The Bounded Strong Law of Large Numbers
In this chapter, we formulate and prove the simplest forms of the game-theoretic strong law of large numbers. In its very simplest form, the strong law of large numbers is concerned with a sequence of events, each with the same two possible outcomes, which we may call heads and tails. The law says that as one proceeds in the sequence, the proportion of heads converges to one-half almost surely. In symbols: