Coin flip simulation never exceeding a streak of 15 heads

Simulating Coin Flips with a Streak Limit: Never Exceeding 15 Heads

Explore how to simulate a series of coin flips in C, specifically designed to prevent a streak of more than 15 consecutive heads. This article covers random number generation, streak tracking, and practical implementation.

Coin flip simulations are a common way to understand probability and random processes. While a true coin flip has a 50/50 chance for heads or tails, simulating specific constraints, such as limiting consecutive streaks, introduces interesting programming challenges. This article will guide you through creating a C program that simulates coin flips while ensuring that a streak of heads never exceeds 15. This scenario is useful for understanding how to inject specific rules into otherwise random processes, which has applications in game development, statistical modeling, and more.

Understanding Randomness and Streaks

At the core of any simulation is the generation of random numbers. In C, the rand() function, combined with srand() for seeding, is typically used. However, simply generating random 0s and 1s (for tails and heads) won't enforce a streak limit. We need a mechanism to track the current streak of heads and, if it approaches the limit, influence the outcome of the next flip to break the streak. This isn't about making the coin 'unfair' in the long run, but rather about imposing a specific constraint on the sequence of outcomes.

Flowchart of the coin flip simulation logic with streak constraint.

Implementing the Streak Limit Logic

To implement the streak limit, we'll need a variable to keep track of the current consecutive heads. Before each flip, we check this variable. If the heads streak is about to reach our limit (e.g., 15), we must force the next flip to be tails. Otherwise, we proceed with a truly random flip. If a random flip results in heads, we increment the streak counter. If it results in tails, the streak is broken, and we reset the counter to zero. This ensures that the 16th consecutive head never occurs.

#include <stdio.h>
#include <stdlib.h>
#include <time.h>

#define MAX_HEADS_STREAK 15

int main() {
    srand(time(NULL)); // Seed the random number generator

    int num_flips = 100000; // Number of coin flips to simulate
    int heads_count = 0;
    int tails_count = 0;
    int current_heads_streak = 0;
    int max_observed_heads_streak = 0;

    printf("Simulating %d coin flips with a max heads streak of %d.\n", num_flips, MAX_HEADS_STREAK);

    for (int i = 0; i < num_flips; i++) {
        int flip_result;

        // If current heads streak is at the limit, force a tail
        if (current_heads_streak == MAX_HEADS_STREAK) {
            flip_result = 0; // 0 for tails
            // printf("Forcing tails to break streak at flip %d.\n", i + 1);
        } else {
            flip_result = rand() % 2; // 0 for tails, 1 for heads
        }

        if (flip_result == 1) { // Heads
            heads_count++;
            current_heads_streak++;
            if (current_heads_streak > max_observed_heads_streak) {
                max_observed_heads_streak = current_heads_streak;
            }
        } else { // Tails
            tails_count++;
            current_heads_streak = 0; // Reset streak on tails
        }
    }

    printf("\nSimulation Results:\n");
    printf("Total Heads: %d\n", heads_count);
    printf("Total Tails: %d\n", tails_count);
    printf("Max Observed Heads Streak: %d\n", max_observed_heads_streak);
    printf("Heads Percentage: %.2f%%\n", (double)heads_count / num_flips * 100);
    printf("Tails Percentage: %.2f%%\n", (double)tails_count / num_flips * 100);

    return 0;
}

C code for coin flip simulation with a maximum heads streak of 15.

Analyzing the Results and Implications

Running the simulation with a large number of flips (e.g., 100,000 or 1,000,000) will demonstrate that the maximum observed heads streak indeed never exceeds 15. You might also notice a slight shift in the heads/tails ratio. Because we are sometimes forcing a tail, the overall probability of heads might drop slightly below 50%, and tails might rise slightly above. This is an expected consequence of imposing a constraint on a random process. The more restrictive the streak limit, the more pronounced this effect will be.