was dealt hands of 6-5-2-0 and 7-5-2-0. fractional percentages of occurring.

On hand # 12, S was dealt 7-5-1-0

IMO, not only are the probability not normal, but also the percentage of extreme distributions is not normal.

Note I did not pick tourneys randomly. Just picking the last two I played in.

#9779
#1 B 4-4-3-2
#2 S 6-4-3-0 %0.0132623
#3 B 5-3-3-2
#4 B 4-3-3-3
#5 B 4-3-3-2
#6 T 5-5-3-0 %0.00895203
#7 T 5-4-2-2
#8 S 6-4-2-1
#9 T 5-4-3-1 W-6-5-2-0 %0.00651056
#10 B 4-3-3-2
#11 B 5-3-3-2 W-7-5-2-0 %0.00361698
#12 T 5-4-2-2 S-7-5-1-0 %0.00108509

[nige1]

mlbridge, on 2019-December-09, 23:31, said:

I played in mostly the $1 robot rebate tourneys. My experience is that the distribution is abnormal in those tourneys. To illustrate, I am pulling the two most tourneys. I am showing the distribution of north (my dummy partner).I coded the hands if B (balance), S (single suited), T (two suited) and 3 (three suited).This post is for tourney #612, played on 12/10/2019.Of the 12 hands for N, 5 were balanced, 5 were single suited and 2 were two suited. Clearly the percentages don't match the probability.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.
#612
#1 S 6-3-2-2
#2 S 6-4-3-0 %0.0132623
#3 B 4-3-3-3
#4 T 5-4-2-2
#5 S 6-4-2-1 %0.0470207
#6 S 7-2-2-2 %0.00512954
#7 B 4-4-3-2
#8 S 6-4-3-0 %0.0132623
#9 B 5-3-3-2
#10 B 4-3-3-3
#11 B 5-3-3-2
#12 T 5-4-2-2

mlbridge, on 2019-December-09, 23:38, said:

In tourney #9779, played on 12/09/2019, the hands were closer to probability as 6 were balanced, 4 were two suited and 2 were single suited. However, what is startling is again the percentage of being dealt a certain distribution. On hands #2 & #6, N was dealt hands with about 1% chance of occurring. So in my two combined tourneys, on 24 hands, N was dealt 5 hands with about 1% chance.If one examines closer, on hands #9 and #11, W was dealt hands of 6-5-2-0 and 7-5-2-0. fractional percentages of occurring.On hand # 12, S was dealt 7-5-1-0IMO, not only are the probability not normal, but also the percentage of extreme distributions is not normal.Note I did not pick tourneys randomly. Just picking the last two I played in.
#9779
#1 B 4-4-3-2
#2 S 6-4-3-0 %0.0132623
#3 B 5-3-3-2
#4 B 4-3-3-3
#5 B 4-3-3-2
#6 T 5-5-3-0 %0.00895203
#7 T 5-4-2-2
#8 S 6-4-2-1
#9 T 5-4-3-1 W-6-5-2-0 %0.00651056
#10 B 4-3-3-2
#11 B 5-3-3-2 W-7-5-2-0 %0.00361698
#12 T 5-4-2-2 S-7-5-1-0 %0.00108509

Interesting but, it might be better if

• Your representative samples of consecutive deals were bigger
• You formulated hypotheses before you examined your sample.

Wikipedia said:

In a discussion between the mathematicians G. H. Hardy and Srinivasa Ramanujan about interesting and uninteresting numbers, Hardy remarked that the number 1729 of the taxicab he had ridden seemed "rather a dull one", and Ramanujan immediately answered that it is interesting, being the smallest number that is the sum of two cubes in two different ways.

[miamijd]

I play all of the daily robot tourneys almost every day. Distributions seem pretty true to me. Half my finesses win. It does seem, however, that lobbing finesses win more than 50%, pushing finesses win 50%, and xx opposite AQ win less than 50%. Probably just my imagination.

[mlbridge]

nige1, on 2019-December-09, 23:50, said:

Interesting but, it might be better if

• Your representative samples of consecutive deals were bigger
• You formulated hypotheses before you examined your sample.

I chose the last 24 hands I played with the robot. I looked at it from my partner's distribution. I did not form any hypotheses before analyzing these numbers. My experience is from playing in hundreds of these tourneys where it is almost a failure to double robot's contracts as they usually make because of distribution. The OP made me looked at it more closely. If I have time, I will do more.

