52 Card Poker Test

Copying pkrhnd

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.


Probabilities

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.


Knuth's Poker Test

If you are interested in 5 card poker with replacement, see Knuth's poker test.


Dice Poker

If you are interested in playing poker with with 5 dice, see the dice poker test.


References

Lincoln L. Chao
Statistics for Management
Palo Alto, CA: The Scientific Press, 1984
Chapter 6, Expected Value and Population Parameters
Section 2, Population Mean and Variance

The chi-square test is similar to:

Chapter 12, Chi-square Tests
Section 3, Testing for Goodness of Fit
Formula 12-3
Example 12-4

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
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

See Probabilities above for information about the probabilities in this book.


The World Almanac and Book of Facts
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

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
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

The probabilities for draw poker are inexact in this book.