Updated 2016-05-01 15:39:11 by gold

Poker Probability and Calculator Demo Example

This page is under development. Comments are welcome, but please load any comments in the comments section at the bottom of the page. Please include your wiki MONIKER in your comment with the same courtesy that I will give you. Its very hard to reply intelligibly without some background of the correspondent. Thanks,gold

Introduction edit

gold Here is some starter code for poker probability. The impetus for this calculator was checking some poker probabilities of 5 card draw in a book. Its easy enough to plug in formulas into the calculating subroutine. Most of the checked testcases involve 5 card poker.

Testcases Section

In planning any software, it is advisable to gather a number of testcases to check the results of the program. The math for the testcases can be checked by pasting statements in the TCL console. Also, some of the pseudocode statements were checked in the google search engine which will take math expressions. The factorial procedure used below was posted by Suchenworth. Aside from the TCL calculator display, when one presses the report button on the calculator, one will have console show access to the factorial function.

Testcase 1

For a system of dealing 5 cards from a 52 card deck, the sample space would be factorial(52)/((factorial(5)*factorial(52-5)) or 52!/(5!*47!). Most of these TCL expressions can be pasted into the console window.
 set space [ expr {  [f 52]/[f 5]/[f 47]} ] ;# generic TCL
    answer%      2598960

The probability of four of a kind would be frequency/ sample space:
  set probability [ expr { (1.* 4 )/2598960} ]
  answer%    1.5391E-6           

The probability of four of a kind would be frequency/ sample space:
 set probability [ expr { (1.* 624 )/2598960} ]
  answer%    2.40E-4           

The probability of three of a kind would be frequency/ sample space:
 set probability [ expr { (1.* 54912 )/2598960} ] 
  answer%   0.021

Testcase 2

Continuing with dealing 5 cards from a 52 card deck, there is an alternate way of estimating the factorial, which is the Swerling formula. The Swerling formula is less accurate for small numbers (<60!), but has some interest in estimating the factorial with large numbers (>60!). The Swerling formula is sometimes used to check the magnitude of large N! in computing. The Swerling formula is implemented and accessible from the report console window.
 set swerlingspace [ expr {  [fact 52]/[fact 5]/[fact 47]} ] 
    answer%      2599403
 # and the answers for probabilites would slightly different
 set probability [ expr { (1.* 4 )/2599403 } ]
  answer%    1.53881E-6  vis previous 1.5391E-6           

Testcase 3

There are 55 poker players who wish to sit four at a table. What is the number of combinations? The sample space would be factorial(55)/((factorial(4)*factorial(55-4)) or 55!/(5!*50!). The calculator gives an answer of 341055.

Testcase 4

Picking up a five card hand, what is the probability and odds of a straight flush, less royal flush ? As caulated before, the sample space is 52!/((5!* (52-5)!) or 2598960. The frequency is (10 choose 1)*(4 choose 1) -(4 choose 1) , 10!/((1!* (10-1)!) * 4!/((1!* (4-1)!) - 4!/((1!* (4-1)!) , 40-4,or 36.
set straight_flush  [expr { (1.*36)/ 2598960    } ]
set straight_flush_odds  [expr { 1./( (1.*36)/ 2598960 )   } ]
answer%  1.39E-5 ,  72192.0
hand choose formula frequency division terms probability odds
royal flush (4 choose 1) 4 4/258960 1.54E-5 64739
straight flush less royal flush (10 choose 1)* (4 choose 1) -(4 choose 1) 36 36/258960 1.39E-572192
four of kind (13 choose 1)* (12 choose 1) *(4 choose 1) 624 624/258960 2.4E-44164
full house (13 choose 1)* (4 choose 3) *(12 choose 2) 858 858/258960 2.11E-246.3
three of kind (13 choose 1)* (4 choose 3) *(12 choose 2)* (4 choose 2) 156 156/258960 1.44E-3693

Testcase 5

Three cards are bought at 100 cents each. Possibly wrongly, but I am told that the chance of receiving a royal card on each draw is "30 percent". The chance of not receiving a royal card on a draw is "70 percent". If all 3 cards are royal, 300 cents are paid;if 2 cards are royal, 150 cents are paid; if one card is royal, 10 cents are paid. What is the weighted pay off or expectation?
choose term term1 * term2 *term3 = wg p(x)pay offwg p(x)* pay off
3 choose 0 1.0 0.7**3 0.3**0 0.343 -100-34.3
3 choose 1 3. 0.7**2 0.3**1 0.441 -90-39.89
3 choose 2 3. 0.7**1 0.3**2 0.22 5011.0
3 choose 3 1.0 0.7**0 0.3**3 0.027 200 5.4
sum >> 1.0 expectation >> -57.79

Now, if there are 3 royal cards and 10 common cards in a suit, the probability of a royal card is 3/(10+3),3/13, or 0.2307. The probability of not receivng a royal card is 10/(10+3),10/13, or 0.769. Checking, the total chances of either a royal card or a common card are 0.2307 + 0.769 or 1. Since the probabilities are different than first represented, the expectation of pay off should be recalculated.
weighted probability pay off p(x)*pay off
.454 -100 -45.4
0.5322 -90 -47.898
0.2076 50 +10.38
0.027 200 +5.4
expectation>> -77.52

So in buying three cards for three dollars, the expectation is a loss of 78 cents.

