BlackJack mathematical strategies

BlackJack mathematical strategies

What statistical and mathematical strategies can I use for online Black Jack? Black Jack is a type of casino game that, unlike others where chance is mainly involved because the odds are fixed (roulette, slots, baccarat), has an important skill component, as bets can be optimised mathematically.

Not splitting pairs of 10’s

When you have a pair of 10s or a pair of jacks (J, Q, K) it adds up to 20 in total. Such a hand is too strong to split, so the best trick is to keep the hand and play it as it is, without drawing any other cards, as this would be against the stand on 17 or more rule discussed above.

When another player has an Ace

The Ace can be worth 11 or 1 depending on the situation. When another player, or the dealer, has an Ace, if they draw a card worth 10 on the next hand, the game is over and they are the winner.

This is a very likely outcome, especially in multi-deck games, and when the deck is unfavourable (i.e. when low value cards have been drawn and there are many high cards left in the deck).


Variance is the difference between the advantage you expect in the game and your actual results.

On the website we have linked to, they state the following as an example:

  • If you play a total of 100 hours with an expected value of $22 per hour, your expectation will be to win $2200 during that time.
  • If you have only won $1800 after 100 hours, the 400 hours below your expectation is the variance.

Keep in mind that the more you play, the closer you are to balancing your variance.

Standard Deviation (SD)

The standard deviation shows how often your Black Jack results deviate from the average. It is a strategy for determining whether you are winning at the game or how much capital you will need to make significant gains.

Standard deviation helps you prepare for what to expect, what to expect, in terms of variance.

You can calculate standard deviation with a standard deviation calculator like this one.

N0 (N-Zero)

N0 is something that players don’t often pay much attention to. It is the number of hands it theoretically takes to reach the goal of beating a standard deviation (4 N0 gives you the hours to beat 2 SD).

To have the most accurate assessment of N0, it is necessary to play with the same rules and the same betting strategies.

Certainty Equivalency (CE)

Also known as “Risk Scared Profit”. It results in the figure closest to what you expect your % profit in Black Jack to be. It is also a good indicator of whether or not the game is going to be worth playing.

It is the result of taking the expected win ratio and adjusting it based on the level of risk in proportion to the current bankroll and the level of risk tolerance.


Although the art of card counting is frowned upon or even banned in some land-based casinos, it is not an illegal practice.

Card counting in Black Jack is one of the most productive strategies for ensuring better performance and making better decisions (such as whether or not to split aces and eights, or calculating the odds that an opponent can draw a 21).

An example of this strategy that made Black Jack and the counting strategy famous was the story of Ken Uston and his MIT team, who managed to win more than 5 million dollars in different casinos in the 1990s.

In the film 21 Black Jack, the MIT team uses the “hi-lo” (High-Low) method of counting: with high cards having a value of 10, and low cards with less than 6 points.


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