After reading throw a dice, I decided to look into throwing 2 dice since many games such as monopoly throw 2 dice on each turn.
Using 2 dice makes life more interesting. The most likely throw is 7 - you can never throw 1, there is 1 way to throw 2, 2 ways to throw 3 (2,1 & 1,2) 3 ways to throw 4 (1,3; 3,1; 2,2) and so on. The following code provides some routines for emulating 1 or 2 dice using the simple rand() function. Paste this code into wish as it uses a Tk based histogram to plot the frequency.
sheila: Many games that I play involve throwing N dice, where N can be > 2. Also, I've played games that use 4, 6, 20, etc. sided die. I wrote a little tcl program once to assist in one of the games. I should go look for it. This one is cool, and would be easy to play with die other than 6 sides.
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 throw2dicesum {} {
set thro [ throw2dice]
return [expr [lindex $thro 0]+[lindex $thro 1]]
}
#throwdice emulates a single dice of 6 sides.
#throw2dice returns a list of the results of 2 throwdice;
#throw2dicesum returns the sum of two dice.
proc getfrequency {n} {
# check how often we arrive at each 'square' from 0 with 2 dice thrown to reach square n at least.
set i 0
array set bins {}
set maxbin $n
while {$i<=$maxbin} { set bins($i) 0; incr i}
set i 0
while {$i<40000} { ;# do this number of repeats to get statistical sample.
set j 0
set pos 0
while {$pos<$n} { ;# continue until we reach N
set thro [throw2dicesum]
incr pos $thro
if {$pos<=$n} { ;# if > n then dont count any more.
incr bins($pos)
}
}
incr i
}
puts "Histogram of frequency of reaching square N from origin."
set i 0
while {$i<$maxbin} {
puts "position\t$i\treached\t$bins($i)\ttimes"
incr i
}
histogram [array get bins] 300 250
return 0
}
global ready
set ready 0
proc histogram {slist wid ht} { ;# render a histogram
global ready
array set scores $slist
set nms [lsort -integer [array names scores]]
catch {destroy .h} {}
catch {destroy .b} {}
canvas .h -width $wid -height $ht -bg beige
pack .h
set nbars [array size scores] ;#how many histogram bars
set nax [expr $nbars/10] ;# axis spacing
set hwid [expr $wid/ $nbars]
set i 0
set hmax -9999999 ;# largest y value
set hmin 9999999 ;# smallest y value
while {$i<$nbars} {
set f $scores([lindex $nms $i])
set hmax [ expr {$f>$hmax} ? $f : $hmax]
set hmin [ expr {$f<$hmin} ? $f : $hmin]
incr i
}
if {$hmax>$hmin} {
set i 0
set nay 100
while {$nay<$hmax} {
set yp [expr $ht-0.75*$nay-20]
.h create line 0 $yp $wid $yp -fill red
incr nay 100
}
set nax 10
while {$i<$nbars} {
set x [expr $hwid*$i]
set rhs [expr $x+$hwid/2]
set f [expr $ht-20-.75*$ht*$scores([lindex $nms $i])/$hmax]
.h create rectangle $x [expr $ht-20] $rhs $f -fill gray
if {[expr $i>=$nax]} {
.h create line $x [expr $ht-20] $x 0 -fill red
incr nax 10
}
incr i
incr x $hwid
}
update
button .b -text "Next" -command "incr ready" ;# when ready is changed, proceeds with commands
pack .b
}
}
getfrequency 36Proc getfrequency finds how often you land on each square 0 to n (eg 0-36) no matter how many throws of the dice this takes. Proc histogram produces a Tk plot of the frequency of landing on each square. You will find that the number of times your throw lands on a particular square increases, then decreases, and then oscillates a little. It is remarkable that the rise and fall for squares up to 13 are almost linear. This is due to the probability of each throw increasing and decreasing linearly rather than in a nice bell shaped curve you might have expected [L1 ]. However landing at 7 can be done by throwing a 7 on first throw, OR by throwing 5&2, 2&5, 4&3, 3&4 or 2&2&3 or 2&3&2 or 3&2&2 (taking longer to get there but increasing the number of ways of reaching 7); this increases the probability of landing on 7 above the simple linear probability.
Histogram of frequency of reaching square N from origin. position 0 reached 0 times position 1 reached 0 times position 2 reached 1128 times position 3 reached 2177 times
... this output is numerical results used in the histogram.