Problem statement

Two friends Kunal and Satyam are playing an interesting game. They take turns drawing a ball from a bag which initially contains R red balls and G green balls. Each player draws a ball alternatively and never put it back. The person who is the first to draw a red balls wins. Satyam always draws first. If there are no more balls in the bag and nobody has drawn a red ball, the satyam wins.

Input -----

The first line will contain the number of test cases T. The first line of each test case will contain a number R (number of red balls) and G(number of green balls )

Cases:

2 1 --> 0.6666667 1 1 ---> 0.50000 10 0 ----> 1.0000

problem link is here:

I tired to solve the problem using top-bottom approach but my codes gives wrong answer at the last case (0 instead of 1)

int probability = 0, c = 0;

void magic(int red, int green, int turn){
	if(green == -1 || red == -1)return ;
	if(red == 0){
		probability++;
		if(turn % 2 == 0) c++;
		return ;
	}
	if(turn == -1) turn = 0;
	else turn++;
	magic(red, green-1, turn % 2);
	magic(red-1, green, turn % 2); 
	return ;
}

int main(){
     
 	ios::sync_with_stdio(0);
    cin.tie(nullptr);
     
    int q;
    cin >> q;
    while(q--){
    	int x, y;
    	cin >> x >> y;
    	magic(x, y, -1);
    	cout << fixed << setprecision(9) << c * 1.0 / probability << '\n';
    	probability = 0, c = 0;
    }
    return 0;
}

I will appreciate any kind of help from all of you, and thanks for your time