# using pseudocode
        proc test1 {   
               # possible problem instances,
               low vs high
               middle vs low
               high vs middle}
        proc test2 {
            initialize algorithm_result = 1.
            initialize terms of tianji combined probability 
        proc test3 {
            combined probability of winning as tianji_win_prob
            tianji_win_prob has terms of unequal probability
        proc test4 {
            use llength(lsearch)/llength  winner list
            to calculate probilities of
            1) prob_1(tianji_low vs king_high)     horses
            2) prob_2(tianji_middle vs king_low)   horses
            3) prob_3(tianji_high vs king_middle)} horses
        proc test5 {
            prob_1 = tianji high probability   * [expr { rand() } ]
            prob_2 = tianji medium probability * [expr { rand() } ]
            prob_3 = tianji low probability    * [expr { rand() } ]
            would need ~100 trials for answer to gel, in iterative solution }
        proc test6 {
             check algorithm
            f(solution) =? initial product
            check_sum = a+b+c+d+e
            set answers and printout with resulting values
            pseudocode: need test cases > small,medium, giant
            pseudocode: need testcases within range of expected operation.
            pseudocode: are there any cases too small or large to be solved?
            pseudocode: limit to size of eTCL list,   ref  versions.   }
                #end of file

        # pretty print from autoindent and ased editor
        # General Tianji' Chinese Horse Race Strategy Calculator
        # written on Windows XP on eTCL
        # working under TCL version 8.5.6 and 1.0.1
        # gold on TCL WIKI, 25feb2017
        package require Tk
        package require math::numtheory
        namespace path {::tcl::mathop ::tcl::mathfunc math::numtheory }
        set tcl_precision 17
        frame .frame -relief flat -bg aquamarine4
        pack .frame -side top -fill y -anchor center
        set names {{} { high grade horse probability percent (a) , usually 50 :} }
        lappend names { medium grade horse probability percent (b) , usually 35:}
        lappend names { low grade horse probability percent (c) , usually 15: }
        lappend names { optional: : }
        lappend names { answers:  check sum all wins =? 3  }
        lappend names { number of King wins, 0 to max 3  }
        lappend names { number of Tianji wins, 0 to max 3 : }
        lappend names { total winnings for Tianji silver dollars :} 
        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 General Tianji's Chinese Horse Race Strategy
            from TCL WIKI,
            written on eTCL "
            tk_messageBox -title "About" -message $msg } 
        proc tianji_horse_race     { xxx1  }   {
            global side1 side2 side3 side4 side5
            global side6 side7 side8 
            set high_grade_prob 50.
            set medium_grade_prob 35.
            set low_grade_prob 15.
            set  tianji_winnings 0.
            set  king_winnings 0.
            # normal 15 percent = low_grade_prob
            # normal 35 percent = medium_grade_prob
            # normal 50 percent = high_grade_prob
            set high_grade_prob $side1
            set medium_grade_prob $side2
            set low_grade_prob $side3
            set tianji_low  [expr $low_grade_prob * [expr { rand() } ] ]
            set king_high [expr $high_grade_prob * [expr { rand() } ] ] 
            set tianji_low 1.0 
            set tianji_medium 1.0 
            set tianji_high 1.0
            set king_low 1.0 
            set king_medium 1.0 
            set king_high 1.0
            set check_sum 0.0
            # 15 percent = low_grade
            # 35 percent = medium_grade
            # 50 percent = high_grade
            set tianji_low [expr $low_grade_prob * [expr { rand() } ] ]
            set king_high [expr $high_grade_prob * [expr { rand() } ] ]  
            if {    [max  $tianji_low $king_high  ] == $tianji_low   } { set tianji_winnings  1. }
            if {    [max  $tianji_low $king_high  ] == $king_high  } { set king_winnings  1.  } 
            set tianji_medium [expr $medium_grade_prob * [expr { rand() } ] ]
            set king_low [expr $low_grade_prob * [expr { rand() } ] ]  
            if {    [max  $tianji_medium $king_low  ] == $tianji_medium   } { set tianji_winnings [+ $tianji_winnings 1.]  }
            if {    [max  $tianji_medium $king_low  ] == $king_low  } { set king_winnings [+ $king_winnings 1. ]   } 
            set tianji_high [expr $high_grade_prob * [expr { rand() } ] ]
            set king_medium [expr $medium_grade_prob * [expr { rand() } ] ]  
            if {    [max  $tianji_high $king_medium  ] == $tianji_high   } { set tianji_winnings [+ $tianji_winnings 1.] }
            if {    [max  $tianji_high $king_medium  ] == $king_medium  } {  set king_winnings [+ $king_winnings 1. ] }
            set check_sum [+ $king_winnings $tianji_winnings ]
            set side5 $check_sum
            set side6 $king_winnings
            return $tianji_winnings }
       proc calculate {     } {
            global answer2
            global side1 side2 side3 side4 side5
            global side6 side7 side8 
            global testcase_number 
            incr testcase_number 
            set side1 [* $side1 1. ]
            set side2 [* $side2 1. ]
            set side3 [* $side3 1. ]
            set side4 [* $side4 1. ]
            set side5 [* $side5 1. ]
            set side6 [* $side6 1. ]
            set side7 [* $side7 1. ]
            set side8 [* $side8 1. ] 
            # initialize placeholder answer
            set answer2 [tianji_horse_race  3 ]
            set side7 $answer2 
            set side8 [* 200. $answer2 ]
                    }
        proc fillup {aa bb cc dd ee ff gg hh} {
            .frame.entry1 insert 0 "$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| value| comment, if any|& "
            puts "&| $testcase_number:|testcase_number | |& "
            puts "&| $side1 :|high grade horse probability percent (a) , usually 50  |   |&"
            puts "&| $side2 :|medium grade horse probability percent (b) , usually 35 | |& "  
            puts "&| $side3 :|low grade horse probability percent (c) , usually 15 | |& "
            puts "&| $side4 :|optional:| |&"
            puts "&| $side5 :|answers: check sum all wins =? 3 : | |& "
            puts "&| $side6 :|number king wins,  0 to max 3 | random results |& " 
            puts "&| $side7 :|number Tianji wins,  0 to max 3 | random results |& "
            puts "&| $side8 :|total winnings for Tianji silver dollars | random results |&" 
            }
        frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 50.  35.  15.  1.0  0.  0.   0.  0.}
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 50.  30.  20.  1.0  0.  0.   0.  0. }
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 50.  40.  10.  1.0  0.  0.   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 . "General Tianji' Chinese Horse Race Strategy Calculator"  
           # end of deck 

