Before revision:  We show, in particular, that their results for statistically independent horse races also apply to a series of races where the stochastic process of winning horses, payoffs, and strategies depend on some ergodic process, including, but not limited to the history of previous races.
After revision:  We show, in particular, that their results for statistically independent horse races also apply to a series of races where the stochastic process of winning horses, payoffs, and strategies depend on some stationary process, including, but not limited to the history of previous races.