Calculate probabilities of breaking even or winning at least the expected value at some point in a series of bets; see http://math.stackexchange.com/questions/261357.

Question261357.java

public class Question261357 {
    final static boolean even = false;
    final static int percent = 74;
    final static double p = percent / 100.;
    final static int win = 7;
    final static int lose = 6;

    static double [] [] cache;
    static boolean [] [] done;

    public static void main (String [] args) {
        for (int n = 1;;n++) {
            cache = new double [n] [n];
            done = new boolean [n] [n];
            System.out.println ("    " + n + " : " + p (n,0,0));
        }
    }

    static double p1 (int n,int w,int k) {
        int e = w * win - (k - w) * lose;
        return (even ? e >= 0 : 100 * e >= k * (percent * win - (100 - percent) * lose)) ? 1 : n == 0 ? 0 : p (n,w,k);
    }

    static double p (int n,int w,int k) {
        if (!done [k] [w]) {
            cache [k] [w] =  p * p1 (n - 1,w + 1,k + 1) + (1 - p) * p1 (n - 1,w,k + 1);
            done [k] [w] = true;
        }
        return cache [k] [w];
    }
}