  puts " %| testcase $testcase_number | value| units |comment |%"
  puts " &| volume| $volume| cubic meters |based on length $side1 and width $side2   |&"  

        # pretty print from autoindent and ased editor
        # initial console program, Chinese horse race problem
        # comma delimited spreadsheet for number of horse races
        # written on Windows XP on eTCL
        # working under TCL version 8.5.6 and eTCL 1.0.1
        # gold on TCL WIKI, 10feb2017
        package require Tk
        package require math::numtheory
        namespace path {::tcl::mathop ::tcl::mathfunc math::numtheory }
        set tcl_precision 17
        console show
        set i 2000
        set horse_race_days 1
        puts "horse race number , trial heat, winner, wins of particular horse, cum. probability, loser,loser, horse_a ,          horse_b ,  horse_c ,  last place "
        while {$i>0} {
            if { $horse_race_days > 180 } { break }
            set horse_a [ expr { rand() } ]
            set horse_b [ expr { rand() } ]
            set horse_c [ expr { rand() } ]
            set trial [ expr { rand() } ]
            if { $trial > 0      &&  $trial < .2     } { set winner_name  "horse_a" ; set loser_name  "horse_b,horse_c"     }
            if { $trial > .2     &&  $trial < .5     } { set winner_name  "horse_b" ; set loser_name  "horse_a,horse_c"      }
            if { $trial > .5     &&  $trial < 1.     } { set winner_name  "horse_c" ; set loser_name  "horse_a,horse_b"      }
            set winner [max $horse_a $horse_b $horse_c]
            set last [min $horse_a $horse_b $horse_c]
            lappend winner_list $winner_name
            lappend loser_list $loser_name
            #set number_wins [ lsearch -all $winner_list  $winner_name ]
            set ee [ llength  $winner_list ]
            set kk [ llength [ lsearch -all $winner_list $winner_name ] ]
            set prob [ expr { ($kk*1.) / $ee  } ]
            if {$winner_name == "horse_c" } {
                puts "$horse_race_days ,$trial ,$winner_name,$kk,$prob,$loser_name,$trial, $winner, $horse_a , $horse_b , $horse_c ,                 $last "}
            incr horse_race_days
            incr i -1
        }
            #end of deck

