For this game, the odds of winning at step n is given by 0.5^n.
Since each step is a discrete outcome (ie, you can't earn money from step n then keep going,) the expected values should be treated as separate for each step. This is given by (return * 0.5^n)
Interestingly, the expected value at each step doesn't start decreasing until it hits 12x, meaning they there's actually no extra expected profit in it for the casino if the player chooses to bet up to that after winning the first toss. This may be why you're feeling the way you are, but rest assured the game is sufficiently unfavorable for the player.