** Over-21 Game Shell and eTCL Slot Calculator Demo Example , numerical analysis**

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[gold]  Here is some eTCL starter code converting a slot calculator into the Over-21 game shell.

Odds for successive draws in a 52 card deck can be found for blackjack as follows. Probability of drawing successive aces would be set probability_2_aces {(4 /52)* ( 3/ 51)}, 0.004524. In blackjack, a winning hand of two cards would be "ace & face ", where ace is counted as 11 and face as 10. Probability of drawing successive 2 cards for winning hand would be  would be set probability_ace_&_face {(4/52)*(16/51)}, 0.02413.  The dealer wins ties, so the dealer will win, even if a dream winning hand is dealt to both player and dealer. For example, four successive cards as first ace&face to the player and second ace&face to dealer would be set double_winner {(4/52)*(16/51)*(3/50)*(15/49)},  0.0004432   . However, some dealers use multiple 2-8 decks and alternate dealing of cards to multiple players. The probability for multiple decks was  set probability_multiple_decks  (N1*4-S1+1)/(N1*52-S1+1)*(F1/(N1*52-S2+1))...). For example , winning hand for 2 decks was {(8/104)*(32/103)}, 0.02389. For 8 decks, the winning hand of ace&face would be {(32/416)*(128/415)}, 0.02372.

There are differences between the Over-21 calculator and the Blackjack game on the tables. Both hands of 2 cards each for dealer and player are shown in display of Over-21 calculator. Whereas on the tables, only one card of the hand must be shown until dealer calls or payoff. Also the Over-21 calculator is using random selection on 52 card deck, not pulling cards off deck like the tables. On the tables, the order of dealt cards to dealer and more than one player might makes a difference in computed probability. On the tables, the ability to call the end of the game, knowledge of played top cards, and winning all ties are considerable advantages to dealer.

General guidelines for computer games suggest the player should win one in five times to keep interest up. Right now, the Over-21 game shell is using the first deal of two cards to estimate win for the player. The winning conditions for the  Over-21 game are 1) player score greater than dealer, 2) player score greater than ~17, and 3) player score less than 22 (not busted). On the tables, the dealer could win on the second or next deal, since the dealer calls or closes the game.  Most of the tables use additional decks (2-8) and pull the dealt cards, which could be implemented in the program with concat or remove list element statements. The next steps for the Over-21 game shell should be tracking the win conditions for the dealer and a  button for second deal.  
 
*** Pseudocode and Equations ***
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dealer and player dealt two initial cards
dealer wins all ties
ace card is 1 or 11
all face cards are 10
all ten cards are 10
sum of cards > 21 set lose condition (bust)
sum of dealer >sum of player =< 21, player in winner state  
sum of player = >sum of dealer =< 21, dealer in winner state  
player or dealer may sit turn, called hold condition 
player has 5 cards not over 21 is winner (rare)
Player and dealer must show one card only, until close or payout.
Normally dealer holds at 16 and above
Normally player wants extra deal if hand <16
Double down, optional if player dealt two cards of same number, but not same suit.
Player on double down must put double money up for two  hands. 
====== 
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***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. Aside from the TCL calculator display, when one presses the report button on the calculator, one will have console show access to the   capacity  functions (subroutines). 

**** Testcase 1 ****
%|table 1|printed in| tcl wiki format|% 
&|quantity|dealer first card value| comment, if any|& 
&|testcase number|1| |&
&| 2 :|dealer first card|   |&
&|7 :|dealer second card| |& 
&| 10 :|player first card| |& 
&| 11 :|player second card  |  |&
&| 9.0  :|dealer score |  |&
&| 21.0  :|player score |  |&
&| 0.0  :|player need card dealt? <0 or 1 >|  |&
&| 1.  :|winner declared <0 or 1 > |  |&

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**** Testcase 2 ****
%|table 2|printed in| tcl wiki format|% 
&|quantity|dealer first card value| comment, if any|& 
&|testcase number|2| |&
&| 7 :|dealer first card|   |&
&|10 :|dealer second card| |& 
&| 5 :|player first card| |& 
&| 6 :|player second card  |  |&
&| 17.0  :|dealer score |  |&
&| 11.0  :|player score |  |&
&| 1.0  :|player need card dealt? <0 or 1 >|  |&
&| 0.  :|winner declared <0 or 1 > |  |&

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**** Testcase 3 ****
%|table 3|printed in| tcl wiki format|% 
&|quantity|dealer first card value| comment, if any|& 
&|testcase number|3| |&
&| J :|dealer first card|   |&
&|5 :|dealer second card| |& 
&| 8 :|player first card| |& 
&| 9 :|player second card  |  |&
&| 15.0  :|dealer score |  |&
&| 17.0  :|player score |  |&
&| 0.0  :|player need card dealt? <0 or 1 >|  |&
&| 0.  :|winner declared <0 or 1 > |  |&

