  We study the capital growth in gambling with (and without) side information
and memory effects. We derive several equalities for gambling, which are of
similar form to the Jarzynski equality and its extension to systems with
feedback controls. Those relations provide us with new measures to quantify the
effects of information on the statistics of capital growth in gambling. We
discuss the implications of the equalities and show that they reproduce the
known upper bounds of average capital growth rates.