[mlbridge]

miamijd, on 2019-December-09, 23:51, said:

I play all of the daily robot tourneys almost every day. Distributions seem pretty true to me. Half my finesses win. It does seem, however, that lobbing finesses win more than 50%, pushing finesses win 50%, and xx opposite AQ win less than 50%. Probably just my imagination.

Are you playing in free tourneys or paid ones?

[FelicityR]

From Wikipedia:-

NORM

In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—except for the zero vector, which is assigned a length of zero. A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors (in addition to the zero vector). A norm must also satisfy certain properties pertaining to scalability and additivity which are given in the formal definition below.
A simple example is two dimensional Euclidean space R2 equipped with the "Euclidean norm" (see below). Elements in this vector space (e.g., (3, 7)) are usually drawn as arrows in a 2-dimensional cartesian coordinate system starting at the origin (0, 0). The Euclidean norm assigns to each vector the length of its arrow. Because of this, the Euclidean norm is often known as the magnitude.
A vector space on which a norm is defined is called a normed vector space. Similarly, a vector space with a seminorm is called a seminormed vector space. It is often possible to supply a norm for a given vector space in more than one way.

Bridge is a game of mathematical possibilities, and, Unusual Distributions became this?

(Help! Can someone translate? )

And YES! The forum members have commented on this again, and again, and again......Time to let sleeping dogs lie, or should that be, unusual distributions die?

[smerriman]

Yikes. mlbridge, you have a serious lack of understanding of statistics.

Your definition of "about 1%" seems to be 1.326% or lower.

On a single hand, the probability you are dealt a distribution which is "about 1%" or lower is about 7%; the sum of all of the low probabilities.

In a 12 board tournament, a given player will be dealt two or more "about 1%" hands 20% of the time. Not abnormal at all.

Over 24 boards, a given player will be dealt 5 or more "about 1%" hands about 2.3% of time.

The fact that it happened doesn't mean the deals aren't random.

But wait, this isn't what you measured. Why did you choose North? Was it perchance because you happened to notice that North had some distributional hands, and you didn't pick South because, whoops, that wouldn't have supported your theory?

In a 12 board tournament, the probability you will be able to find a player with 2 or more "about 1%" hands is about 58%. That's right it's actually more likely this will happen than it won't.

Over 24 boards, you'll be able to find a player with five or more 1% hands 9% of the time.

It would be extremely unusual if you *didn't* notice such things happening.

[zhoraster]

johnu, on 2019-December-09, 04:09, said:

This might be the time for another public service announcement.

If you want to get better suit breaks and honors located where your finesses work, you need to subscribe to premium services.

A. Silver Premium membership - "normal" distributions, but finesses only work about 25%
B. Gold Premium membership - "normal" distributions, and finesses work 50%
C. Double Platinum membership - you always get the most even breaks, and finesses work 90%

There's a better one:
D. Ultimate (aka Solitaire) membership - always most even breaks, finesses always work: defenders' cards are rearranged if you misguess. In the case of overtricks, the contract is upgraded to the actual number of tricks taken (unless the contract is (re)doubled).

[hrothgar]

Nigel hits on the key issue here: The importance of formulating a hypothesis BEFORE choosing the data set.

From the sounds of things, mlbridge plays a fair number of robot tournaments.

Might I suggest the following:

1. Let's all (collectively) agree on a hypothesis that we want to test.
2. Having done so, lets agree how we plan to test this.

I recommend that we use next 20 tournaments that mlbridge players after we generate the hypothesis.
The sample is a bit small, but should be sufficient.

[aawk]

Another case of only remembering bad results and blaming the distribution for bad scores. If I learned one thing in bridge is that who gets angry at the table is the one who made the mistake.

[Joe_Old]

I love this thread. Americans are addicted to conspiracy theories, the more irrational, the better. Facts are irrelevant, to the deceived they are just part of the conspiracy. No one is ever going to convince someone like the poster that his worldview is skewed.

That's why conspiracy theories are central to the American psyche: they are a convenient excuse for failures that plainly can't be our own.

[miamijd]

mlbridge, on 2019-December-09, 23:55, said:

Are you playing in free tourneys or paid ones?

Paid

[mlbridge]

smerriman, on 2019-December-10, 02:42, said:

Yikes. mlbridge, you have a serious lack of understanding of statistics.

Your definition of "about 1%" seems to be 1.326% or lower.

On a single hand, the probability you are dealt a distribution which is "about 1%" or lower is about 7%; the sum of all of the low probabilities.

In a 12 board tournament, a given player will be dealt two or more "about 1%" hands 20% of the time. Not abnormal at all.

Over 24 boards, a given player will be dealt 5 or more "about 1%" hands about 2.3% of time.

