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The Monty Hall 3 Doors puzzle has been discussed for many
years, and
there are several interesting references to it on the web.
For example:
| Monty Hall and Marilyn vos Savant | |
| A Simulation You Can Play Yourself | |
| Cut The Knot |
This puzzle illustrates how easy it is to make logical errors when working with combinatorics and probabilities. Here is one version of the puzzle.
Monty is a game show host who offers a contestant the chance to select one of three doors and to keep whatever prize is behind that door.
Behind one door is a good prize, and behind the other 2 doors there are "junk" prizes.
After the contestant chooses a door, Monty always shows everybody what is behind one of the doors that was not chosen and asks the contestant if she would like to stick with the door she originally picked or switch to the door which she neither saw behind nor chose.
What is the best strategy for the contestant ?
Should she switch doors or stick with her original choice ?
Does it matter whether she switches or not ?
A Solution For The Monty Hall 3 Doors Puzzle
The
"Quotations Part A" page
contains a mixture of wisdom and foolishness I found
on various web sites several years ago.
Most of the quotes have nothing to do with
either craps or gambling,
and many of them are already familiar to a lot of people.
Some quotes were added on 02 January 2008.
The "Quotations Part B" page contains a little more wisdom and foolishness.
That page was created one day when I tried to make a game out of
a small batch of quotations and
invited my co-workers to play it according to these instructions:
Some of the following quotations are interesting, but others
seem less profound after you've read them a few dozen times.
Can you separate the important statements from
the not-so-important statements ?
Scoring:
Give yourself 150 points for each correct answer.
No penalties for guessing.
Give yourself 2 bonus points if you can supply the
name, social security number, and astrological sign
of each missing author.
Time Limit:
4 hours and 19 minutes ( 4 hours 21 minutes for supervisors )
Warning:
Participants must be at least 21 years of age and
not a citizen of France.
Since this is not Jeopardy,
please phrase your answers in the form of an answer.
End of instructions.
Sadly, not many co-workers ( zero so far ) have expressed an interest in playing the game.
Most of the poems I like are ones you already know.
Here are two that are less popular.
In the first one an
Indian remembers his grandfather
.
The second poem also deals with
past memories
.
Whenever you need to figure out how many ways
you can choose r things
from a set of n things you need to evaluate
a binomial coefficient.
You could do that with a scientific calculator or
computer program.
But there are two other useful methods for
evaluating binomial coefficients
-- (1) a formula and (2) Pascal's Triangle
If you are given a particular date
and want to know what day of the week that was,
you can use a
Zeller formula
for computing weekdays.
For example, 04 July 1776 was a Thursday.
The bracket function is a useful tool in number theory and
other areas of mathematics.
To help students who are learning elementary calculus, it can
be used to create examples of important concepts related to
discontinuous functions and areas under curves.
It is also needed when deriving the
Zeller formula
for calculating the weekday that corresponds to a given date.
There are certain
properties of the bracket function
you should know.
In the 1950's many people opposed the use of recursion in programming languages. In fact FORTRAN forbid its use. But this opposition was mainly due to the fact that at that time recursion couldn't be implemented efficiently. Fortunately that is no longer true, and recursion is now an important tool for dealing in a natural and simple way with lists, trees, and a few other structures. Many programming books introduce the idea of recursion by showing you how to compute the factorial of a number using a recursive function. However, computing factorials is not a proper use of recursion. In my opinion there is a much better example of recursion that a student should learn.
Here is another link to the same page referenced
in the Part 2 Exercise 1 solution showing
a very brief look at
continued fractions
.
You can estimate the probability of
significantly improving
your hand
after the flop but before the turn
by using the
rule of four
.
Michael Shackleford and Jing Ding provide a very nice
calculator for the pre-flop analysis of any heads up game of
Texas Holdem.
You can play with it at
Calculator for a 2-person game of Texas Holdem.
You can download a zip file of a java application ( not applet )
that computes the probability of each player to win, lose, or tie
in a heads-up ( i.e. only two players ) game of Texas Holdem
before the flop is dealt to the table.
To use the application you need to be able to compile and run
java programs on your computer.
My tool is slower and more awkward to use than the Wizard of Odds
calculator whose link is above. Each analysis takes about 36 seconds
in version 1.4 ( 20 seconds in version 1.3 ). The source code is split
up into about 22 java files.
In version 1.4 we added a progress bar for the analysis section.
Unfortunately, our program now runs slower because I don't yet
know enough about threaded execution and progress bars.
If you have any suggestions for revising the code please send them to
schoolmarm@crapsmath.com
If you download this tool, unzip it into any convenient folder on your
computer and read the file named a_ReadMe.txt
for usage instructions.
Click here to download version 1.3 of the tool.
