using System;

using System.Linq;

​

Random random = new(12345);

​

const int DieFaceCount = 20;

const int SessionRoles = 160;

const int SessionSamples = 10_000_000;

​

var result = Enumerable

    .Range(1, SessionSamples)

    .Select(s => (

            Session: s, 

            Result: Enumerable

                .Range(1, SessionRoles)

                .Select(result => random.Next(1, DieFaceCount + 1))

                .Sum() / (double)SessionRoles

    ))

    .FirstOrDefault(r => r.Result < 8);

​

if (result == default) 

    Console.WriteLine($"No matching mean found after {SessionSamples} sessions of {SessionRoles} roles.");

else 

    Console.WriteLine($"Found a mean of {result.Result} on session # {result.Session}.");