A new interpretation of information rate

If the input symbols to a communication channel represent the outcomes of a chance event on which bets are available at odds consistent with their probabilities (i.e., "fair" odds), a gambler can use the knowledge given him by the received symbols to cause his money to grow exponentially. The maximum exponential rate of growth of the gambler\´s capital is equal to the rate of transmission of information over the channel. This result is generalized to include the case of arbitrary odds. Thus we find a situation in which the transmission rate has significance even though no coding is contemplated. Previously this quantity was given significance only by a theorem of Shannon\´s which asserted that, with suitable encoding, binary digits could be transmitted over the channel at this rate with an arbitrarily small probability of error.