A generalized martingale betting strategy is analyzed for which bets are increased by a factor of $m \geq 1$ after each loss, but return to the initial bet amount after each win. The average amount bet and the average final fortune are derived for sequences of $n$ bets, for the number of bets $T$ that results in the first win, and for $\min (T,\;n)$.
"A Generalized Martingale Betting Strategy." Missouri J. Math. Sci. 21 (3) 183 - 197, October 2009. https://doi.org/10.35834/mjms/1316024884