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Level 7 [Omega Protocol]» Forums » Strategy

Subject: Dice Odds for Level 7 Omega Protocol rss

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Bryan Livingston
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Utah
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Could someone with a better grasp of probabilities than me work up a chart with the basic dice odds? The way the armor and skill checks work in this game it's always pretty pass or fail so a simple table with the odds of passing any check should be doable and very handy.

For instance, what are the odds that 3 black dice will have 3 or more hits?

A black die has 0, 0, 1, 1, 1, 2 and a red die has 0, 1, 1, 1, 1, 2. They're also unbalanced.
 
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Bryan Livingston
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Re: Dice Odds for
Never mind, I just wrote a quick permutator in C#.

Here are my results. What do you think?

0 Red, 1 Black - 1: 66.67 %, 2: 16.67 %, 3: 0.00 %, 4: 0.00 %, 5: 0.00 %, 6: 0.00 %, 7: 0.00 %
0 Red, 2 Black - 1: 88.89 %, 2: 55.56 %, 3: 19.44 %, 4: 2.78 %, 5: 0.00 %, 6: 0.00 %, 7: 0.00 %
0 Red, 3 Black - 1: 96.30 %, 2: 79.63 %, 3: 49.07 %, 4: 19.91 %, 5: 4.63 %, 6: 0.46 %, 7: 0.00 %
0 Red, 4 Black - 1: 98.77 %, 2: 91.36 %, 3: 72.22 %, 4: 44.44 %, 5: 19.68 %, 6: 5.79 %, 7: 1.00 %
0 Red, 5 Black - 1: 99.59 %, 2: 96.50 %, 3: 86.21 %, 4: 66.15 %, 5: 40.82 %, 6: 19.17 %, 7: 6.51 %
0 Red, 6 Black - 1: 99.86 %, 2: 98.63 %, 3: 93.59 %, 4: 81.24 %, 5: 61.05 %, 6: 37.83 %, 7: 18.56 %
1 Red, 0 Black - 1: 83.33 %, 2: 16.67 %, 3: 0.00 %, 4: 0.00 %, 5: 0.00 %, 6: 0.00 %, 7: 0.00 %
1 Red, 1 Black - 1: 94.44 %, 2: 63.89 %, 3: 22.22 %, 4: 2.78 %, 5: 0.00 %, 6: 0.00 %, 7: 0.00 %
1 Red, 2 Black - 1: 98.15 %, 2: 85.19 %, 3: 55.09 %, 4: 22.69 %, 5: 5.09 %, 6: 0.46 %, 7: 0.00 %
1 Red, 3 Black - 1: 99.38 %, 2: 94.14 %, 3: 77.31 %, 4: 49.31 %, 5: 22.22 %, 6: 6.48 %, 7: 1.08 %
1 Red, 4 Black - 1: 99.79 %, 2: 97.74 %, 3: 89.40 %, 4: 70.78 %, 5: 44.95 %, 6: 21.49 %, 7: 7.30 %
1 Red, 5 Black - 1: 99.93 %, 2: 99.14 %, 3: 95.30 %, 4: 84.59 %, 5: 65.27 %, 6: 41.43 %, 7: 20.67 %
1 Red, 6 Black - 1: 99.98 %, 2: 99.68 %, 3: 97.99 %, 4: 92.37 %, 5: 79.93 %, 6: 60.55 %, 7: 38.49 %
2 Red, 0 Black - 1: 97.22 %, 2: 75.00 %, 3: 25.00 %, 4: 2.78 %, 5: 0.00 %, 6: 0.00 %, 7: 0.00 %
2 Red, 1 Black - 1: 99.07 %, 2: 90.28 %, 3: 62.04 %, 4: 25.93 %, 5: 5.56 %, 6: 0.46 %, 7: 0.00 %
2 Red, 2 Black - 1: 99.69 %, 2: 96.30 %, 3: 82.33 %, 4: 54.71 %, 5: 25.15 %, 6: 7.25 %, 7: 1.16 %
2 Red, 3 Black - 1: 99.90 %, 2: 98.61 %, 3: 92.21 %, 4: 75.45 %, 5: 49.46 %, 6: 24.11 %, 7: 8.20 %
2 Red, 4 Black - 1: 99.97 %, 2: 99.49 %, 3: 96.69 %, 4: 87.69 %, 5: 69.58 %, 6: 45.34 %, 7: 23.03 %
2 Red, 5 Black - 1: 99.99 %, 2: 99.81 %, 3: 98.63 %, 4: 94.16 %, 5: 83.15 %, 6: 64.52 %, 7: 41.95 %
2 Red, 6 Black - 1: 100.00 %, 2: 99.93 %, 3: 99.45 %, 4: 97.34 %, 5: 91.23 %, 6: 78.78 %, 7: 60.10 %
3 Red, 0 Black - 1: 99.54 %, 2: 93.98 %, 3: 70.37 %, 4: 29.63 %, 5: 6.02 %, 6: 0.46 %, 7: 0.00 %
3 Red, 1 Black - 1: 99.85 %, 2: 97.76 %, 3: 87.04 %, 4: 60.73 %, 5: 28.55 %, 6: 8.10 %, 7: 1.23 %
3 Red, 2 Black - 1: 99.95 %, 2: 99.18 %, 3: 94.53 %, 4: 80.05 %, 5: 54.39 %, 6: 27.10 %, 7: 9.22 %
3 Red, 3 Black - 1: 99.98 %, 2: 99.70 %, 3: 97.76 %, 4: 90.48 %, 5: 73.91 %, 6: 49.57 %, 7: 25.69 %
3 Red, 4 Black - 1: 99.99 %, 2: 99.89 %, 3: 99.10 %, 4: 95.66 %, 5: 86.17 %, 6: 68.56 %, 7: 45.66 %
3 Red, 5 Black - 1: 100.00 %, 2: 99.96 %, 3: 99.64 %, 4: 98.08 %, 5: 93.07 %, 6: 81.88 %, 7: 63.86 %
3 Red, 6 Black - 1: 100.00 %, 2: 99.99 %, 3: 99.86 %, 4: 99.18 %, 5: 96.67 %, 6: 90.18 %, 7: 77.74 %
4 Red, 0 Black - 1: 99.92 %, 2: 98.69 %, 3: 90.97 %, 4: 67.52 %, 5: 32.48 %, 6: 9.03 %, 7: 1.31 %
4 Red, 1 Black - 1: 99.97 %, 2: 99.52 %, 3: 96.32 %, 4: 84.44 %, 5: 59.75 %, 6: 30.50 %, 7: 10.37 %
4 Red, 2 Black - 1: 99.99 %, 2: 99.83 %, 3: 98.53 %, 4: 92.89 %, 5: 78.19 %, 6: 54.12 %, 7: 28.67 %
4 Red, 3 Black - 1: 100.00 %, 2: 99.94 %, 3: 99.42 %, 4: 96.87 %, 5: 88.93 %, 6: 72.62 %, 7: 49.64 %
4 Red, 4 Black - 1: 100.00 %, 2: 99.98 %, 3: 99.78 %, 4: 98.66 %, 5: 94.65 %, 6: 84.82 %, 7: 67.68 %
4 Red, 5 Black - 1: 100.00 %, 2: 99.99 %, 3: 99.91 %, 4: 99.44 %, 5: 97.51 %, 6: 92.04 %, 7: 80.74 %
4 Red, 6 Black - 1: 100.00 %, 2: 100.00 %, 3: 99.97 %, 4: 99.77 %, 5: 98.87 %, 6: 96.01 %, 7: 89.19 %


