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Re: [Phys-L] From a Math Prof (physics BS major) at my institution( math challenge)



The odds of getting a perfect bridge hand are quite small, but there have
been some verified cases of this. However, there are a lot of unverified
cases from small bridge clubs. Some people love to have fun! If you are
dealt all one suit, but the others aren't there is no way to guarantee a win
because your bid can always be overcalled by no trump as long as you are not
in the lead. You have to be cagy and psyche them out.

John M. Clement
Houston, TX



I found Bob's story very hard to believe, so I just dealt
myself a poker hand and got the 2 of spades, the 7 of hearts,
the 8 of spades, the Jack of clubs and the Jack of hearts.
I'm sure you can imagine my surprise! I calculate the odds
of getting that hand to be only one in nearly 2.6 million!

Sorry for doubting you, Bob!

John Mallinckrodt
Cal Poly Pomona

On Feb 18, 2014, at 8:01 AM, LaMontagne, Bob wrote:

I was playing poker last night and was dealt a hand that
was 5-6-7-8-9 all hearts. Was that random - or did the dealer
fix the hand?

There is no test that can truly tell the randomness of the
two lists with so few numbers.

Bob at PC

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf
Of Rauber,
Joel
Sent: Tuesday, February 18, 2014 10:47 AM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my
institution ( math challenge)

The second list was the random list. As noted, one cannot prove
which one was the random list, you can only make a
probabilistic guess.

I looked at two factors, the number of times consecutive numbers
appear -> leads to 2nd list is random The number of times
numbers in
the range [30-35] appeared compared to the other decade
ranges, which
also lends evidence that the second list was the random one.

I didn't personally calculate it, but the Math Prof. told
me that the
probability of consecutive numbers appearing on a truly
random list
is 48%, much higher than most people would guess.

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf
Of Jeffrey
Schnick
Sent: Monday, February 17, 2014 8:49 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my
institution ( math challenge)

Only two of the numbers in the first list end in 0. Thus, I think
the first list was made up by people.
________________________________________
From: Phys-l [phys-l-bounces@phys-l.org] on behalf of
Philip Keller
[pkeller@holmdelschools.org]
Sent: Monday, February 17, 2014 6:59 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my
institution ( math challenge)

I am going the other way here. I think the students would
feel the
need to choose a wide range of numbers. But I calculate
that in 21
sets like this, we would expect just under 5 of the sets
to have no
single-digit numbers. The first batch has 2 like that, and the
second has 6. So I pick the second batch as real, 1st
batch as student-generated.


On 2/17/2014 4:04 PM, Donald Polvani wrote:
Not being familiar with random number tests, I had to
take a simple
(and
crude) test. If the numbers are truly random and have
been arranged
in numerical order, then the first column would be
expected the have
numbers from 1 - 7, with successive columns having
numbers between 8
- 14, 15 - 21,
22 - 28, and 29 - 35.

So a very simple test is to simply count the number of times that
numbers in each column exceed (or fall below) the expected column
limits. For the first set of numbers, I find that the
column limits
were exceeded, respectively, 5, 8, 6, 4, and 5 times (for
the last
column I counted the number of times the listed number fell below
the lower column limit). Doing this for the second set
of numbers
produced the excess numbers 8, 11, 10, 4, and 7 (again,
for the last
column I counted the number of times the listed number fell below
the
lower column limit).

Clearly the second set of numbers failed the column limit
tests more
often and should be (i.e. "probably is") the student list.

Don

Dr. Donald Polvani
Anne Arundel Community College
Adjunct Faculty, Physics (Retired)
Arnold, MD

--Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf
Of Rauber,
Joel
Sent: Monday, February 17, 2014 2:08 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my
institution ( math challenge)

Before giving it away, both lists are in numerical order
smallest to
largest; so that has been ordered after the numbers were
generated.

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf
Of Jeffrey
Schnick
Sent: Monday, February 17, 2014 11:32 AM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my
institution ( math challenge)

Each set of five numbers in the first set is listed in numerical
order from smallest to largest. Thus, I think the first
group was
student
generated.

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On
Behalf Of Paul
Nord
Sent: Monday, February 17, 2014 12:28 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my
institution ( math challenge)

That's easy.

The first group is the real lottery numbers. It is more
uniformly
distributed.
In the second set, the student-generated numbers, numbers in the
20's are much preferred.

Paul


On Feb 17, 2014, at 10:33 AM, Rauber, Joel
<Joel.Rauber@SDSTATE.EDU>
wrote:

The below may be tangentially related to discussions of entropy
(See subject heading)


I asked my Math 316 (Discrete Math) to randomly pick 5 numbers
from
1 to
35. This is the same as the "South Dakota Cash Lottery"
that has
drawings twice a week. I told them that I would compare their
"random" numbers to actual numbers drawn in the lottery.
They were
instructed to try to make their numbers as random as possible so
they looked just like the real random numbers. I had 21
responses,
they are in one of the two lists below. The other list is the
numbers drawn in the lottery from Dec 7, 2013 to Feb 15,
2014. Can
you tell which list is the student's list? Hint: there
is an easy,
almost trivial,
way to do this, or least to locate the most likely student list.

02-06-07-25-34
03-09-12-15-34
06-16-21-28-32
06-10-13-21-23
04-18-26-27-34
03-06-17-27-32
03-11-21-22-35
01-02-08-17-27
07-12-14-24-31
03-07-14-18-27
07-13-22-25-31
07-12-23-31-32
04-17-18-22-35
08-15-17-20-25
12-16-18-29-34
02-07-11-16-21
08-23-24-32-35
17-19-23-29-31
09-16-27-28-32
06-15-19-26-32
06-13-15-23-31



11-17-19-28-31
03-11-29-32-35
14-21-24-28-33
09-14-22-23-31
03-21-26-30-31
05-15-20-27-29
02-23-24-25-26
07-13-20-24-25
03-23-26-27-28
06-20-21-26-29
01-10-14-19-35
12-18-27-32-35
02-06-24-27-28
03-08-11-21-30
09-14-20-25-31
04-13-19-21-28
10-11-12-21-31
02-07-11-20-24
06-17-25-29-30
13-23-24-26-34
09-17-21-25-26
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Forum for Physics Educators
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Forum for Physics Educators
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