#include <iostream>
#include <iomanip>      // std::setprecision


using namespace std;

long double getNThProb(int n, double long x){
    long double sol = x*1.0;
    for(int i = 2; i <= n; i++){
        sol = sol + (1-sol)*x;
    }
    return sol;
}

long double initProbs[100]={0,0.1, 0.1, 0.6, 0.455652142}, sumProbs[100], incraseRate[100]={0,0.1, 0.1, 0.6, 0.455652142};
int main(){
    int n = 4;
    int k = 4;

    for(int iter = 1; iter <= k; iter++){
        int poz = 1;
        for(int i = 1; i <= n; i++){
            if (incraseRate[i] > incraseRate[poz]){
                poz = i;
            } else if(incraseRate[i] == incraseRate[poz]){
                if(initProbs[i] > initProbs[poz]){ //recheck
                    poz=i;
                }
            }
        }
        sumProbs[poz] += (1-sumProbs[poz])*initProbs[poz];
        incraseRate[poz] = (1-sumProbs[poz])*initProbs[poz];
    }

    double long result=0.0;
    for(int i = 1; i <= n; i++){
        result += sumProbs[i];
//        cout<<initProbs[i]<<' '<<sumProbs[i]<<' '<<incraseRate[i]<<'\n';
    }
    cout<<setprecision(7)<<result;

    return 0;
}