pkrhnd is a program that allows you to deal thousands of poker hands to see if they pass the chi-square test. The poker hands in this test are based on a 52 card deck without replacement. The aces high and low counting method is used in this program.
pkrhnd has one parameter:
Example of how to run the program.
pkrhnd 100000
In this example, the program deals 100 thousand hands. The program prints the probability distribution, the observed frequency, and the chi-square.
The Chi-square number should fit within the Range 95 percent of the time.
The probabilities in the pkrhnd program
count aces high and low, to conform to
Scarne's Guide.
The following hands are affected by this counting
method.
The
Hopkins
book, below, contains inexact values for the
probabilities of a poker hand. The chi-square
test fails consistently with their probabilities.
If you are interested in 5 card poker with
replacement, see
Knuth's poker test.
If you are interested in playing poker with
with 5 dice, see
the dice poker test.
Lincoln L. Chao
The chi-square test is similar to:
Chapter 12, Chi-square Tests
In Table 12-3, each category in the
chi-square test has a different expected
frequency. This corresponds to the different
expected frequencies for the number of successes.
John Scarne
See
Probabilities
above for information about the probabilities
in this book.
The World Almanac and Book of Facts
The World Almanac
uses the same counting method as
Scarne's Guide.
See
Probabilities
above for information about the probabilities
in this book.
Nigel J. Hopkins
The probabilities for draw poker are inexact
in this book.
Probabilities
Knuth's Poker Test
Dice Poker
References
Statistics for Management
Palo Alto, CA: The Scientific Press, 1984
Chapter 6, Expected Value and Population Parameters
Section 2, Population Mean and Variance
Section 3, Testing for Goodness of Fit
Formula 12-3
Example 12-4
Scarne's New Complete Guide to Gambling
Fully revised, expanded, updated edition
New York: Simon & Schuster, 1961, 1974, 1986
A Fireside book, 871 p.
ISBN: 0-671-21734-8 hardback
ISBN: 0-671-63063-6 paperback
Chapter 27, Poker: America's Favorite Card Game
Section: Poker Odds and Probabilities
New York: World Almanac Books, 1868 to present
ISBN: 0-88687-883-7 hardback
(2003 edition)
ISBN: 0-88687-882-9 paperback
(2003 edition)
Chapter: Weights and Measures
Section: Playing Cards and Dice Chances
John W. Mayne
John R. Hudson
The Numbers You Need
(C) Orbita Consultants Ltd.
Detroit: Gale Research, Inc., 1992
ISBN: 0-8103-8373-X
Page 138, Section 6.6, Draw Poker