Coin Flip Simulator

A fair coin has exactly 50% probability of landing on Heads and 50% on Tails. Each flip is independent - previous results don't affect future flips.

Key principle: The coin has no memory. Past flips don't influence future outcomes.

The gambler's fallacy is the mistaken belief that past random events affect future probabilities.

Example: After 5 heads in a row, many people think tails is "due" - but the next flip still has exactly 50% chance of heads!

This simulator helps visualize this concept by tracking streaks and showing that unlikely runs happen naturally in random sequences.

• Streak: Consecutive identical outcomes (e.g., HHHH is a 4-heads streak)
• Run: Any sequence of consecutive identical outcomes
• Expected behavior: In 100 flips, expect to see runs of 5-7 in a row
• Surprising fact: Long streaks are more common than intuition suggests

A biased coin has unequal probabilities for heads and tails. Real coins can be slightly biased due to:

• Weight distribution (design asymmetry)
• Wear and damage
• Flipping technique

Use the bias slider to simulate unfair coins and see how bias affects long-term proportions.

As the number of flips increases, the proportion of heads approaches the true probability (0.5 for fair coin).

Important: This doesn't mean short-term runs "balance out" - it means the percentage gets closer to 50%, not that the count difference gets smaller.

Example:

• 10 flips: 7H, 3T (70% heads) - not unusual
• 1000 flips: 520H, 480T (52% heads) - closer to 50%
• 10000 flips: 5020H, 4980T (50.2% heads) - very close to 50%

• Decision Making: Fair, random choices between two options
• Sports: Determining possession, serve, etc.
• Education: Teaching probability and statistics
• Gaming: 50/50 chance mechanics
• Cryptography: Generating random bits
• Simulation: Binary random processes

• Heads/Tails Count: Total number of each outcome
• Proportion: Percentage of each outcome (should approach 50% for fair coin)
• Longest Streak: Maximum consecutive identical flips
• Number of Runs: How many streaks occurred
• Average Run Length: Mean streak length
• Alternations: How often the result switched (H→T or T→H)