The exact cost of all Galaxy Gates (excluding ABG)

Quote:

Originally Posted by Palladium<3

Intro:
Over the summer I made a little program which build hundreds of virtual gates per second, so with a large sample I am able to accurately determine the cost of any gate given the number of parts. Many thanks to [Only registered and activated users can see links. Click Here To Register...] for helping me with my first project. I hope this is useful in terms of planning for a few of you.

Assumptions:

Each spin has a chance of 13% to hit a part/multiplier (although when you spin with a full nano, it may be between 13-17, I do not know how much it actually is, depends on how BP programmed it. i.e the extra 4% might become ammo straight away).
That the cheapest method of building gates is to use multipliers straight away (x2) until it gets up to 6 parts away from being completed and then it will hit the multiplier.This program spins 1 spin at a time.
That my random number generation is truly random, I used a cryptographically secure pseudo-random number generator which I believe is 'random enough'.

Results:
Delta:

Number of gates built: 100,000

Minimum spins required: 1166

Maximum spins required: 3494

Sample standard deviation: 265

Average spins required: 1966

Epsilon:

Number of gates built: 100,000

Minimum spins required: 804

Maximum spins required: 2994

Sample standard deviation: 236

Average spins required: 1522

Zeta:

Number of gates built: 100,000

Minimum spins required: 907

Maximum spins required: 3298

Sample standard deviation: 248

Average spins required: 1706

Kappa:

Number of gates built: 100,000

Minimum spins required: 1042

Maximum spins required: 3514

Sample standard deviation: 258

Average spins required: 1844

Lambda:

Number of gates built: 100,000

Minimum spins required: 257

Maximum spins required: 1785

Sample standard deviation: 153

Average spins required: 683

Hades:

Number of gates built: 100,000

Minimum spins required: 257

Maximum spins required: 1673

Sample standard deviation: 153

Average spins required: 683

Kuiper:

Number of gates built: 100,000

Minimum spins required: 782

Maximum spins required: 2875

Sample standard deviation: 237

Average spins required: 1538

Code:
Written in C#, you can copy/paste this directly into a console application, if you want- although it's just a bunch of nested loops :P

Spoiler

Code:

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Security.Cryptography;

namespace ConsoleApplication2
{
    class Program
    {
        public static string GetSecureRandom()
        {
            using (RNGCryptoServiceProvider rng = new RNGCryptoServiceProvider())
            {
                byte[] randomNumber = new byte[sizeof(Int64)];// sizeof(int) == 4 because an integer consists of 4 bytes
                rng.GetBytes(randomNumber);
                int value = BitConverter.ToInt32(randomNumber, 0);
                return value.ToString();
            }
        }
        static double GetRandom()//gets a random number between 0 and 99
        {
            double RandomInt32 = Convert.ToDouble(GetSecureRandom()) + Int32.MaxValue;
            double RandomZeroAndOne = (RandomInt32 / (Int32.MaxValue));
            double RandomZero = (RandomZeroAndOne / 2);
            double Finals = RandomZero * 100;
            double floor1 = Math.Floor(Finals);
            return floor1;//returns a value between 0-99
        }
        static bool AreGatePartsEntered;//public variable used in loop
        static bool DoesUserWantToRepeat;
        static int NumberOfPartsRequiredInt = 0;//finds number of parts required to make the gate
        static int GetGateParts()//function to request gate parts from the user
        {
            if (AreGatePartsEntered==false)//Asks you to enter gate parts only once
            {
                Console.WriteLine("Please enter number of gate parts.");
                NumberOfPartsRequiredInt = Convert.ToInt32(Console.ReadLine());
                AreGatePartsEntered = true;
                return NumberOfPartsRequiredInt;
            }
            else
            {
                return NumberOfPartsRequiredInt;
            }
        }
        static double GetRandom2()//returns a value between 0-GateParts-1
        {
            double RandomInt32 = Convert.ToDouble(GetSecureRandom()) + Int32.MaxValue;
            double RandomZeroAndOne = (RandomInt32 / (Int32.MaxValue));
            double RandomZero = (RandomZeroAndOne / 2);
            double Finals = RandomZero * GetGateParts();
            double floor1 = Math.Floor(Finals);
            return floor1;
        }
        static void Repeat1()
        {

            try
            {
                Console.WriteLine("How many times should we repeat the program?");
                int Repeats = Convert.ToInt32(Console.ReadLine());
                double SumOfSpins = 0;
                double MeanSpins = 0;
                double SumOfSquares =0;
                double StandardDeviaion = 0;
                int MaxValue=int.MinValue;
                int MinValue=int.MaxValue;                
                for (int y = 0; y < Repeats; y++)
                {
                    int spins = GetNumberOfSpins();
                    Console.WriteLine("Gate required {0} spins. ({1}/{2})", spins, (y+1),Repeats);
                    SumOfSpins += spins;
                    MeanSpins = (SumOfSpins / Repeats);
                    SumOfSquares += (spins * spins);
                    if (spins > MaxValue)
                    {
                        MaxValue = spins;
                    }
                    if (spins < MinValue)
                    {
                        MinValue = spins;
                    }
                    