The fact that it happened doesn't mean the deals aren't random.

But wait, this isn't what you measured. Why did you choose North? Was it perchance because you happened to notice that North had some distributional hands, and you didn't pick South because, whoops, that wouldn't have supported your theory?

In a 12 board tournament, the probability you will be able to find a player with 2 or more "about 1%" hands is about 58%. That's right it's actually more likely this will happen than it won't.

Over 24 boards, you'll be able to find a player with five or more 1% hands 9% of the time.

It would be extremely unusual if you *didn't* notice such things happening.

I choose north because that's my pard. Did not go thru in advance all four to see which one have the most lowest percentage distribution.

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.

[strags]

If you play the Robot Tournaments almost exclusively, as I do, and you suspect that significantly more than half of your finesses lose in those games...you're correct. In fact, one longtime friend and I have a running joke where we will often mention whimsically in our conversations, "Hey, did I tell you that a finesse worked for me on BBO the other day?"

But it has nothing to do with faulty software or unrealistic deal probabilities. It's simply a function of two perfectly innocent factors:

• The "Best Hand for South" format
  
• The opening-lead tendencies of the BBO bots

Put simply: if you're playing a Robot Tournament, you're sitting South and are dealt the best hand at the table. Therefore, you are more likely than your robot North partner to (a) become declarer, and (b) hold high-card tenace positions like AQ or KJ in which you wish to take a finesse.

Ergo, you will be taking these finesses disproportionately into the West hand. And, West will disproportionally happen to be the opening leader.

BBO bots are notoriously passive leaders. That much, I hope everyone agrees on. This is hardly surprising, since there have been a raft of books published in the last 10 years that have analyzed opening lead probabilities and concluded that passive is usually better. Indeed, the one counterexample those books have shown is to lead very aggressively (i.e., away from a king or queen) in a side suit against a small suit slam. And, in my experience, that's also the one time a BBO bot can be counted on to have led away from a royal.

So...in BBO Robot Tournament games, West is usually on opening lead. West will lead very passively, usually from a suit in which he holds no honor above a 10. You will more often finesse (in some other suit) through East and into West because of the "Best Hand" format. Ergo, it's more likely -- I'd wager between 55% and 60% -- that these finesses will lose. There's nothing sinister about this. It's just a consequence of the unusual form of bridge we enjoy on BBO.

[smerriman]

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.

As mentioned, the probability at least one of the four players has 5 of 24 "1%" hands (by your definition) is 9%. It's not "normal", but it will happen regularly enough, so having it happen definitely doesn't mean anything odd is going on.

If you don't understand why, try this calculator:

https://stattrek.com...r/binomial.aspx

The probability of a '1%' hand is 7%, since there are so many '1%' distributions. Fill in 0.07, 24 trials, 5 successes, and you'll see P(X>=x) = 2.3%.

Then for this to apply to all four players is 1 - (1-0.023)^4 = 9%.

(Not this isn't 100% accurate due to the lack of independence, and my calculations earlier were more accurate, but they're close enough).

[barmar]

Those of you having trouble believing the probabilities that smerriman is describing might want to google "birthday paradox".

[mlbridge]

Okay - so I did a different analysis looking at all four hands. From Googling, on a particular hand, it seems that the probability of any player having been dealt a void is about 5.1% So for 12 boards, one would expect less than one instance occurring for the group. Just finished Robot rebate tourney #4584 - 12/14/2019.

W - Two voids, boards 7 & 9

S - One void, board 12

N - One void, board 9.

So on board 9, two players were dealt voids.

Also, W had the most volatile distributions. Of the other 10 boards without voids, W was dealt a singleton 6 times. So on 12 boards, W had 2 voids and 6 singletons.

[hrothgar]

strags, on 2019-December-10, 13:00, said:

If you play the Robot Tournaments almost exclusively, as I do, and you suspect that significantly more than half of your finesses lose in those games...you're correct. In fact, one longtime friend and I have a running joke where we will often mention whimsically in our conversations, "Hey, did I tell you that a finesse worked for me on BBO the other day?"

But it has nothing to do with faulty software or unrealistic deal probabilities. It's simply a function of two perfectly innocent factors:

• The "Best Hand for South" format
  
• The opening-lead tendencies of the BBO bots

Interesting piece

thanks for posting it

[johnu]

hrothgar, on 2019-December-09, 19:08, said:

The quality of the trolls is really declining...

Can we send this one back and get something better?

I find it interesting that pink flag signed up for the forums on the day of their first 2 and only posts which happen to be in this thread.

[mlbridge]

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.