Penney Ante: Counterintuitive Probabilities in Coin Tossing

Coin-tossing is generally viewed as the quintessential example of a random process. We focus on some counterintuitive aspects of sequences that cointossing produces. Equally-likely sequences of heads and tails of a specified length are not all equally likely to occur first. This realizationleads naturallyto other surprising facts about coin-tossing. However, aspects of the outcomes of coin-tossing that may be counterintuitive when first encountered can be made acceptable to intuition after reflection and analysis.