BlackJack Negative EV Question

[squiffy]

I know, I know. This question is poorly defined. But if you're so smart, please help me define it.

I know BlackJack is typically slightly negative EV. So I suppose the simple answer is, unless you can count cards effectively or unless you start with a sizable bonus, you should not play even a single hand.

But here is my question. Typically, when I play online BlackJack, my bankroll will cycle up and down, it seems like several times.

I presume this curve would be some type of modified sine curve.

I presume this curve would go above my starting bankroll and below my starting bankroll multiple times.

I have several questions. First, is there some way to define a typical curve of bankroll versus time? Second, will the number of times I go above breakeven vary depending on the size of the starting bankroll? Third, is there a typical expected short-term profit?

In other words. If I start with $1000 or $10,000 or $1 million dollars. I know I should not play 50 million hands of blackjack because I will tend to lose money.

But can I say with a sufficient degree of certainty that over the first 10,000 hands, I have say 95% probability of having a 20 bet profit, assuming I have a large enough bankroll to avoid going bust?

I guess my question is Even though BlackJack is a negative EV game as the number of hands played tends toward infinity, can you say that it is profitable to take a $1 million dollar bankroll and play 10,000 hands at $500 a bet because there is a 99% chance that at 100 points during that time you will be ahead by 20 bets????

And if the numbers I chose at random don't work, is there some bankroll size and bet size that are optimal and would give you a 90% chance of making a very small profit of a few hundred dollars?

I hope this makes sense. I guess the question is, can a game be long-term negative EV, yet short-term positive EV if you are willing to quit with a small profit and never play again as long as you live?

If so, what is the optimal number of hands, what is the optimal profit, what is the optimal bankroll?

I suspect that I just don't understand what EV really is.