Gambler’s Fallacy

Understand why past independent events don’t affect future probabilities

Overview

The Gambler’s Fallacy is the mistaken belief that if something happens more frequently than normal during some period, it will happen less frequently in the future, or vice versa. This interactive tool demonstrates that independent random events have no memory - past outcomes don’t influence future probabilities.

Tips

  1. Observe long streaks: Run simulations until you see streaks of 5-10 identical outcomes, then verify that the next outcome still has the same 50-50 probability.

  2. Track post-streak probabilities: After witnessing a long streak, record the next 100 outcomes to confirm they match the expected distribution.

  3. Compare “hot” and “cold” sequences: Test whether outcomes following streaks differ from outcomes in balanced sequences - they don’t.

  4. Remember the Monte Carlo 1913 event: Keep in mind that black came up 26 times in a row at roulette, yet red was never “due” - each spin remained independent.

  5. Don’t confuse with Law of Large Numbers: The overall proportion converges to 50% through dilution over many trials, not by “correcting” past imbalances.