Sample This! (A Quiz)

[uuDevil]

Using only the information given, select the best answer:

1. In the last 10 hands you played, the player to your left has either raised when you limped or folded when you raised. You are dealt AA. Should you consider limp/reraising?

A. Yes.
B. No-- you can't be sure he'll raise because the sample size is too small.

2. (With apologies to D. Rowntree.) A 10 cm tall gnome sits on your shoulder and begins to comment on your play. What can we infer about the average height of gnomes?

A. The most probable average height of gnomes is 10 cm.
B. Nothing-- a sample size of one is meaningless.

3. Due to a massive coronary, Fat Jack has just collapsed over his keyboard, jelly doughnut in one hand, mouse in the other. This tragedy befell him just as he was about to click the call button to play his 10,000th hand of internet poker. Ironically, he was holding JJ, his biggest losing pair over the course his internet career. As far as Jack is concerned, What can we say about the EV of JJ?

A. If he lives, JJ is -EV for Jack. It is 0 EV if he dies.
B. Nothing-- the sample size is too small.

4. The last 3 posts I read on these forums concerned poker. It is most likely that

A. The next post I read here will be about poker.
B. I was actually reading RGP.
C. The next post I read here will be a flame post.
D. Based on a sample size of 3 posts, you can't say anything about future posts.

5. The answers to all of the above are A. Given the first sentence of this post, I don't think this is debatable. What is to be learned from this quiz?

A. Sample size ain't everything.
B. Statisticians should not play poker.
C. Poker players should not use statistics.
D. Debate is inevitable.
E. Nothing-- sample size is the only thing, and in this case, it's too small.

[Lori]

You have totally ruined my next rant, great post.

Lori

[TimTimSalabim]

Use *only* the information given to answer this:

I flip a coin 3 times, it comes up heads 3 times. What is the probability of heads coming up the 4th time:

A. 100%
B. 50%

I say it's B, because in order to even understand the question, I have to know what a coin is. Knowing what a coin is, I know that the answer is B. Similarly, I think all of the answers in your quiz are not automatically A. In order to understand any question, you have to have some logic and life experience, which is always blended with the available data to yield the best answer.

[Sloats]

[ QUOTE ]
Using only the information given, select the best answer:

1. Limp. Once is a occurance, twice is a coincidence, three times is a pattern, five times is a trait. William Covey, I believe

2. Gnomes only exist in France.

3. Some 2+2 Poster will bitch about the disconnect policy on Party

4. I'm at work and can't d/l porn

5. Actuaries with a gambling problem are like Musicians with a drinking problem.


[/ QUOTE ]

[TimTimSalabim]

I would also add that, in the example I gave, if the coin was flipped 20 times instead of 3 times and it came up heads every time, then that gives me a strong reason to suspect that the coin is biased. Sample size is indeed important.

[Lori]

It is more likely to come up heads, even after 3 flips.

Either it is unbaised with a near 100% probability, or it is biased, and most likely towards heads.

You say yourself that if the next 17 flips were heads, you would start to suspect bias.
Given the absence of any other information, it is more likely, if only by a tiny fraction, to come up heads next spin.
If you had to bet your life on it, I doubt you would pick tails.

Lori

[gmunny]

[ QUOTE ]
if the coin was flipped 20 times instead of 3 times and it came up heads every time, then that gives me a strong reason to suspect that the coin is biased.

[/ QUOTE ]

If it comes up heads 20 times in a row, I'm thinking to check for a 2-headed coin!! /images/graemlins/laugh.gif

[TimTimSalabim]

Good point. However, I was simply trying to say that the sample size is important in any conclusion that is drawn from the information given. You yourself are not saying that there is a 100% chance of it being heads the 4th flip, only that the chance is something slightly greater than 50%, taking into consideration that you know some coins are biased (which is information not strictly given in the problem, but since I used it too I'll have to give you that one).

[uuDevil]

[ QUOTE ]
Sample size is indeed important.

[/ QUOTE ]
TimTimSalabim,

I agree. Of course the quiz is rigged.

AND, I forgot the disclaimer: I am not a statistician. Anything I may say about the topic is unreliable. /images/graemlins/blush.gif

My point is that playing poker requires us to make choices and act on the basis of incomplete, unreliable information. Are these decisions statistically unjustified? Maybe. (I don't know how a statistician would answer, though I'd like to hear from one.) Are they justified at all? I say yes.

I confess that despite 4 (at least) university courses in statistics, I still get confused about some basic ideas. Since it's hard to find a statistician when you need one, I'm still trying to understand the topic.

[uuDevil]

[ QUOTE ]
You have totally ruined my next rant, great post.


[/ QUOTE ]

Thanks. /images/graemlins/blush.gif

I seriously doubt that your rant is "ruined." On behalf of myself and the many other posters I'm sure would like to see it, I insist you post it anyway. Show me how it's supposed to be done. /images/graemlins/wink.gif

[TimTimSalabim]

I think I see what you are saying now. You're saying that even if a sample size is not "statistically significant" by the strictest definition, it still suggests the slightest probability balance tilting in that direction, given no other information. Or, as Lori put it, even if there are only 3 coin flips, if they all come up heads, it makes it ever so slightly more likely that the coin may be biased towards heads than that it is unbiased or biased towards tails. In other words, statistical significance is not an either or, but a gradual function of sample size. Hmmm. Okay, I might have to agree with you and Lori then. But I'd also like to hear from a statistician.

[Lori]

In other words, statistical significance is not an either or, but a gradual function of sample size

But interestingly, it only takes one flip to change our choice from not mattering, to being 100% correct to choose a certain side.
All that then changes is how much we gain from playing correctly.