And here is the code I used to generate it:

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

namespace ConsoleApplication4
{
class Program
{
static int[] blackDie = { 0, 0, 1, 1, 1, 2 };
static int[] redDie = { 0, 1, 1, 1, 1, 2 };

static void Main(string[] args)
{
GiveOdds(0, 1);
GiveOdds(0, 2);
GiveOdds(0, 3);
GiveOdds(0, 4);
GiveOdds(0, 5);
GiveOdds(0, 6);
GiveOdds(1, 0);
GiveOdds(1, 1);
GiveOdds(1, 2);
GiveOdds(1, 3);
GiveOdds(1, 4);
GiveOdds(1, 5);
GiveOdds(1, 6);
GiveOdds(2, 0);
GiveOdds(2, 1);
GiveOdds(2, 2);
GiveOdds(2, 3);
GiveOdds(2, 4);
GiveOdds(2, 5);
GiveOdds(2, 6);
GiveOdds(3, 0);
GiveOdds(3, 1);
GiveOdds(3, 2);
GiveOdds(3, 3);
GiveOdds(3, 4);
GiveOdds(3, 5);
GiveOdds(3, 6);
GiveOdds(4, 0);
GiveOdds(4, 1);
GiveOdds(4, 2);
GiveOdds(4, 3);
GiveOdds(4, 4);
GiveOdds(4, 5);
GiveOdds(4, 6);
Console.ReadLine();
}

