Probability guide
Gambler’s Fallacy and Independent Random Events
The gambler’s fallacy is the belief that a random result becomes due after a streak of the opposite result. For independent events, the next probability does not change because of prior outcomes.
Independent means no memory
On a fair coin flip, five heads in a row do not make tails more likely next. A properly implemented independent RNG likewise does not remember that a player lost.
Streaks are normal
Random sequences naturally contain clusters and runs. Seeing a pattern does not prove prediction is possible or that the generator is balancing outcomes.
What fairness verification can show
Commit-reveal verification can show that a seed was committed before play and that recorded inputs reproduce a result. It does not turn random history into a forecasting tool.
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