ScreenShot Section:


References:


Appendix Code

appendix TCL programs and scripts

        # pretty print from autoindent and ased editor
        # poker probability calculator
        # written on Windows XP on eTCL
        # working under TCL version 8.5.6 and eTCL 1.0.1
        # gold on TCL WIKI , 12jul2013
        package require Tk
        frame .frame -relief flat -bg aquamarine4
        pack .frame -side top -fill y -anchor center
        set names {{} {number of cards in deck:} }
        lappend names {distinct hands:}
        lappend names {frequency: }
        lappend names {sample space:}
        lappend names {probability:}
        lappend names {odds:1}
        foreach i {1 2 3 4 5 6} {
            label .frame.label$i -text [lindex $names $i] -anchor e
            entry .frame.entry$i -width 35 -textvariable side$i
            grid .frame.label$i .frame.entry$i -sticky ew -pady 2 -padx 1 }
        proc about {} {
            set msg "Calculator for Poker Probability
            from TCL WIKI,
            written on eTCL "
            tk_messageBox -title "About" -message $msg }
       proc f n { expr {$n < 2 ? 1 : $n * [f [incr n -1]]} }
       proc fact n {expr {            
            $n<2? 1:
            $n>20? pow($n,$n)*exp(-$n)*sqrt(2*acos(-1)*$n):
            wide($n)*[fact [incr n -1]]}}   
       proc calculate {     } {
            global answer2
            global side1 side2 side3 side4 side5
            global side6
        set aa [ expr { int($side1) } ]
        set bb [ expr { int($side2) } ]
        set cc [ expr { $aa-$bb } ]
        set cc [ expr { int($cc) } ]
        set dd [ expr { int($side3) } ]
        set term1 [ f $aa ]
        set term2 [ f $bb ]
        set term3 [ f $cc ] 
        set samplespace [ expr {$term1*1./(1.*$term2*$term3)} ]
        set pokerprob [ expr { (1.*$dd)/$samplespace } ]
        set pokerodds [ expr { 1./$pokerprob } ]
        set side4 $samplespace
        set side5 $pokerprob
        set side6 $pokerodds }
        proc fillup {aa bb cc dd ee ff} {
            .frame.entry1 insert 0 "$aa"
            .frame.entry2 insert 0 "$bb"
            .frame.entry3 insert 0 "$cc"
            .frame.entry4 insert 0 "$dd"
            .frame.entry5 insert 0 "$ee"
            .frame.entry6 insert 0 "$ff" }
        proc clearx {} {
            foreach i {1 2 3 4 5 6 } {
                .frame.entry$i delete 0 end } }
        proc reportx {} {
            global side1 side2 side3 side4 side5
            global side6
            console show;
            puts "number of cards: $side1 "
            puts "distinct hards: $side2 "
            puts "frequency: $side3    "
            puts "answer sample space: $side4    "
            puts "hand probability: $side5    "
            puts "integer odds:1 $side6    " }
        frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 52. 5. 4. 2.59E6  1.5E-6 6.49E5 }
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 52. 5. 624. 8.  2.4E-4 4164 }
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 52. 5. 54912. 4096.  2.11E-2 47.3 }
        ::ttk::button .clearallx -text clear -command {clearx }
        ::ttk::button .about -text about -command about
        ::ttk::button .cons -text report -command { reportx }
        ::ttk::button .exit -text exit -command {exit}
        pack .calculator  -in .buttons -side top -padx 10 -pady 5
        pack  .clearallx .cons .about .exit .test4 .test3 .test2   -side bottom -in .buttons
        grid .frame .buttons -sticky ns -pady {0 10}
        . configure -background aquamarine4 -highlightcolor brown -relief raised -border 30
        wm title . "Poker Probability Calculator "

For the push buttons, the recommended procedure is push testcase and fill frame, change first three entries etc, push solve, and then push report. Report allows copy and paste from console. While the testcases are in units of cards, the units cancel out in the calculator equations.

gold This page is copyrighted under the TCL/TK license terms, this license.

Comments Section edit

Please place any comments here, Thanks.