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**** Testcase 4 ****
%|table 4|printed in| tcl wiki format|% 
&|quantity|dealer first card value| comment, if any|& 
&|testcase number|20| |&
&| 9 :|dealer first card|   |&
&| 6 :|dealer second card| |& 
&| 10 :|player first card| |& 
&| K :|player second card  |  |&
&| 15.0 :|dealer score |  |&
&| 20.0 :|player score |  |&
&| 0.0 :|player need card dealt? <0 or 1 >|  |&
&| 0.0 :|winner declared <0 or 1 > |  |&
?????????
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***Screenshots Section***
****figure 1.****
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***References:***
   
   * Blackjack Game Project Report - Andrew Thomas BSc (Hons)  
    

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**Appendix Code**

***appendix TCL programs and scripts ***

====== 
        # pretty print from autoindent and ased editor
        # Over-21 Game Shell calculator
        # written on Windows XP on eTCL
        # working under TCL version 8.5.6 and eTCL 1.0.1
        # gold on TCL WIKI, 15oct2014
        package require Tk
        namespace path {::tcl::mathop ::tcl::mathfunc}
        frame .frame -relief flat -bg aquamarine4
        pack .frame -side top -fill y -anchor center
        set names {{} {dealer first card:} }
        lappend names {dealer second card:}
        lappend names {player first card: }
        lappend names {player second card :}
        lappend names {dealer score :}
        lappend names {player score : }
        lappend names {player need card dealt? < 0 or 1 > : }
        lappend names {player declared winner < 0 or 1 >:}
        foreach i {1 2 3 4 5 6 7 8} {
            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 Over 21 Game Shell
            from TCL WIKI,
            written on eTCL "
            tk_messageBox -title "About" -message $msg }       
        proc lpick L {lindex $L [expr int(rand()*[llength $L])];}
        proc swapx { text } {
            #set text [string map [list $item $replacewith] $text] #RS
             set text [string map [list "A" "11.0"] $text] 
             set text [string map [list "J" "10.0"] $text] 
             set text [string map [list "Q" "10.0"] $text] 
             set text [string map [list "K" "10.0"] $text]
             return $text                  
                                                    }  
        proc calculate {     } {
            global answer2
            global side1 side2 side3 side4 side5
            global side6 side7 side8
            global testcase_number
            incr testcase_number 
            set cds { 1 2 3 4 5 6 7 8 9 10 J Q K A } 
            set list_values { 1 2 3 4 5 6 7 8 9 10 10 10 10 11 }
            set list_cards [ concat $cds $cds $cds $cds ]
            puts "lists cards in current deck"
            puts "$list_cards"
            set side7 0.0
            set side8 0.0
            set side1  [ lpick $list_cards ]
            set side2  [ lpick $list_cards ]
            set side3  [ lpick $list_cards ]
            set side4  [ lpick $list_cards ]
            set side5 [+  [swapx $side1 ] [swapx $side2 ] ]
            set side6 [+  [swapx $side3 ] [swapx $side4 ] ]
            set side5 [* $side5 1. ]
            set side6 [* $side6 1. ]
            puts " dealer $side5 against player $side6 "
            puts "logic values p>16 [ expr { $side6 > 16. } ]"
            puts "logic values  p<16  [ expr { $side6 < 16. } ]  "
            puts "logic values p>d [ expr { $side6 > $side5 } ] "
            puts "logic values p>17 [ expr { $side6 > 17. } ] "
            puts "logic values p<22  [ expr { $side6 < 22. } ]  "
            if { $side6 > 16. }  { set side7 0. } 
            if { $side6 < 16. }  { set side7 1. }              
            if { $side6 > $side5 && $side6 < 22. &&  $side6 > 17. }  { set side8 1. }       
                                       }
        proc fillup {aa bb cc dd ee ff gg hh} {
            .frame.entry1 insert 0 "$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 "$ff" 
            .frame.entry7 insert 0 "$gg"
            .frame.entry8 insert 0 "$hh" 
             }
        proc clearx {} {
            foreach i {1 2 3 4 5 6 7 8 } {
                .frame.entry$i delete 0 end } }
        proc reportx {} {
            global side1 side2 side3 side4 side5
            global side6 side7 side8 
            global testcase_number
            console show;
            puts "%|table $testcase_number|printed in| tcl wiki format|% "
            puts "&|quantity|dealer first card value| comment, if any|& "
            puts "&|testcase number|$testcase_number| |&"
            puts "&| $side1 :|dealer first card|   |&"
            puts "&| $side2 :|dealer second card| |& "
            puts "&| $side3 :|player first card| |& "
            puts "&| $side4 :|player second card  |  |&"
            puts "&| $side5 :|dealer score |  |&"
            puts "&| $side6 :|player score |  |&"
            puts "&| $side7 :|player need card dealt? <0 or 1 >|  |&"
            puts "&| $side8 :|winner declared <0 or 1 > |  |&"
         }
        frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Deal" -command { calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 1.0 7.0 10.0 10.0   8.  20.0 0. 0.}
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 5.0 10.0 2.0 8.0   15.  10. 1. 0. }
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 4.00 5.0 5.0 6.0   9.0  11.0  1.0 0. }
        ::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 . "Over-21 Game Shell Calculator "
======

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