Strange attractors in a chaotic coin flip simulation

Presented is a computer simulation used to model a variation of the game known as the gambler's ruin. A rich player gambles with a set amount of money m. The poor player starts out with zero capital, and is allowed to flip a coin in order to try to win the money. If the coin is heads, the poor player wins a dollar but if it is tails, the player loses a dollar. The poor player is always allowed to win the first flip, and is allowed to flip n times, even when the amount of money lost reaches zero. The dynamics of this process is chaotic due to fluctuations in the variance of the amount of money