/**************************************************************************
.... find the probability of the attacker winning a battle ..........
**************************************************************************/
int chance_of_winning(struct unit *attacker, struct unit *defender)
{
	double p;
	int dfp,afp;
	int dhp,ahp;
	int attackpower=get_total_attack_power(attacker,defender);
	int defensepower=get_total_defense_power(attacker,defender);

	if (!attackpower) return 0;
	if (!defensepower) return 100;

	p=(double)(attackpower)/(double)(attackpower+defensepower);

	if(is_sailing_unit(defender) && map_get_city(defender->x, defender->y))  {
		afp=1;   /* defending ships in port only get a FP of at most 1 */
	} else {
		afp=get_unit_type(attacker->type)->firepower;
	};
	dfp=get_unit_type(defender->type)->firepower;
	dhp=defender->hp+afp-1;   /* add afp-1 so we round up instead of down */
	ahp=attacker->hp+dfp-1;

	p=sum_binomial(p,dhp/afp,ahp/dfp);
	
	return((int)(100*p));
}

/**************************************************************************
 sums the area under a binomial distribution with parameters p and n = x+y-1
 from x to n.  This is the chance a unit has of winning if the probably of
 it winning a round is p, the attacker needs to win x times, and the defender
 needs to win y times.
**************************************************************************/
double sum_binomial(double p, int x, int y)
{
	double q=1-p;
	double r,b,s;
	int n=x+y-1,k;

	if(x<y)  {
		r=p/q; s=b=pow(q,n);
		for(k=1;k<x;k++) s+=(b*=(double)(n-k+1)/k*r);
		return(1-s);
	} else {
		r=q/p; s=b=pow(p,n);
		for(k=1;k<y;k++) s+=(b*=(double)(n-k+1)/k*r);
		return(s);
	};
}