Optimal Bet Fraction of Account Value (short C++ code)

Hi,
here's a short C++ program that computes the optimal fraction of account that one should bet
for a set of user defined probabilities and their payouts:

Code:

/*
optimal_bet_fraction.cpp

Author: U.M. in Germany (user botpro @ www.elitetrader.com)

2016-02-02-Tu: init

Solution to this online posting:
  http://www.elitetrader.com/et/index.php?threads/how-much-should-you-risk.297565/
    There is a 35% chance that you win   20% of your bet;
    There is a 25% chance that you lose  15% of your bet;
    There is a 20% chance that you win   12% of your bet;
    There is a 15% chance that you lose   6% of your bet;
    There is a  4% chance that you win   50% of your bet;
    There is a  1% chance that you lose 100% of your bet.
    What percentage of your betting account should you risk to maximize your potential gain?

Compile using a C++11 conformant C++ compiler, here using GNU g++ under Linux:
  g++ -Wall -O2 -std=c++11 optimal_bet_fraction.cpp -o optimal_bet_fraction.exe
 
Run:
  ./optimal_bet_fraction.exe >data.csv 

And the answer is:
  MaxGrowthRate=2.87735% @ fraction=77.79000%

Misc:
  You can change the pre-set conditions, and also add new conditions or del some conditions,
  then recompile and execute the program.

*/

#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <vector>

using namespace std;


int optimal_betfraction()
  { /* creates a csv file of all iterations (this can be analysed in Excel/LibreOffice-Calc),
       and prints the maximum to stderr
    */
 
 
    // set these input data (vp and vr must both be same size):
    const vector<double> vp = { 0.35,  0.25,  0.2,   0.15,  0.04,  0.01 };  // probabilities
    const vector<double> vr = { 0.2,  -0.15,  0.12, -0.06,  0.5,  -1.0  };  // payouts


    const double PctStep = 0.01;  // 0.001;   // 1.0;

    double MaxGrowthRate = -1e9, xPctForMaxGR = 0;   // will be filled below

    printf("r,f\n");
    for (double xPct = 0.0; xPct <= 100.0; xPct += PctStep)
      {
        const double x = xPct / 100.0;
       
        double GrowthRate = 1.0;
        for (size_t i = 0; i < vp.size(); ++i)
          {
            if (vr[i] >= 0.0)
              GrowthRate *= pow(1.0 + x * fabs(vr[i]), vp[i]);
            else 
              GrowthRate *= pow(1.0 - x * fabs(vr[i]), vp[i]);
          }
           
       printf("%.5f,%.5f\n", (GrowthRate - 1.0) * 100.0, xPct);

       if (GrowthRate > MaxGrowthRate)
         MaxGrowthRate = GrowthRate, xPctForMaxGR = xPct;
      }
    fprintf(stderr, "MaxGrowthRate=%.5f%% @ fraction=%.5f%%\n", (MaxGrowthRate - 1.0) * 100.0, xPctForMaxGR);

    return 0;
  }


int main()
  {
    optimal_betfraction();

    return 0;
  }

And the same also in a zip file:

 

Just curious - why does this need C++11? (I didn't read thru the code)

 

I think it's because of the vector initializer method used here.
Of course one can change that easily, then C++11 should not be required anymore.
One can of course also replace the two vectors wholly by classic arrays.