#!/usr/local/bin/perl -w
# reads a (difference in potential) and n (game to n) from command line 
# and returns the prob that team 1 would win 
#
# = sum_x=0..n-1   p^x q^n  ( x+n-1 choose x )
#
# x being the loser's score

$a=-1;
$n=-1;

eval "\$$1=\$2" while @ARGV && $ARGV[0]=~ /^(\w+)=(.*)/ && shift;

if ( $a < 0  || $n < 1 ) { print STDERR "You must supply a and n\n"  ; 
			   &print_usage ();
			   exit(0);
		       }

sub print_usage {
    print STDERR " win.p a=1 n=15\n" ; 
}

$p = 1.0 / ( 1.0 + exp ( - $a ) ) ; 
$q = 1.0 / ( 1.0 + exp ( $a ) ) ; 
if ( $p > $q ) { $p = 1.0 - $q ; }
else { $q = 1.0 - $p ; }
printf "p = %9.3g, q = %9.3g\n" , $p , $q ; 

$pwin = 0.0 ; $plose = 0.0 ; 
$choose = 1 ; 
$pxqn = $q ** $n ; # prob of an n - nil loss 
$qxpn = $p ** $n ; # prob of an n - nil win
for ( $x = 0 ; $x <= $n-1 ;  ) {
    $pwintox = $qxpn * $choose ;
    $pwin +=  $pwintox ; 
    $plosetox = $pxqn * $choose ; 
    $plose +=  $plosetox ; 
    printf "(win %2d:%2d) = %9.3g, [%9.3g] (lose %2d:%2d) = %9.3g [%9.3g]\n" , $n , $x , $pwintox , $pwin , $x, $n , $plosetox , $plose ; 
    $pxqn *= ($p) ; 
    $qxpn *= ($q); 
    $x ++ ; 
    $choose *= ($x + $n - 1.0 ) / $x ; 
}
printf "prob(win) = %9.3g, prob(lose) = %9.3g\n" , $pwin , $plose ; 
				#