static void GiveOdds(int redCount, int blackCount)
{
Console.Write("{0} Red, {1} Black - ", redCount, blackCount);
Console.WriteLine("1: {0}, 2: {1}, 3: {2}, 4: {3}, 5: {4}, 6: {5}, 7: {6}", Permute(redCount, blackCount, 1), Permute(redCount, blackCount, 2), Permute(redCount, blackCount, 3), Permute(redCount, blackCount, 4), Permute(redCount, blackCount, 5), Permute(redCount, blackCount, 6), Permute(redCount, blackCount, 7));
}

static double Permute(int redCount, int blackCount, int passAmount)
{
var checks = 0.0;
var passes = 0.0;
var combination = new int[redCount + blackCount];

while (true)
{
checks++;

// add it up
var permuteAmount = 0;
for (int i = 0; i < combination.Length; i++)
{
if (i >= redCount)
permuteAmount += blackDie[combination[i]];
else
permuteAmount += redDie[combination[i]];
}

// see if it passes
if (permuteAmount >= passAmount)
passes++;

// increment
combination[combination.Length - 1]++;
for (int i = combination.Length - 1; i >= 0; i--)
{
if (combination[i] == 6)
{
// exit if we've checked all the permutations
if (i == 0)
return passes / checks;

combination[i - 1]++;
combination[i] = 0;
}
}

// debug to check that incrementing is correct.
//foreach (var value in combination)
//{
// Console.Write("{0} ", value);
//}
//Console.WriteLine();
}
}
}
}
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Frank Clarke
Canada
Surrey
BC
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If you want to play around with the C#, you can copy and paste the code here:

http://www.tutorialspoint.com/compile_csharp_online.php

Compile and Execute.

Thanks!
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Frank Jones
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LoneCoder wrote:
Never mind, I just wrote a quick permutator in C#.

Here are my results. What do you think?

