Blackjack Strategy Deviations

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Standard Deviation is a measure of how results are distributed within a range of possible outcomes. This score is useful when comparing averages – for example two scores may have the same average of ‘50’ with one comprising of results entirely between 45 and 55 and the other having results ranging from 1 through to 100. The second set of scores is more widely distributed than the first, which will be reflected in a higher standard deviation score.

In Blackjack the standard deviation can be used to show you what the probability of winning or losing a number of betting units is, based on the number of hands you play. We could use this score to answer questions such as ‘what is the probability of winning more than 20 betting units over the course of 100 hands?’ or “Is winning 30 bets over 200 hands a normal outcome, or did I get lucky?’

This article will show you how to calculate (with the help of a calculator) your standard deviation in Blackjack and how to use this information to your advantage, whether you play live or in an online casino.

Calculating The Standard Deviation In Blackjack – A Note About Distribution Curves

You get to the probability of an event occurring by comparing your standard distribution score to a ‘bell-curve’ of possible outcomes, known as a ‘normal distribution’. The score is calculated in such a way as to show that 68% of outcomes will fall within 1 standard deviation of your average, 95% of outcomes fall within 2 standard deviations and 99.7% of outcomes fall within 3 standard deviations.

A blackjack deviation is any occurrence when the player adjusts their play to make a decision that is outside the realm of basic blackjack strategy. Most blackjack deviations can be broken down into one of two types. There are betting deviations and playing deviations. 😍 Click to Visit My Favorite Casino 😍. The first scientific and mathematically sound attempts to devise a basic strategy were published by Roger Baldwin, et al in 1953. In 1962, Edward Thorp published his findings of an optimal blackjack strategy using a high-speed digital computer. The progression strategy you will use depends upon being able to win multiple hands of blackjack in a row, and you can only expect to do that when you know what the count is. Basic strategy, card counting, and a betting progression all work hand in hand to help you become successful at playing blackjack. Our advice is to learn this chart, then move on to learning card counting and the blackjack deviations associated with the game you will be playing (H17 vs S17). There are also slight variations in strategy when you play a 6 deck game versus a single deck game.

In other words, once we have worked out what the standard deviation score is for a certain set of data we then compare this to the normal distribution curve to arrive at a probability of any single score being within the normal set of expected outcomes.

Blackjack Standard Deviation – How Can We Chart The Distribution Of Blackjack Outcomes?

Outcomes of a single blackjack hand can be mapped precisely – since we know the rules, probabilities and all of the cards in the deck. The most common outcome is to win or lose one betting unit, with splits, doubles and blackjack making it possible to win or lose more. With the larger number of single units dominating it is possible to work out that the standard deviation for a single hand of 6-deck Blackjack is exactly 1.1418 based on card distributions and rules alone.

This table reflects a standard deviation of 1.1418.

By applying this number directly to a ‘normal distribution’ – or bell curve - we find that over an infinite sample, in a single hand of blackjack you will win or lose 1.1418 betting units or less 68% of the time, win or lose 2 standard deviations or 2.2836 betting units or less 95% of the time and win or lose 3 standard deviations or 3.4254 units or less 99.7% of the time.

While this score is interesting, the application of it benefits from adding a second variable – the number of hands played.

Standard Deviation In Blackjack – Using The Information To Predict Win / Loss Runs

Finally we get to the key practical application of working out standard deviations in blackjack games – assessing the likelihood of winning or losing certain amounts of units over specified numbers of hands. Here is the formula to work this out based on your hand sample size:

(Square Root Of The Number Of Hands Played)*1.1418

Here are some working examples:

100 hands played, square root = 10 * 1.1418 = 11.418

This shows that 68% of the time you will win or lose 11.418 units or less over the course of 100 blackjack hands, 95% of the time you will fall within 2 standard distributions and win or lose less than 22.836 units – while 99.7% of the time your outcome over 100 hands will be within 3 standard deviations, or + / - 34.2 units.

300 hands played, square root = 17.32 * 1.1418 = 19.77

Here the distribution of blackjack outcomes predicts you will win or lose 19.77 units 68% of the time you play 300 hands, 95% of the time you will fall within 2 standard deviations and win or lose 39.54 units and 99.7% of the time you will fall within 3 standard distributions and win or lose < 59.31 units.

As you can see, the higher the number of hands played the smaller the relative impact of chance. Of course you also need to take into account the house edge of 0.05% or so when making these calculations!

What Are Blackjack Deviations

Do not worry if you do not have a pocket calculator with you at the casino, it is straight forward to work out the blackjack standard deviations for different sized sessions in advance and gain an insight into how the average distribution of outcomes affects your chances of either winning or losing certain amounts of cash. Once you get an idea of the types of swings which are normal in the game you will feel more comfortable at the blackjack tables, whether live or online!

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Importance of Blackjack Variances

The importance of blackjack variances and a proper understanding of variance in gambling cannot be underestimated. Blackjack players can come to think they 'know how to beat blackjack' if they go on a lucky streak, or they might come to think that blackjack isn't their game if they have a high negative variance in the early rounds of their blackjack playing. So given how important variances are to your expectations in blackjack, I'll try to explain what blackjack variance is and why it's important to keep in mind when analyzing your blackjack results.

So what are blackjack variances? To answer that question, I'll need to define a few blackjack terms -- so please bear with me.

