An n-gram is a word of length that we can create from a set of letters. With two letters , we can form these 3-grams: , , , , , , , and . We will let stand for tails and for heads, so that a 3-gram can represent an outcome if we flip a coin 3 times.
Penney’s game concerns two good friends and their -grams. The game is simple and seemingly fair. Soon Player 1 will call off their long friendship and leave, however. We will find that, whenever , Player 2 is always more likely to win.