Edit: should read how much we expect to gain....

Lori

[Dylan Wade]

I've seen plenty of pictures of gnomes, and although I can't infer their size from these pictures I can confirm that their heights are aproximately normally distributed like all other creatures on earth. Therefore on average the gnome on my shoulder is an average gnome, and so I can infer that the most probable average height of gnomes is 10cm.

[karlson]

I understand your point, and it's a good one. However, I take issue with example 3 (and 1 to some extent).

You still have some prior information to consider. So it's actually a difficult problem. Clearly, JJ are +EV for most players. So, is it more likely that Jack plays JJ that badly, or that he had a bad run, and this hand is actually +EV? You should probably also say that it's more likely that JJ is +/- EV, not that it is +/- EV.

The same for 1. Assuming (I think you imply this) that limping with AA is, without prior information, worse than raising, it's not clear that you should limp. You would have a difficult calculation.

The coin analogy would be this: suppose I gave you coin and said that there's 50% chance it's fair, and 50% it's biased (say, 60-40) towards heads. You flip it 100 times and find 51 heads and 49 tails. You would conclude that it's more likely the coin is fair than biased.

Again, you say use only the info given, but clearly you already expect some info (like limp-reraising AA is more +EV given a raise behind you than raising given a fold behind you).

I'm usually not this picky, but this thread seems to ask for this type of stuff.

[CarlNiclas]

For number 1 - (limping/raising AA) it is obviously A that is the correct answer. Consider limping. That answer does NOT mean you actually HAVE to limp, just that you should consider doing it.

No hand in poker should be played always be played the same way. There are always nuances that should be taken into account regardless of the hand you have, even if that hand happens to be AA. You should always consider the possibilities!

[Lori]

You would conclude that it's more likely the coin is fair than biased.

But I would still pick heads.

Please remember the initial post only had five A answers, maybe this was a coincidence /images/graemlins/laugh.gif

Lori

[William]

Lori,

Why do you sometimes post as Lori and some other times as Lorinda?

Just wondering... /images/graemlins/smile.gif

William /images/graemlins/cool.gif

[Lori]

I changed names when Granny left, now Granny is back I have a problem as many newbies are used to this ID, but the old-timers prefer Lorinda.
I also get PM's to both names, so I have yet to decide which to use.
I'll probably end up as Lorinda in the zoo and Lori outside.

Lori

[uuDevil]

[ QUOTE ]
I'm usually not this picky, but this thread seems to ask for this type of stuff.


[/ QUOTE ]
karlson,

I concede that the questions are flawed. Since there are very clever people here, I didn't want to spend too much time constructing airtight situations that would later turn out not to be so perfect as I thought.

It's true I wanted to (gently) provoke people. I thought replies would be of the humorous counterexample variety, which is fine and good, so long as the point gets across.

One thing that motivated me was reading posts where someone says something like, "I just got PokerTracker. I imported 1,500 hands, and my stats are.... What do you think?" Sometimes, the first reply is something like, "Your sample size is too small [end of reply]." Can it be really be right that no analysis is possible, however small the sample? The replies that follow, though acknowledging the small sample size, will attempt some analysis. Is this wrong?

I think that the impulse to draw conclusions despite small sample size is actually more correct. Conclusions can be adjusted as more data is collected. We should keep in mind the degree of uncertainty associated with the sample size, but I see no compelling reason to wait for more data to think about and act on the data we have.

[uuDevil]

[ QUOTE ]
Please remember the initial post only had five A answers, maybe this was a coincidence

[/ QUOTE ]

Nope. As you imply, it was all A's because it wasn't intended to be "fair" in any way.

For some reason I was thinking of Craig Kilborn's "Five questions" segments (on the "Late Late Show," don't know if this is seen outside the US). I wanted to include a question using David Sklansky's 238 posts, but couldn't think of a good one and 6 seemed excessive anyway....

[M2d]

for 1), I think that the sample size is more than sufficient. given human nature and that this guy seems to have it in for you, I definately think that we can infer a lot from the past ten repititions.

[Peter Harris]

1) yes. if i play 10 hands that will be over at least 50 table hands and it is more than mere chance that the player has raised my limps and folded my raises. while i've limp/reraised once in 3,000 hands (small sample), i'd consider doing it now.

2)b.

3)a. and lol.

4)a.

5)d.

thanks for stimulating my brain,
Pete

[Dylan Wade]

Actually, although I realize your post was not entirely serious, it's important to know that a small sample size can be useful if you have a aproximate model for your data.

This is how scientific polling works. You'd be surprised to see how very small the sample sizes are in some of the very well respected polls. Nelson ratings for TV are an example. They actually poll a very small ammount of people, and then fit the results to a normal model to extrapolate an accurate indication of the entire population's TV watching habits.

This, I think, especially applies to the Gnome problem. One Gnome is a special case, but let's say you see 4-5 Gnomes. If all these Gnomes are close to 10cm, and we know we're selection of Gnomes is appropriate, (ie. we didn't just select gnomes from the GNBA, or gnome kids), we can make some fairly certain claims about the entire population of gnomes. Only because all creature heights are normally distributed...... you know, if you grab 4-5 adult humans

[uuDevil]

[ QUOTE ]
This, I think, especially applies to the Gnome problem.

[/ QUOTE ]
Well it's certainly interesting what people will pick up on.... /images/graemlins/grin.gif

Except for the Nielsen reference, you've pretty well summarized pp. 83-85 of Derek Rowntree's "Statistics Without Tears" (most highly recommended, btw).

http://www.cc.utah.edu/~lra21170/gnome.gif

[LivingLegend58]

That is the craziest answer I have ever heard, great post. Go Wolf PAck or Rebels?