I have a biased coin with sides 'spin' and 'no spin' with probabilities $0.4$ and $0.6$ respectively. If it lands on spin, I spin a wheel with a chance of winning. This chance increases after each coin toss dependent on the result.
Starting at $0$, if I toss a spin the probability of winning on the wheel increases by $0.02$ before the wheel is spun, whereas if I toss no spin it increases by $0.015$.
Is it possible to calculate the probability of winning on the wheel after $n$ coin tosses?