Updated 2017-03-12 13:46:44 by gold

## Introduction edit

gold Here is some eTCL starter code for General Tianji' Horse Race Strategy from China in calculator shell. Additional console programs below are used to check or improve subroutines in calculator shell.

The tale of the General Tianji and General Sun Bin ( died 316 BCE) was found in the Chinese history book, Shujing. The Shujing history book was literally saved from the flames of the book burning first empire. I have a rare English translation of the Shichih (sic) commentary in my library. Here the particular issue was how the grades of horses were defined in ancient China. The analysis assumed the best grade horse won 50 percent of his races, the middle grade won 35 percent, and the low grade won 15 percent. The eTCL calculator has entries for the grade probabilities to be changed so the effects or rewards of better or lesser random models can be studied.

An alternate method for selecting winners for random horses is somewhat like the sieve method or throwing different colored apples into separate buckets for each horse. The output of the random generator is a decimal fraction between 0.0 and 1.0. Each random horse is assigned a range or band between 0.0 and 1.0, or between the equivalent 0 percent and 100 percent probability. Meaning, the developed formula is 100 percent times the probability of the variable 1.0 from the generator. For example, random horse_a could be assigned the band 0 to 20 percent, random horse_b could be assigned 20 to 30 percent, and random horse_c could be assigned 50 to 100 percent. In different expressions, the probability bands for the horses are 0. > horse_a < 20. , 20> horse_b < 50., and 50. > horse_c < 100.

Some trial code for racehorse accidents or racehorse troubles can be developed for random horses. For the example below, there is a 15 percent chance of hoof infection. If the statement on hoof infection fires, there is a 0.1 factor or 10 percent loss as short_fall of the finish line or 10 percent reduction in normal horse speed. Also, horse speed may not be constant, so a different exponential curve or exponential constant could be selected, reduced, or changed for the horse speed. Notice the potential loss for the horse is calculated independent of whether the hoof infection flag is yes or no (0 or 1). The potential for trouble is there whether or not the accident actually occurs. The potential for trouble can be calculated, so strategy or insurance can be adjusted for the horse race.

The Tainji horserace as a computer contest problem is featured in ACM student contests with an average of 6000 Chinese entries ( computer programs ). Most of the entries featured bipartite matching algorithms. For the eTCL calculator, the calculator is returning the results of random models so the random results are not always the same with each solve. Over a number of cases, the cumulative or average results should approach the results or winnings of General Tianji.

## Pseudocode Section edit

```            # 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```

### 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 value comment, if any
1:testcase_number
50.0 :high grade horse probability percent (a) , usually 50
35.0 :medium grade horse probability percent (b) , usually 35
15.0 :low grade horse probability percent (c) , usually 15
1.0 :optional:
1.0 :optional:
1.0 :optional:
3.0 :optional: number Tianji wins, 0 to max 3 random results
600.0 :answer: total winnings silver dollars random results

#### Testcase 2

table 1 printed in tcl wiki format
quantity value comment, if any
2 :testcase_number
50.0 :high grade horse probability percent (a) , usually 50
30.0 :medium grade horse probability percent (b) , usually 35
20.0 :low grade horse probability percent (c) , usually 15
1.0 :optional:
1.0 :optional:
1.0 :optional:
1.0 :optional: number Tianji wins, 0 to max 3 random results
200.0 :answer: total winnings silver dollars random results

#### Testcase 3

table 3 printed in tcl wiki format
quantity value comment, if any
3 :testcase_number
50.0 :high grade horse probability percent (a) , usually 50
40.0 :medium grade horse probability percent (b) , usually 35
10.0 :low grade horse probability percent (c) , usually 15
1.0 :optional:
1.0 :optional:
1.0 :optional:
1.0 :optional: number Tianji wins, 0 to max 3 random results
200.0 :answer: total winnings silver dollars random results

### References:

• Horseracing in Tcl by RS
• Plugging a Math Gap with Harvard mathematician Shing-Tung Yau,
• Forbes Magazine 2007, Institute of Mathematical Sciences
• in Hong Kong studies betting on horse races and predicting the weather.
• Tian Ji , The Horse Racing, Peking University, Ying Fuchen,Xu Pengcheng,Xie Di, ACM Programmer's Contest
• The Ambitious Horse, Ancient Chinese Mathematics Problems, Lawence W. Swienciki, Ph.D.
• Game-theoreticanalysis of anancient Chinese horse race problem, Mingming Leng, Mahmut Parlar,
• DeGroote School of Business, McMaster University, Hamilton, Ont., Canada L8S 4M4
• 10 December 2004
• Random Walk Equation Slot Calculator Example
• Plugging a Math Gap with Harvard mathematician Shing-Tung Yau, Forbes Magazine 2007,
• Institute of Mathematical Sciences
• in Hong Kong studies betting on horse races and predicting the weather
• Sumerian Construction Rates and eTCL Slot Calculator Demo Example
• Chabert, J. "Methods of False Position." Ch. 3 in A History of Algorithms: From the Pebble to the Microchip. , 1999.
• John Hannah , False position in Leonardo of Pisa's Liber Abbaci,Historia Mathematica Volume 34 issue 3 2007
• Eugene C. Boman,False Position, Double False Position and Cramer's Rule, College Mathematics Journal
• Howard Eves ,On the practicality of the rule of false position, Mathematics Teacher Volume 51
• Joy B. Easton, the rule of double false position, Mathematics Teacher Volume 60
• Vera Sanford, the rule of false position, Mathematics Teacher Volume 44 issue 5 1951
• Karine Chemla, Reflections on the World-wide History of the Rule of False Double Position, or: How a Loop Was Closed
• Thomas G. Edwards -- Using the Ancient Method of False Position to Find Solutions, Mathematics Teaching in the Middle School Volume 14 issue 4 2008
• Oneliner's Pie in the Sky
• One Liners
• Category Algorithm
• [Babylonian Number Series and eTCL demo example calculator]
• Brahmagupta Area of Cyclic Quadrilateral and eTCL demo example calculator
• Gauss Approximate Number of Primes and eTCL demo example calculator
• Taking a Weighted Average, Dr Math, mathforum.org/dr.math, dated 03/20/2003
• google <Weighted Average, Dr Math>, mathforum.org/dr.math
• Using Weighted Criteria to Make Decisions, Dr Math>, mathforum.org/dr.math, dated 07/18/2008
• google <Weighted sum product model Decision >
• harmonic mean discussed in Additional math functions
• harmonic mean discussed in Tcl Normalized Extended Benchmarks
• see arithmetic mean on tcl-wiki Stats 2011-05-22, RLE
• see similar 1/(1/nth) terms method used in
• Babylonian Combined Market Rates and eTCL demo example calculator, numerical analysis
• Zhang Baichun and Jürgen Renn (eds.) , Transformation and Transmission:
• Chinese Mechanical Knowledge and the Jesuit Intervention
• Joint Research Group of the MPIWG and its Partner Group at the IHNS of the CAS.
• Probability models on horse-race outcomes,
• MUKHTAR M. ALI, Department of Economics, University of Kentucky, USA
• Probability and Optimization Probability and Optimization Models for Racing Horse Models,
• Victor S. Y. Lo University of British Columbia University of British Columbia, Fidelity Investments
• Designing competitions between teams of individuals, Pingzhong Tanga,Yoav Shohamb,c, Fangzhen Lina,
• Mentions ACM horse race problems relative to teams of computer students.
• Sun Bin: Distinguished Military Strategist After Sun Zi, By David Wu, Epoch Times
• Lecture 4: Matching Algorithms for Bipartite Graphs
• Professor: Clifford Stein
• Lecture notes on bipartite matching
• 100: “Matchings” Fall 2012
• Bayes Theorem,Bayes Theorem in short is a method of analysing data.
• Massachusetts Institute of Technology Handout 3
• Combinatorial Optimization February 9th, 2009 Michel X. Goemans
• Paper mentions Tianji horse race problem.
• Designing competitions between teams of individuals,
• Pingzhong Tanga, Yoav Shohamb, Fangzhen Lin,
• Department of Computer Science, Hong Kong University of Science and Technology,
• Clear Water Bay, Hong Kong
• Computer Science Department, Stanford University, CA 94305, United States
• Microsoft Israel R&D Center, Herzliya, Israel.

## Appendix Code edit

### appendix TCL programs and scripts

