probability_of_streaks.pl

$p = 50/100; # Probability of event
$m = 3; # Number of events in a row
$n = 100; # Number of trials

#--------------------------------------
#//////////////////////////////////////
$iter = int( $n/($m+1) ); #ceiling( ($n-$m)/($m+1) )
$last = $n - ($iter-1)*($m+1) - $m - 1;

$c = (1-$p)*$p**$m;

$prob[$m] = $p**$m;

print "hi = ",$last,"\n";


for ($j = 1; $j <= $iter; $j++) {
print "wtf=",$prob[$m],"\n";
$prob[0] = $prob[$m] + (1-$prob[0])*$c;

for ($i = 1; $i <= $m; $i++) {
$prob[$i] = $prob[$i-1] + (1-$prob[$i])*$c;
}

}

print "Probability of ", $m, " events of probability ", $p, " in a row in ", $n, " trials = ", $prob[$last], " or ", 1/$prob[$last]-1, " to 1";