Intuitively, a martingale is a gambler that starts with some finite amount of money (say, one dollar). It reads a sequence of bits indefinitely. After reading the finite prefix formula_9, it bets some of its current money that the next bit will be a 0, and the remainder of its money that the next bit will be a 1. It doubles whatever money was placed on the bit that appears next, and it loses the money placed on the bit that did not appear. It must bet all of its money, but it may "bet nothing" by placing half of its money on each bit. For a martingale "d", "d"("w") represents the amount of money "d" has after reading the string "w". Although the definition of a martingale has the martingale calculating how much money it will have, rather than calculating what bets to place, because of the constrained nature of the game, knowledge the values "d"("w"), "d"("w"0), and "d"("w"1) suffices to calculate the bets that "d" placed on 0 and 1 after seeing the string "w". The fact that the martingale is a function that takes as input the string seen so far means that the bets placed are solely a function of the bits already read; no other information may affect the bets (other information being the so-called "filtration" in the generalized theory of martingales).