```        # 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  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 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 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 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 .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 ```

### Pushbutton Operation

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.

For testcases in a computer session, the eTCL calculator increments a new testcase number internally, eg. TC(1), TC(2) , TC(3) , TC(N). The testcase number is internal to the calculator and will not be printed until the report button is pushed for the current result numbers. The current result numbers will be cleared on the next solve button. The command { calculate; reportx } or { calculate ; reportx; clearx } can be added or changed to report automatically. Another wrinkle would be to print out the current text, delimiters, and numbers in a TCL wiki style table as
```  puts " %| testcase \$testcase_number | value| units |comment |%"
puts " &| volume| \$volume| cubic meters |based on length \$side1 and width \$side2   |&"  ```

## Console program for race output as CVS spreadsheet, includes > equal probability horses <  edit

```        # 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```

## cvs output for > wins only < of horse_c edit

horse race number , trial heat, winner, wins of particular horse, cum. probability, loser,loser, horse_a , horse_b , horse_c , last place 2 ,0.72403450297379612 ,horse_c,1,0.5,horse_a,horse_b,0.72403450297379612, 0.86678423540051297, 0.13588783151278638 , 0.86678423540051297 , 0.042644376420716001 , 0.042644376420716001 3 ,0.87722261151169545 ,horse_c,2,0.66666666666666663,horse_a,horse_b,0.87722261151169545, 0.84789148059109765, 0.84789148059109765 , 0.51211429457744317 , 0.104948963087494 , 0.104948963087494 4 ,0.86264225927304583 ,horse_c,3,0.75,horse_a,horse_b,0.86264225927304583, 0.61519644810594454, 0.48043167706599071 , 0.61519644810594454 , 0.60670331660970267 , 0.48043167706599071 7 ,0.73498046013292873 ,horse_c,4,0.5714285714285714,horse_a,horse_b,0.73498046013292873, 0.27436126688232704, 0.27436126688232704 , 0.18981249127062619 , 0.17854078541441856 , 0.17854078541441856 8 ,0.96185003824618176 ,horse_c,5,0.625,horse_a,horse_b,0.96185003824618176, 0.81659345413399553, 0.81659345413399553 , 0.48618363006328402 , 0.28827047361446101 , 0.28827047361446101 10 ,0.76152973378148381 ,horse_c,6,0.59999999999999998,horse_a,horse_b,0.76152973378148381, 0.95698579864436095, 0.078298148735565204 , 0.95698579864436095 , 0.060317815775199707 , 0.060317815775199707

## Console program for tianji horse race and combined unequal probability edit

```               # 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```

## output follows for list of winners in trial races with three 3 heats, > unequal probability horses < edit

```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 {
}  ```

## Example eTCL code for selecting winners for random horses in a race edit

```            # 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]```

## Example eTCL code for horse accidents or shortfalls edit

```    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```