I'm looking at a betting game where I have \$100 and want to double my money by repeatedly betting on a biased coin; it shows heads with probability $p<\frac{1}{2} in which case I win even money.
I imagine my best strategy is to go all-in, but I also wanted to investigate what happens if I bet a constant fraction 0
My question is why does a dip in success probability occur? Shouldn't such a graph be monotone increasing? (I'm hoping this isn't a simple implementation error!)
Any input greatly appreciated, John