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Standard Deviation is a measure of how results are distributed within a range of possible outcomes. 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.
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. 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.
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. This table reflects a standard deviation of 1. Chart provided by WizardofOdds. While this score is interesting, the application of it benefits from adding a second variable — the number of hands played. 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:. Here the distribution of blackjack outcomes predicts you will win or lose 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. 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.