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!! [img]/images/graemlins/laugh.gif[/img]

[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. [img]/images/graemlins/blush.gif[/img]

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. [img]/images/graemlins/blush.gif[/img]

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. [img]/images/graemlins/wink.gif[/img]