               # pretty print from autoindent and ased editor 
               # subroutine for tianji horse race and combined unequal probability
               # working under TCL version 8.5.6 and eTCL 1.0.1
               # console program written on Windows XP on eTCL
               # written on Windows XP on eTCL
               # working under TCL version 8.5.6 and eTCL 1.0.1
               # gold on TCL WIKI, 2mar2017
        package require Tk
        package require math::numtheory
        namespace path {::tcl::mathop ::tcl::mathfunc math::numtheory }
        set tcl_precision 17
        console show
        proc tianji_horse_race     { xxx1  }   {
            set i 2000
            set horse_race 1
            set trial 1.
            set trialx 1.
            set tianji_low 1.
            set tianji_middle 1.
            set tianji_high 1.
            set king_low 1.
            set king_middle 1.
            set king_high 1.
            set program_result {}
            set winner_list1 {}
            set winner_list2 {}
            while {$i>0} {
            if { $horse_race > 10 } { break }
            set trial [ expr { rand() } ]
            set counter 1
            set tianji_low  [expr 15.* [expr { rand() } ] ]
            set king_high [expr 50.* [expr { rand() } ] ]  
            # 15 percent = low_grade
            # 35 percent = medium_grade
            # 50 percent = high_grade
    if {    [max  $tianji_low $king_high  ] == $tianji_low   } {  lappend winner_list2   " horse_race$horse_race heat$counter "   tianji_low }
     if {    [max  $tianji_low $king_high  ] == $king_high  } {  lappend winner_list2  " horse_race$horse_race heat$counter "   king_high  }                 
            incr counter 
            set tianji_middle [expr 35.* [expr { rand() } ] ]
            set king_low [expr 15.* [expr { rand() } ] ]  
            if {    [max  $tianji_middle $king_low  ] == $tianji_middle   } {  lappend winner_list2   "  horse_race$horse_race heat$counter  "   tianji_middle }
        if {    [max  $tianji_middle $king_low  ] == $king_low  } {  lappend winner_list2  "  horse_race$horse_race heat$counter  "   king_low  } 
            incr counter 
            set tianji_high [expr 50.* [expr { rand() } ] ]
            set king_middle [expr 35.* [expr { rand() } ] ]  
            if {    [max  $tianji_high $king_middle  ] == $tianji_high   } {  lappend winner_list2  " horse_race$horse_race  heat$counter  "   tianji_high  \n}
            if {    [max  $tianji_high $king_middle  ] == $king_middle  } {  lappend winner_list2  "  horse_race$horse_race  heat$counter  "   king_middle \n }       
            incr horse_race
            incr i -1
        } 
           return  $winner_list2   }
           set program_result [  tianji_horse_race  3 ]   
           puts " list of winners  = \n  $program_result  "
           #end of deck

list of winners  = 
  { horse_race1 heat1 } king_high {  horse_race1 heat2  } tianji_middle { horse_race1  heat3  } tianji_high {
} { horse_race2 heat1 } king_high {  horse_race2 heat2  } king_low {  horse_race2  heat3  } king_middle {
} { horse_race3 heat1 } tianji_low {  horse_race3 heat2  } tianji_middle { horse_race3  heat3  } tianji_high {
} { horse_race4 heat1 } king_high {  horse_race4 heat2  } tianji_middle { horse_race4  heat3  } tianji_high {
} { horse_race5 heat1 } king_high {  horse_race5 heat2  } tianji_middle { horse_race5  heat3  } tianji_high {
} { horse_race6 heat1 } king_high {  horse_race6 heat2  } tianji_middle { horse_race6  heat3  } tianji_high {
} { horse_race7 heat1 } king_high {  horse_race7 heat2  } king_low { horse_race7  heat3  } tianji_high {
} { horse_race8 heat1 } tianji_low {  horse_race8 heat2  } tianji_middle { horse_race8  heat3  } tianji_high {
} { horse_race9 heat1 } king_high {  horse_race9 heat2  } king_low {  horse_race9  heat3  } king_middle {
} { horse_race10 heat1 } king_high {  horse_race10 heat2  } tianji_middle {  horse_race10  heat3  } king_middle {
}  

            # random horses in a race
            set horse_a [ expr { rand() } ]
            set horse_b [ expr { rand() } ]
            set horse_c [ expr { rand() } ]
            set trial [ expr { rand() } ]
            if { $trial > 0      &&  $trial < .2     } { set winner_name  "horse_a" ; set loser_name  "horse_b,horse_c"     }
            if { $trial > .2     &&  $trial < .5     } { set winner_name  "horse_b" ; set loser_name  "horse_a,horse_c"      }
            if { $trial > .5     &&  $trial < 1.     } { set winner_name  "horse_c" ; set loser_name  "horse_a,horse_b"      }
            set winner [max $horse_a $horse_b $horse_c]

    if { [ expr { rand() } ] <= .15 } {set hoof_infection_this_year 1 }
    set race_meters_shortfall [ expr { $meters*.1*rand() } ] 
    set race_meters_shortfall [ expr { int($race_meters_shortfall ) } ] 
    (...many...)
     set total_meters [ expr { $meters - $race_meters_shortfall*.1*$hoof_infection_this_year
    # or decrement speed of horse if more effective in program
    set total_meters_speed  [ expr { $normal_meters_speed - $race_speed_shortfall*.1*$hoof_infection_this_year
    set total_meters_speed_exponent  [ expr { $normal_meters_speed_exponent*.1*$hoof_infection_this_year