Clustering And Runs

3 pages on this site touch on this topic.

• Clustering and runs: randomness looks lumpy — Random sequences produce longer streaks and tighter clusters than most people guess, so clustering alone is weak evidence of a real pattern.
• Runs of Heads — Predict the longest run of heads in a sequence of coin flips, then check your intuition against an exact calculation and a repeated simulation.
• The law of large numbers: chance evens out slowly — Over many repeats, outcomes converge toward their true probability, but the law says nothing about any single short run.