# Fama: Efficient Capital Markets: A Review of Theory and Empirical Work - are martingales incorrect?

In his paper, Eugene Fama gives the definition of a "fair game" as given below. I disagree. AFAIK, a martingale has the following property: $$E[X_{t+\tau} | X_t] = X_t$$. What am I missing?

Footnote 9 says:

And again, in a previous statement:

• What does Footnote 9 say? – noob2 Jul 15 at 17:47
• @noob2 Nothing that would justify the zero in my opinion. I've updated. – s5s Jul 15 at 18:00
• What does it mean for martingales to be "incorrect"? – Acccumulation Jul 16 at 5:46

In equation 2 $$x_{j, t + 1}$$ is defined as the change in of $$p_j$$ over the period $$t$$ to $$t + 1$$. The formula says that the expectation of the change is zero which is the same as saying that the expectation of the original variable at $$t+1$$ is equal to its current value.