Expected value doesn't tell you much about the outcome of successive bets. Someone else can probably explain this better since it comes up on HN a lot (something about ergodicity and the difference between ensemble average and time average).
Quick example is if play a game of double or nothing on coin flips. This is a "fair game" because you pay x and get back 2x * 0.5 + 0 * 0.5 = x. But if you play more than one game you will very quickly get a "nothing" and can't continue.