0 Red, 1 Black - 1: 66.67 %, 2: 16.67 %, 3: 0.00 %, 4: 0.00 %, 5: 0.00 %, 6: 0.00 %, 7: 0.00 %
0 Red, 2 Black - 1: 88.89 %, 2: 55.56 %, 3: 19.44 %, 4: 2.78 %, 5: 0.00 %, 6: 0.00 %, 7: 0.00 %
0 Red, 3 Black - 1: 96.30 %, 2: 79.63 %, 3: 49.07 %, 4: 19.91 %, 5: 4.63 %, 6: 0.46 %, 7: 0.00 %
0 Red, 4 Black - 1: 98.77 %, 2: 91.36 %, 3: 72.22 %, 4: 44.44 %, 5: 19.68 %, 6: 5.79 %, 7: 1.00 %
0 Red, 5 Black - 1: 99.59 %, 2: 96.50 %, 3: 86.21 %, 4: 66.15 %, 5: 40.82 %, 6: 19.17 %, 7: 6.51 %
0 Red, 6 Black - 1: 99.86 %, 2: 98.63 %, 3: 93.59 %, 4: 81.24 %, 5: 61.05 %, 6: 37.83 %, 7: 18.56 %
1 Red, 0 Black - 1: 83.33 %, 2: 16.67 %, 3: 0.00 %, 4: 0.00 %, 5: 0.00 %, 6: 0.00 %, 7: 0.00 %
1 Red, 1 Black - 1: 94.44 %, 2: 63.89 %, 3: 22.22 %, 4: 2.78 %, 5: 0.00 %, 6: 0.00 %, 7: 0.00 %
1 Red, 2 Black - 1: 98.15 %, 2: 85.19 %, 3: 55.09 %, 4: 22.69 %, 5: 5.09 %, 6: 0.46 %, 7: 0.00 %
1 Red, 3 Black - 1: 99.38 %, 2: 94.14 %, 3: 77.31 %, 4: 49.31 %, 5: 22.22 %, 6: 6.48 %, 7: 1.08 %
1 Red, 4 Black - 1: 99.79 %, 2: 97.74 %, 3: 89.40 %, 4: 70.78 %, 5: 44.95 %, 6: 21.49 %, 7: 7.30 %
1 Red, 5 Black - 1: 99.93 %, 2: 99.14 %, 3: 95.30 %, 4: 84.59 %, 5: 65.27 %, 6: 41.43 %, 7: 20.67 %
1 Red, 6 Black - 1: 99.98 %, 2: 99.68 %, 3: 97.99 %, 4: 92.37 %, 5: 79.93 %, 6: 60.55 %, 7: 38.49 %
2 Red, 0 Black - 1: 97.22 %, 2: 75.00 %, 3: 25.00 %, 4: 2.78 %, 5: 0.00 %, 6: 0.00 %, 7: 0.00 %
2 Red, 1 Black - 1: 99.07 %, 2: 90.28 %, 3: 62.04 %, 4: 25.93 %, 5: 5.56 %, 6: 0.46 %, 7: 0.00 %
2 Red, 2 Black - 1: 99.69 %, 2: 96.30 %, 3: 82.33 %, 4: 54.71 %, 5: 25.15 %, 6: 7.25 %, 7: 1.16 %
2 Red, 3 Black - 1: 99.90 %, 2: 98.61 %, 3: 92.21 %, 4: 75.45 %, 5: 49.46 %, 6: 24.11 %, 7: 8.20 %
2 Red, 4 Black - 1: 99.97 %, 2: 99.49 %, 3: 96.69 %, 4: 87.69 %, 5: 69.58 %, 6: 45.34 %, 7: 23.03 %
2 Red, 5 Black - 1: 99.99 %, 2: 99.81 %, 3: 98.63 %, 4: 94.16 %, 5: 83.15 %, 6: 64.52 %, 7: 41.95 %
2 Red, 6 Black - 1: 100.00 %, 2: 99.93 %, 3: 99.45 %, 4: 97.34 %, 5: 91.23 %, 6: 78.78 %, 7: 60.10 %
3 Red, 0 Black - 1: 99.54 %, 2: 93.98 %, 3: 70.37 %, 4: 29.63 %, 5: 6.02 %, 6: 0.46 %, 7: 0.00 %
3 Red, 1 Black - 1: 99.85 %, 2: 97.76 %, 3: 87.04 %, 4: 60.73 %, 5: 28.55 %, 6: 8.10 %, 7: 1.23 %
3 Red, 2 Black - 1: 99.95 %, 2: 99.18 %, 3: 94.53 %, 4: 80.05 %, 5: 54.39 %, 6: 27.10 %, 7: 9.22 %
3 Red, 3 Black - 1: 99.98 %, 2: 99.70 %, 3: 97.76 %, 4: 90.48 %, 5: 73.91 %, 6: 49.57 %, 7: 25.69 %
3 Red, 4 Black - 1: 99.99 %, 2: 99.89 %, 3: 99.10 %, 4: 95.66 %, 5: 86.17 %, 6: 68.56 %, 7: 45.66 %
3 Red, 5 Black - 1: 100.00 %, 2: 99.96 %, 3: 99.64 %, 4: 98.08 %, 5: 93.07 %, 6: 81.88 %, 7: 63.86 %
3 Red, 6 Black - 1: 100.00 %, 2: 99.99 %, 3: 99.86 %, 4: 99.18 %, 5: 96.67 %, 6: 90.18 %, 7: 77.74 %
4 Red, 0 Black - 1: 99.92 %, 2: 98.69 %, 3: 90.97 %, 4: 67.52 %, 5: 32.48 %, 6: 9.03 %, 7: 1.31 %
4 Red, 1 Black - 1: 99.97 %, 2: 99.52 %, 3: 96.32 %, 4: 84.44 %, 5: 59.75 %, 6: 30.50 %, 7: 10.37 %
4 Red, 2 Black - 1: 99.99 %, 2: 99.83 %, 3: 98.53 %, 4: 92.89 %, 5: 78.19 %, 6: 54.12 %, 7: 28.67 %
4 Red, 3 Black - 1: 100.00 %, 2: 99.94 %, 3: 99.42 %, 4: 96.87 %, 5: 88.93 %, 6: 72.62 %, 7: 49.64 %
4 Red, 4 Black - 1: 100.00 %, 2: 99.98 %, 3: 99.78 %, 4: 98.66 %, 5: 94.65 %, 6: 84.82 %, 7: 67.68 %
4 Red, 5 Black - 1: 100.00 %, 2: 99.99 %, 3: 99.91 %, 4: 99.44 %, 5: 97.51 %, 6: 92.04 %, 7: 80.74 %
4 Red, 6 Black - 1: 100.00 %, 2: 100.00 %, 3: 99.97 %, 4: 99.77 %, 5: 98.87 %, 6: 96.01 %, 7: 89.19 %



Looks good. Maybe it could use one more row: 5 red and zero black (for melee attacks by an enemy against a maxed-adrenaline commando.

Also, info for 8 hits and 9 hits would be cool (Chronos has 8 for his 2nd range defense number, and he could have cover, which would make it 9).
 
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