Bias

[maureencro]

Has anybody else encountered the bias against E/A. We only play on Casual, sometimes 2 of us, sometimes 4. When we play foursome we take it in turns to be E/W because we know that E/W always get low point scores. When 2 of us play we always get taken to a table as E/W and again get very low point scores.

[Vampyr]

Has anybody else encountered the bias against E/A. We only play on Casual, sometimes 2 of us, sometimes 4. When we play foursome we take it in turns to be E/W because we know that E/W always get low point scores. When 2 of us play we always get taken to a table as E/W and again get very low point scores.

 

Don’t you read any bridge books or the newspaper? Of course south always has the best hand.😉

[hrothgar]

Has anybody else encountered the bias against E/A.

 

This has been discussed ad nauseum

 

The hand dealers are not biased

[rdylan]

This topic HAS been addressed ad nauseum, and yet people still ask the same question. In fact, there are a lot of people who believe in the EW bias. As a former computer engineer, avid poker player, and lover of statistical analysis, I quickly dismissed these complaints as the usual cognitive illusion. I see many responders to these threads doing the same (in a rather entertaining fashion I might add).

 

But then I started playing with a casual group and quickly began to experience my own cognitive bias against EW, as did the people I play with. Already, no one in our group wants to play EW. So I decided to do my own analysis. I've only just begun, but with 76 hands I can start to see a pattern emerging.

 

The problem isn't actually EW: it's EAST. My initial stats show that N,S,W all run fairly close but that NS averages 2 HCP per hand higher than EW, and it is all attributable to EAST. In our 76 games, EAST has gotten an unusually high number of 9-point hands, and a significantly high number of 8-point hands. What do I mean by unusually high? Over 76 hands, EAST was dealt 19 9-point hands. The odds of that many in 76 hands is approx 1 in 25,000. When you combine that with the 10 8-point hands that EAST was dealt (an unlucky 6% chance), EAST's run of bad luck is 1 in 400,000.

 

Interestingly, EAST has also experienced a significantly lower deviation from the mean than the other hands: 3.3 vs ~4 for the others. This, of course, is explained by the large number of 8 and 9-point hands over the sample. EAST's min and max values are also set off the pack by the same -2 points as its mean.

 

For those of you saying, "It's only 76 hands," agreed, and I'm going to keep tracking our hands to see how things develop. However, 76 hands at a confidence level of 99% produces a confidence interval of approx 13% for a sample probability of 25%. In other words, we can expect that 99 times out of 100, BBO's dealer is dealing EAST a 9-point hand between 12-37% of the time, when you would expect it to be dealt only 9% of the time. That IS a statistical relevant result.

 

My stats are also showing that this causes NS to have the balance of points in approx 57% of hands, while EW have the balance of points in approx 33% of hands; which is why it feels like NS gets all the cards.

 

So, YES, I do believe there is a bias, but it is against EAST. Since EAST always plays with EW, that's why no one in my group wants to play EW.

[smerriman]

You're making the same basic mistake as everyone else. It is completely illogical to look at the data, see there are an unusual number of 9 point hands, and then calculate the odds of that happening. If you look at the data, there is always going to be something highly unusual in the results; the fact that it happens is meaningless; it is not statistically significant in the slightest.

 

You must make an hypothesis, then look at the results from that point forwards.

[hrothgar]

So, for kicks and giggles, I just looked at the last two days of JEC matches

 

I used JEC because I know that he plays a lot of boards

I used two days as the stopping point because that's the number that you get by default

 

47 Boards in total

 

Average HCP N/S 19.36170213

Average HCP E/W 20.63829787

 

Average HCP North 9.595744681

Average HCP East 10.53191489

Average HCP South 9.765957447

Average HCP West 10.10638298

 

You don't need to track your own board results

Just look at what's happening at other tables

 

Admitted, this is a small small, but it is completely at odds with what you are experiencing.

 

You're claiming East held precisely 9 HCP in 25% of all the hands that got played

This is ridiculously high.

The number should be about 9.35%

 

In a similar vein, you're claiming that East held precisely 8 HCP 13.15% of the time

That number should be 8.9 or so

 

First and foremost, if those numbers were representative of what other people are experiencing the serious players would have noticed.

