Trying to calculate the true probability of getting a 9 with "Judge" on Game and Watch from Super Smash Bros Ultimate. Each number is equally likely to appear (9 possibilities so 1/9 for a 9), but no number can appear twice in a row. I ran some simulations and it seems to me like that there is a 11.1% chance of getting a 9.

GameAndWatch.cpp

//
//  main.cpp
//  GameAndWatch
//
//  Created by Bharddwaj Vemulapalli on 2/7/20.
//  Copyright © 2020 Bharddwaj Vemulapalli. All rights reserved.
//

#include <iostream>
#include <random>
#include <unordered_map>
#include <vector>

int main(int argc, const char * argv[]) {
    std::cout << "Hello, World!\n";
    std::vector<double> probabilities = {};
    for (int j = 0 ; j < 10; j++) {
        std::cout << j << std::endl;
        std::random_device dev;
        std::mt19937 rng(dev());
        std::uniform_int_distribution<std::mt19937::result_type> dist9(1,9); // distribution in range [1, 9]
        int num = dist9(rng);
        int prev = 1;
        std::vector<int> v = {};
        for (int i = 0; i < 1000000; i++) {
            while (num != prev) {
                 std::random_device dev;
                 std::mt19937 rng(dev());
                 std::uniform_int_distribution<std::mt19937::result_type> dist9(1,9); // distribution in range [1, 9]
                 num = dist9(rng);
            }
            std::random_device dev;
            std::mt19937 rng(dev());
            std::uniform_int_distribution<std::mt19937::result_type> dist9(1,9); // distribution in range [1, 9]
            num = dist9(rng);
            v.push_back(num);
            prev = num;
        }
        std::unordered_map<int, int> u = {
            {1,0},
            {2,0},
            {3,0},
            {4,0},
            {5,0},
            {6,0},
            {7,0},
            {8,0},
            {9,0}
        };
        for (int i = 0; i < v.size(); i++) {
            u[v[i]] += 1;
            //std::cout << v[i];
        }
        probabilities.push_back((double)(u[9])/v.size());
    }
    std::cout << "Now for printing out the probabilities" << std::endl;
    for(int k = 0; k < probabilities.size();k++){
        std::cout <<probabilities[k] << std::endl;
    }
    return 0;
}
//0.111182
//0.111793
//0.110979