                }
                StandardDeviaion = Math.Sqrt((SumOfSquares - Repeats * MeanSpins * MeanSpins) / (Repeats - 1));
                Console.WriteLine(Convert.ToString("\nMean spins required are: " + Math.Round(MeanSpins)));
                Console.WriteLine(Convert.ToString("Sample standard deviation: " + Math.Round(StandardDeviaion)));
                Console.WriteLine(Convert.ToString("Cheapest gate: "+MinValue));
                Console.WriteLine(Convert.ToString("Most Expensive gate: " + MaxValue));
            }
            catch(FormatException)
            {
                Console.WriteLine("Invalid responce, restarting program... \n------------------------------\n\n\n");
                Repeat1();
            }
            catch(OverflowException)
            {
                Console.WriteLine("Invalid responce, restarting program... \n------------------------------\n\n\n");
                Repeat1();
            }


        }
        static void RepeatingProgram()
        {
            if (DoesUserWantToRepeat == true)
            {
                DoesUserWantToRepeat = false;
                Repeat1();
                Restart();
            }
        }
        static void Main(string[] args)
        {
            Console.WriteLine("Welcome to FakeSpinner... Enjoy :)");
            Repeat1();
            Restart();
            while(DoesUserWantToRepeat==true)
            {
                RepeatingProgram();
            }
            //Console.ReadLine();
        }
        static int GetNumberOfSpins()
        {
            int NumberOfGatePartsAchieved = 0;
            int NumberOfSpinsRequiredInTotal = 0;
            int Multiplier = 1;

            while ((NumberOfGatePartsAchieved + 6) < GetGateParts())//spins until 6 from the end
            {
                if (Multiplier == 1)
                {
                    if (GetRandom() < 13)//part or multiplier found!
                    {
                        if ((GetRandom2() + 1) > NumberOfGatePartsAchieved)//actual part found!
                        {
                            NumberOfGatePartsAchieved++;
                        }
                        else
                        {
                            Multiplier++;
                        }
                    }
                }
                else if (Multiplier == 2)
                {
                    if (GetRandom() < 13)//part or multiplier found!
                    {
                        NumberOfGatePartsAchieved++;
                        NumberOfGatePartsAchieved++;
                    }
                    Multiplier = 1;
                }
                NumberOfSpinsRequiredInTotal++;
            }
            while (NumberOfGatePartsAchieved + 6 >= GetGateParts() && NumberOfGatePartsAchieved < GetGateParts())//checks if it is at least 6 from the end
            {
                if (Multiplier < (GetGateParts() - NumberOfGatePartsAchieved))//if the multiplier WONT finish the gate yet
                {
                    if (GetRandom() < 13)//part or multiplier found!
                    {
                        if ((GetRandom2() + 1) > NumberOfGatePartsAchieved)//actual part found!
                        {
                            NumberOfGatePartsAchieved++;
                        }
                        else
                        {
                            Multiplier++;
                        }
                    }
                }
                else if (Multiplier == (GetGateParts() - NumberOfGatePartsAchieved))//if the multiplier WILL finish the gate
                {
                    if (GetRandom() < 13)//part or multiplier found!
                    {
                        NumberOfGatePartsAchieved = NumberOfGatePartsAchieved + Multiplier;
                    }
                    Multiplier = 1;
                }
                else
                {
                    Console.WriteLine("ERROR code 1");
                }
                NumberOfSpinsRequiredInTotal++;
            }
            return NumberOfSpinsRequiredInTotal;
        }
        static void Restart()
        {
            Console.WriteLine("Thanks for using FakeSpinner. Would you like to run another test? ('yes' or 'no')");
            string RepeatQuestion = null;
            RepeatQuestion = Console.ReadLine();
            if (RepeatQuestion == "yes")
            {
                AreGatePartsEntered = false;
                DoesUserWantToRepeat = true;
            }
            else if (RepeatQuestion == "no")
            {
                DoesUserWantToRepeat = false;
            }
            else
            {
                Console.WriteLine("Sorry this is not a valid responce. Please try again.");
                Restart();
            }
        }
    }
}

well done mate :) thx!