Probability
Law of large numbers
10 min
Learning goals
- •You can state the law of large numbers in your own words.
- •You can explain why the relative deviation |k/n − p| shrinks while the absolute deviation |k − n·p| typically grows.
- •You can refute the gambler's fallacy using simulation evidence.
Total rolls
0
Last outcome
–
Observed relative frequency vs. true probability
The dashed lines mark the theoretical p. As n grows, the bars converge towards them.
Convergence over time
One line per outcome. Fluctuations shrink as n grows.
Gambler's fallacy
The relative deviation |k/n − p| shrinks with n. The absolute deviation |k − n·p| typically keeps growing like √n. The coin therefore does not even out — it merely dilutes its deviation across more and more rolls.
Expected at n = 0
0.0
n · p = 0 · 0.167
|k − n · p| (absolute)
0.0
Observed: 0
|k/n − p| (relative)
0.00 pp
Rel. frequency: 0