Try It With Cards

Test the rule with ten playing cards. Shuffle, lay them face-down, and flip one at a time, trying to stop on the highest card before the row runs out.

Use the rule: flip the first 3 or 4 cards, remember the highest, then stop on the next card that beats it. Reshuffle and repeat. Over many rounds you will catch the top card far more often than the 1-in-10 you would expect from luck alone.