Regarding the paradox where a martingale strategy is both better and no better at the same time, I think the answer lies in a trade off between expected value and variance. In one case the bet size is fixed and in the other case the bet size is a random variable. The latter thus has a higher variance.
I was sloppy and need to correct myself again
The variance is of course smaller for the martingale, which is bad news for the player. The player has a negative ev and therefore needs a high variance to have any chance at all. The martingale strategy is therefore as safe for the house as single bets because even though the edge is smaller, the probability of losing much is also smaller.