 

My guess is that either

 

1. You got really unlucky

2. You are biasing your sample (you noticed something weird and then start counting that)

3. Someone is accidentally (or deliberately) biasing the hands that you are playing

[rdylan]

Well, my sample is my entire play history, so we can strike 2. Three sounds like conspiracy theory. I admit it could be really bad luck. I calculate that bad luck at 1 in 400,000. I'm not saying it isn't possible. Of note, your results over 47 hands don't actually exclude my results based on confidence levels, so they aren't "completely at odds" with what I'm experiencing.

 

As for making a hypothesis and then looking at the results, that is exactly what I have done. The hypothesis is that the deal is random and that the odds of getting dealt a 9-point hand are 9.356%. The experiment deviates from the expected results by a statistically significant amount.

 

All I am saying is that casual players are experiencing a phenomenon that is at least backed up by my initial set of hands. There are many potential explanations for this, including extraordinarily bad luck. But simply dismissing the idea out of hand lacks rigor.

 

I'd be very interested for one of the programmers to confirm that the code for dealing the casual tables is identical to the code for the competitive and money players. I'd also love to know how the code does its random generation.

[hrothgar]

 

As for making a hypothesis and then looking at the results, that is exactly what I have done. The hypothesis is that the deal is random and that the odds of getting dealt a 9-point hand are 9.356%. The experiment deviates from the expected results by a statistically significant amount.

 

 

Great!

 

We now have a hypothesis

 

Let's test it by looking the next 100 hands that JEC plays.

 

Or if you prefer, the ACBL is spinning up a big teams event starting tomorrow.

Lets look at the results from the first round of play for the top 4 seeds and see what's what

[smerriman]

As for making a hypothesis and then looking at the results, that is exactly what I have done. The hypothesis is that the deal is random and that the odds of getting dealt a 9-point hand are 9.356%. The experiment deviates from the expected results by a statistically significant amount.

So you're saying before playing those 76 deals, you specifically thought 'I wonder if East gets more 9 point hands than normal'; you then played 76 hands and looked at those statistics?

 

Your story above seemed to suggest otherwise - that you came up with the hypothesis of 9 point hands *after* playing the hands and seeing the results. Which is a complete misuse of statistical analysis, and nullifies any statistical significance.

 

With perfectly random hands, it is virtually guaranteed that you will be able to cherry-pick a statistic of interest that falls in the 'significant' range. You *must* make your hypothesis before generating a sample.

[rdylan]

I understand what you are saying, and yes, I suppose at least some of the initial sample is biased, because I did start it when the other players were complaining and I did look back. This tainted the first 40 hands. I will ditch that sample and carry on.

 

Using the tournament sample won't help. I should refine the hypothesis to state that hands are dealt randomly in the casual table IMP games.

 

We just played another 20 hands or so. I'll let you know what my results look like when I hit 100 untainted games.

[smerriman]

We just played another 20 hands or so. I'll let you know what my results look like when I hit 100 untainted games.

You don't need to wait, or use such a tiny sample size; there is plenty of data available. I just picked a player at random (well, the first one I saw at a table) named 0752 and fed their username into http://www.bridgebase.com/myhands/index.php , going back 1 month.

 

A quick script to pull out just the MBC hands gives a sample of 979 hands; East held 9 points on 78 occasions, for a probability of 7.97%. With random dealing, a 99% confidence interval around the known population proportion is (6.96%, 11.75%). As always, within normal expectations.

 

I've done this so many times it's not funny.

[rdylan]

It's at least a little funny. You win, I concede.

[barmar]

Several years ago we gave the designer of BigDeal something like a year's worth of data, and had him perform a statistical analysis of it.

 

He didn't find any systematic bias, and we've been satisfied with our implementation since then.

[hrothgar]

He didn't find any systematic bias, and we've been satisfied with our implementation since then.

 

I think that a more important consideration is whether or not you have changed your implementation since then

[barmar]

I think that a more important consideration is whether or not you have changed your implementation since then

We haven't.