Payout Percentages and the House Edge

The short answer is that blackjack variances are the deviations from expected payback in blackjack. 'Expected payout' is the amount of money (as a percentage) that you might expect to win back when betting on blackjack. It is closely tied to the house edge. The house edge exists so the casino stays in business, because casino games are typically weighted in the favor of the casino and against the player. The house edge in blackjack for a player using 'perfect' or optimal basic strategy is only around 0.5%, which means your expected payout will be around 99.5%.

This makes blackjack actually one of the best games in the casino. So for every $100 you bet at the blackjack table, you can expect to win back $99.50. You'll only lose $0.50 on every hundred dollars you spend (if you play perfect strategy, which all new players won't). For those managing expectations, though, the low house edge makes blackjack variances more subtle and more difficult to analyze, at least when you're going with your 'gut' or gamblers instinct.

Variances in Wins and Losses

That's because your expected payout or expectation is only an average. It's a theoretical expecation, and one not likely to occur too many times in your blackjack sessions. Sometimes you'll lose a whole lot more than $0.50 per $100 bet. You might lose $50.00 on a hundred dollar bet, if the cards aren't hitting right. On the other hand, you'll sometimes walk away from the table with more than you started out. You wouldn't play the game if you never won. So you'll win sometimes, but to account for the winning opportunities, you'll lose more than expected at other times. Losing more than you're expected to lose is a variance from your payback expectations, while winning your bets is also a variance from those expectations. Therefore, the amount your blackjack session deviates from expectation is the variance.

Blackjack Deviations

Your results will vary each time you bet on blackjack. Most of the time when playing blackjack, your results will vary widely, from large losses to large wins. Seldom will a player with a 99.5% expectation actually walk away with 99.5% of the money he or she bet. Expectation involves the odds about what you can expect to win or lose over a long period of time. Actually, it's over an infinite number of blackjack hands, because the possibility always exists that you'll just keep winning more than expected or losing more than expected.

This kind of deviation can fool a player at the blackjack table. If you're not a serious player, but just having fun, you might get the sensation you're having good luck or bad luck. You'll get the feeling you're getting lucky and that's that. Where the problem comes in is when you are a professional or serious amateur blackjack player, and you are trying out some new blackjack tips, recently learned blackjack strategy or card counting techniques. Because even really long sessions of blackjack are just a small sampling of the possibilities. Six months of blackjack sessions aren't a tiny sample, when compared to the idea that the expectation is based on a theoretical infinite number of hands. So you're not getting a full picture (or even a half-full picture) about whether your new blackjack method is working. You may just be riding the highs or lows of the blackjack variances.

So the importance of blackjack variances is they can fool us into false assumptions about our blackjack playing. Maybe you'll come away thinking you have learned how to beat blackjack, or you're a much better player than you really are. Or maybe you're doing all the right things, but the cards aren't falling your way. Players need to understand the nature of blackjack variances, then, and learn to analyze their game based not entirely on results, but on the soundness of the strategy being employed. You can make all the right moves and lose, and you can make all the wrong moves and win. That's the essence of blackjack variances. Sometimes you beat the odds.

Blackjack Betting Deviations

Standard Deviation

Blackjack Basic Strategy Deviations

To get an idea about our real expectations when playing blackjack, consider the standard deviation. This will give you some idea of the kind of blackjack variances you can expect. It's pretty interesting, because it shows how small the gambling margins can be in the short term, even though in the long term, blackjack is a negative expectation game.

Blackjack Playing Deviations

You can figure what is called a 'standard deviation'. You might remember this from grade school, where you get an average of a group of numbers, then calculate the standard deviation from that number. In calculating a blackjack standard deviation with a computer software program, though, you won't be testing a select group of five or ten numbers. You'll be testing well over a million deviations.

The standard deviation in blackjack is simply calculating the probabilities you will win or lose and extracting your odds from that. That is, the standard deviation can tell you your odds of winning, losing or pushing when playing blackjack. Without getting too far into the numbers, at least one gambling math expert has figured there are over 723,000,000 (yes, that's 723 million) card combination scenarios where you walk away from the table a winner. But there are over 836,000,000 combinations where you walk away a loser. And there are only a paltry 144,000,000 potential cases where you walk away with the same money you started with or 'push'.

Considering all these numbers as percentages of 100%, the standard deviation will tell you that your chances of walking away a net winner in blackjack is around 42.42% of the time, rounded up. Your odds of walking away from the blackjack table a loser are around 49.10%, rounded up. Your odds of walking away with a push is somewhere around 8.47% of the time.

What Is The Best Blackjack Strategy

If you want to read more about the numbers behind blackjack variances and standard deviation, visit the blackjack variance page on the Wizard of Odds website. The Wizard of Odds has run statistical breakdowns of the odds on virtually every major game you'll find in a casino.

Negative Expectation, But With Hope

Standard Deviation Blackjack

So blackjack is a negative expectation game. There's a house edge that says you will lose in the long run, if you play an infinite number of hands. But in the short term, you'll walk away a winner 42% of the time. In fact, you'll walk away not losing nearly 51% of the time. And over 91% of the time, you'll experience a variance from the expected payouts in blackjack. Blackjack variances will happen 9 out of 10 times you walk up to the blackjack table. You need to keep this in mind when playing blackjack and analyzing your results.