So, let's look at some of the practical considerations of bankrolling your play. Essentially, what you are up against is what mathematicians call normal fluctuation.
As shown by our computer simulation results, even when you have a strong advantage over the house, you'll still sometimes lose, because in the short run, anything can happen.

This is true even for the casinos— although the house enjoys a large edge on their slot machines, on any given day some slot players will win more than they lose, which is why people return to the slots. If all slot players lost every time they played, no one would play. All casino games are designed to allow players to go home winners fairly regularly—just not often enough to compensate for their long run losses.

Let's stick with blackjack, though. Assume you learn to play basic strategy, so that you nearly eliminate the house edge. How much can you win or lose due to normal fluctuation?
To answer that, start by imagining that all of your bets are of equal size. Rather than assigning some dollar value, let's say instead that you bet one unit on each hand. We will assume you are in a traditional single-deck Las Vegas Strip game, playing perfect basic strategy, so that for all intents and purposes, the game is dead even. Over the long run, you'd expect to win nothing and lose nothing. It's like flipping a coin.

Of course, if you try flipping a coin a thousand times, and recording the results, you'd be highly unlikely to come up with exactly 500 wins and 500 losses. There are precise mathematical formulas for predicting the limits of normal fluctuation, and with an introductory course in probability and statistics, you would know how to make such estimations. But for now, let's develop some practical guidelines describing the best and worst you might expect due to normal fluctuation.

Statisticians use the term standard deviation to explain variations from the expected result. For instance, if you flip an honest coin 10 times, your expected result is five heads and five tails. If, however, you came up with 7 heads and 3 tails, this would not be indicative that the coin was dishonest. It would be considered a normal fluctuation.

However, if you flipped a coin ten thousand times, and it came up 7,000 heads and only 3,000 tails, it would be very unlikely that this was an honest coin. Even though the ratio of heads to tails has remained 7 to 3, the large number of tosses makes the result highly unlikely.

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