What's typically happens in an evening of blackjack play is that the player's bankroll goes up and down within a range like this...

"It turns out" that there a 75% chance that this range will be between -20 and +20 times your bet assuming you bet the same amount on each hand. So a player who starts with a $500 bankroll and bets $15 on each hand has a 75% chance of walking away with a bankroll of between $200 and $800. Of course, there's still a 25% chance that the walkaway bankroll will be more than $800 or less than $200, but if you want to play with a reasonable exit strategy "for the evening," this is it.

The scare quotes is this blurb are where things get a bit complicated as described in the next section.

Standard deviation tells us how spread out individual "values" are from their mean. It's calculated by taking the distance from the mean for each value (variance) and averaging them. If the values are evenly spread (a normal distribution), we can use this average (the standard deviation for one unit) to determine the probability for all the values in a sample.

For blackjack, the "values" we are concerned about are profits or loss after each hand. After looking at millions of date sets containing profits and losses, mathematicians have calculated that the standard deviation for blackjack (for one betting unit) is 1.14. By multiplying this times the number of bets we can get the standard deviation for the entire sample. Since blackjack results are random (evenly distributed between profits and losses), we can also use this results to determine the probability that future profits and losses will fall into the same range.

For example, if we play 240 hands of blackjack at $15 per hand given the SD of 1.14, we know that 68% of the profits will be within +/-$265 of our starting bankroll (the square root of 240 hands[1] x $15 x 1.14).

To bring this back to our starting proposition that a player should quit after winning or losing 20x his or her bet, let's restate this result another way. A player playing in a blackjack game 4 hours long (an evening) with 60 hands played per hour (an average rate) and a constant bet of $15 will have a 68% chance (one standard deviation) of winning or losing $265, which is almost 18 times his average bet of $15. I increased the probability a little (to about a 75% chance) and rounded it off to get my 20x recommendation.

[1] According to central limits theorum, which says that uncertainty grows slower than the number of hands played, we need to use the square root of the number of hands played in this calculation. This is because variance scales linearly with hands played, but standard deviation does not, it scales up based on the square root of the variances. (Don't worry about it, just use the square root of the number of hands.)

With this average, we can determine the probability of all profits and losses within a range. For example, using the standard deviation, we could say that there's a 68% probability that a $500 bankroll will shrink to $300 or grow to $700 and a 95% probability that it will shrink to $400 or grow to $800.

This calculation doesn't just involve the standard deviation for one bet. 

in blackjack, which is about 1.15. It also needs to take into account the hands played, the average bet, the house edge, and the player's handicap. Here's the formula:

associated with each profit and loss total.

that a certain percentage of the profits and losses 

Since luck is random, profits and losses occur evenly around the starting bankroll (a "normal distribution).

Applying this to a normal or symetrical distribution of winnings and losses around the   

winnings 

for blackjack is how far your current bankroll deviates from your starting bankroll after each hand. This is easier to see with a real example. Let's say you start with a bankroll of $500, what the standard deviation says is that after 100 hands there's a 68% chance that your bankroll will be between  

Luck is everything.

But what about Basic Strategy, house edge, table rules, the risk of ruin, the Martingale system, the count, penetration, expected value...? What about the Four Horsemen...? I say, forget all of that. To paraphrase General Patton, “Compared to luck, all other aspects of the game shrink to puny insignificance.”

You won’t see this in a blackjack book’s blurb or as part of a website’s introduction, but it’s true. For the average player, playing blackjack for an evening and betting the minimum, all you need to know is … leave when you’ve won or lost 20x your bet.

Of course, it’s helpful if you also know the rules of the game, generally when to hit, stand, double, or split, and how much of a bankroll to bring, but most people already know these things or they can suss them out pretty quickly. The one thing that’s not easy to understand, the one thing that they stumble on after losing a personal fortune is … leave when you’ve won or lost 20x your bet.

I've played a million hands of blackjack -- at least it seems that way -- and I've yet to find a perfect basic strategy player. Perhaps this is because I play at the poor-player's table, but even so, the perfect player should not this hard to find.

The reason he or she is so invisible I believe is that most normal people are not obsessed with playing an absolutely perfect game. They know 80%, or 90%, or 95%, or 99% of basic strategy and wing it for the rest. Which leads me to conclude that players should learn the rules that make a difference and not worry about the exceptions. Armed with this pragmatic opinion, I've reorganized the traditional basic strategy rules into "the essentials" shown below.

Let's start with the essential table rules... It's true that the basic strategy decisions can change when table rules change, but in most cases the changes are not significant and not worth the effort to learn. Instead, I would learn the decision for rarities like surrender and "dealer standing on soft 17" when it's necessary. Here are the five I've assumed are the baseline.

➢ Dealer hits on soft 17
➢ Double and split are allowed
➢ Surrender is not allowed
➢ Four or more decks are in use
➢ Dealer peeks for blackjack

Here are the biggies.

• HIT with 8 points or less
• STAND with 17 points or more
• HIT with 12-16 points if facing 6 or less
• STAND with 12-16 points when facing 7 or more
• DOUBLE with 10 or 11 points or a pair of aces or 8s
• HIT a pair of 4s and DOUBLE a pair of 5s
• SPLIT all other pairs when facing 6 or less
• HIT all other pairs when facing 7 or more