- a property, opportunity to buy it or pay rent (including station, utility)
- a chance card (draw a card which might give you money or take it or tell you where to go)
- a community chest (draw a card but different results)
- pay a tax or receive income (at Go) or even free parking.
- be in or visiting Jail

# monotony.tcl -- # module for analysing frequency of landing on various squares in the # game of monopoly ((c) Waddingtons). # This code does not infringe on their copyright because it only analyses the rules # it is not a player or emulator for the game. # # Basic facts: # every turn a player tosses 2 dice, giving equal chance of each number (1-6). # therefore every pair of numbers can score: # 2 1&1 -once in 36 # 3 1&2 or 2&1 (2 in 36) etc. # namespace eval ::monopoly { # code for each square: pi=property of set i # c:community chest; C chance; s station; j jail J go to Jail # f free parking; t=100 tax, T 200 tax; g-go array set squares { 1 p1 2 Chest 3 p1 4 T 5 Station 6 p2 7 Chance 8 p2 9 p2 10 jail \ 11 p3 12 electric 13 p3 14 p3 15 Station 16 p4 17 Chest 18 p4 19 p4 20 freePark \ 21 p5 22 Chance 23 p5 24 p5 25 Station 26 p6 27 water 28 p6 29 p6 30 toJail \ 31 p7 32 Chest 33 p7 34 p3 35 Station 36 Chance 37 p8 38 t 39 p8 0 Go} # namespace export + - / * conj exp sin cos tan real imag mod arg log pow sqrt tostring } # dice thrower proc getchance {pos} { # 16 chance cards; 1 takes you to Pall Mall (sq 11), 1 to Jail, 1 to Go set luck [expr int(16*rand())] if {$luck>6} {return $pos} ;# no change if {$luck==0} {return 11} ;# Pall Mall forward if {$luck==1} {return 39} ;# mayfair if {$luck==2} {return 10} ;# Jail if {$luck==3} {return 15} ;# marylebone Sta if {$luck==4} {return [expr $pos-3]} ;# back 3 spp if {$luck==5} {return 24} ;# Trafalgar sq if {$luck==6} {return 0} ;# Go # all others are 'make repairs' receive money etc return $pos ;# no change } proc getcc {pos} { # 15 cards; 1 takes you to Old Kent Rd (sq 1), 1 to Jail, 1 to Go set luck [expr int(15*rand())] if {$luck>2} {return $pos} ;# no change if {$luck==0} {return 1} ;# Old Kent Road (go back) if {$luck==1} {return 0} ;# Go if {$luck==2} {return 10} ;# Jail return $pos ;# no change } proc throwdice {} { set ok 0 while {!$ok} { set sc [expr 1+int(6*rand())] if {$sc<7} {set ok 1} } return $sc } proc throw2dice {} { lappend all [throwdice] lappend all [throwdice] return $all } proc monotony {nthr} { set bins { 1 2 3 4 5 6 7 8 9 10 11 12} array set throes {} foreach bin $bins { set throes($bin) 0 } set i 0 while {$i<40} { set landss($i) 0 incr i } set pos 40 ;# at Go set ndubs 0 ;# when 3 doubles in a row, go to jail! set n3s 0 while {$i<$nthr} { set thr [throw2dice] set s1 [lindex $thr 0] set s2 [lindex $thr 1] set total [expr $s1 + $s2 ] set pos [expr ($pos+$total)%40] incr throes($total) if {$s1==$s2} { ;#count doubles incr ndubs } else { set ndubs 0 } if {$ndubs>=3} { ;# when 3 doubles in a row, go to jail! set ndubs 0 set pos 10 ;# jail incr n3s } else { # handle special squares if {[string compare $::monopoly::squares($pos) "toJail"]==0} { set pos 10 } if {[string compare $::monopoly::squares($pos) "Chest"]==0} { set pos [getcc $pos] } if {[string compare $::monopoly::squares($pos) "Chance"]==0} { set pos [getchance $pos] } } incr landss($pos) incr i } set i 1 while {$i<13} { puts "Threw $i [expr $throes($i)/double($nthr)]" incr i } set i 0 while {$i<40} { puts "Landed on $i $::monopoly::squares($i) [expr $landss($i)/double($nthr)]" incr i } puts "Sent to jail $n3s times from $nthr [expr double($nthr)/double($n3s)]" } monotony 200000The end result shows the slightly distorted frequency of visiting each square:

Landed on 0 g 0.031275 Landed on 1 p1 0.026454 Landed on 2 Chest 0.0174255 Landed on 3 p1 0.0221405 Landed on 4 T 0.023662 Landed on 5 Station 0.022662 Landed on 6 p2 0.023248 ...where pN means one of the properties N (N=1-8, Old Kent Road to Mayfair) and so on.The reference [1] quotes slightly different probabilities - this is due to 2 effects:

- reference used 32 billion dice rolls, the above only 200,000.
- reference [2] suggests there are 10 chance cards which move your position; my set only has 7.

[ Category Games | Category Education ]