Why a Bigger Sample Tames Randomness
The usual name for this pattern is the law of large numbers. If repeated observations are independent and come from the same process, their average tends to settle near the process’s long-run average as the number of observations grows. “Independent” means one result does not change the odds of the next; “same process” means the underlying chances have not shifted.
The mechanism is dilution. A lucky win adds a fixed amount to the total, but its influence on the average gets smaller with every additional round. A later loss can pull the average the other way. Across many rounds, these ups and downs tend to offset one another, while the average becomes less sensitive to any single result.
A Stable Average Is Not a Promise
Suppose a game pays out unpredictably but has a fixed average payout over the long run. A short session may land far above or below that average. A much longer session is more likely to have an average closer to it—but there is no point at which the law guarantees an exact match. Nor does a steadier average make the next round easier to predict.
The conditions matter: if the odds change over time, or results are linked, simply collecting more observations may not produce the same settling effect. When the conditions do hold, the practical payoff is that a large group’s average can be useful for planning even while each individual outcome remains uncertain.
