[Dov]

I don't think this is true.

I think the infinite bankroll overcomes the house edge in the end.

This is because when you do complete a series you will have an EV of your old BR+1 betting unit.

You are still EV+, you just can't know the EV of a particular wager until the series is completed. You would have to divide your 1 betting unit of profit over all of the bets in the series.

You are correct in that during a losing series you will have experienced -EV bets. However, the metagame conditions allow this to actually be a +EV situation.

Taken from the perspective that there may be a more efficient use of your funds, I can understand that the Martingale would be -EV.

Under these conditions, though, I would expect that your BR would grow with the average # of trials in a series. If you are saying that the longer you play, the wider your variance will get, (which is true), it will still even out in the end when you do actually win, assuming that your winning chances are above 0.

As a matter of fact, I can't think of a situation where you have any chance to win that wouldn't guarantee that you do win except when you are a guaranteed loser. (like drawing dead)

I think you have somehow overlapped 2 concepts that don't, but I'm not completely sure where your error is or if I am the one who is mistaken. (I don't really think that I am, though, because by definition, you WILL win, and when you do, your BR will be larger than when it started.)