The law of large numbers states that the average of many trials converges to the expected value, but it does not imply that future trials will compensate for past deviations. The gambler's fallacy is the mistaken belief that if early trials deviate from the mean, later trials must produce opposite outcomes to 'balance out' the average immediately.
Conditions: The speaker is contrasting a common intuition with the actual meaning of the theorem.; Trials are independent.
The law of large numbers states that the average of many trials converges to the expected value, but it does not imply that future trials will compensate for past deviations. The gambler's fallacy is the mistaken belief that if early trials deviate from the mean, later trials must produce opposite outcomes to 'balance out' the average immediately.
Conditions: The speaker is contrasting a common intuition with the actual meaning of the theorem.; Trials are independent.