Click here to download version 1.4 of the tool
[ 30 dec 2006 update: replaced SP.java file ]
You can download this amateur application and use it to edit files
on a Windows system
provided that you are able to
compile and run
java programs on your computer.
The zipped download file uses about 110 kilobytes of space, and
the compiled program needs approximately 855 kilobytes of space.
|
The Text Editor was created using version 1.4.2 of
the Sun java Software Development Kit ( SDK ), and the editor has these capabilities: |
|||
| 1 ) Open and close files | |||
| 2 ) Insert line nbrs into the file being edited | |||
| 3 ) Indent all lines in the file being edited | |||
| 4 ) Change the font used to VIEW the file being edited | |||
| 5 ) Launch a calendar or a clock or a calculator | |||
|
6 ) Limited Sort capability -- |
|||
|
If you edit a file consisting of <first-name, last-name> pairs, then you can sort the file by last names |
|||
| 7 ) User can extend its functionality by modifying the java source code | |||
| The calculator component of the Text Editor has these features: | |||
| 1 ) Source code is provided | |||
| 2 ) Display area is editable ( to allow cut and paste operations ) | |||
| 3 ) Provides 3 temporary storage locations | |||
| 4 ) Has large font buttons to help visually impaired people | |||
|
5 ) Provides for these operations ( among others ) : a ) recalling the constants pi, pi / 2, and e b ) finding common and natural logs c ) finding factorials of non-negative integers d ) finding sine, cosine, and tangent ( using degrees or radians ) e ) Pow button -- for raising a number to a power f ) Mod button -- for finding the value of x modulo y g ) nCr button -- for finding the number of combinations of n things taken r at a time |
|||
If you download the Text Editor, unzip it into any convenient folder on your
computer. Its Read_Me file is in the downloaded help_box folder.
Click here to download version 2.0 ( older version ) of the Text Editor
Click here to download version 2.1 of the Text Editor
Click here to download version 2.2 of the Text Editor
Changes made in version 2.2 of the Text Editor include:
In the calendar ( by Ian Darwin ) component, we
extended the range of selectable years
Changes made in version 2.1 of the Text Editor include:
Added a crude version of a FIND operation.
Changes made in version 2.0 of the Text Editor include:
Updated the calculator component version from v34 to v35
Added a left margin to the calculator's display area
Changed the color scheme of the calculator buttons
Enhanced the option to do file sorting
Provided an alphabetized list of all the methods used in
the main program ( to aid maintenance and debugging )
To see version 4.0 of the calculator,
Click here
Note that you can enter data into the calculator either by
clicking the calculator buttons or by pressing appropriate
keyboard keys on your computer.
The calculator is written as a java program ( named Calc.java )
which can be run either as an applet or as an application.
If you download and unzip the calculator with its source code then
you can run the calculator on your computer by double clicking the
unzipped file named Applet_Helper.htm and then clicking the link it provides.
Click here to download version 1.0 of the Big Button simple Calculator
Update on 03 May 2008:
We've finished installing the MOD operator.
And we've added a factorial operator.
Click here to download version 3.1 of the
Big Button simple Calculator
Update on 12 May 2008:
We've added sin, cos, tan, and sqrt buttons.
And we've also added a degree / radian toggle button.
Click here to download version 4.0 of the
Big Button Calculator
Sometime before Feb 2008, a very nice java applet for playing
video poker and
analyzing poker hands
was found at
Cindy Liu @ Gamblingtools.net
Her site also had tools for keno and blackjack.
| Note: | |||
| On 16 Feb 2008 we noticed that the above link | |||
| Cindy Liu @ Gamblingtools.net | |||
| no longer takes you to the site we wanted to recommend. | |||
|
We don't know if her Video Poker Analyzer is still available. ( and if it is available, we don't know where it is. ) |
|||
Several versions of Video Poker are available.
You can play for fun and get advice on best play for each hand.
The jacks or better version can be found at
Wizard of Odds VP Jacks or Better
If you know how to do arithmetic in base 3 then you might like a card trick
described thirty some years ago by Martin Gardner in one of the Mathematical
Games sections of Scientific American magazine.
Click here for a description of the trick.
Our main theme describes how to derive Kepler's laws of
planetary
motion from Newton's laws.
We also derive various ellipse formulas,
the Vis-Viva Equation, and
some formulas related to the three anomalies.
We provide separate windows with information about :
| uniform circular motion | ||
| gravitational potential energy | ||
| apogee Vs perigee | ||
| escape velocity | ||
| oblique launches | ||
We've included several links to other sites that deal with orbital mechanics.
Click here to see our derivations
| This Site : | Top-of-Page | Home | Part 1 | Part 2 | Other Topics |
Last Update: 12 May 2008