Mathematical Aspects

Math Beyond Blackjack

Like in most games of chance, Blackjack strategies never present players with one hundred percent guarantees of winning. In essence, utilizing mathematical probabilities is simply a way to minimize the innate house edge and make decisions based on the cards that you and the dealer have as well as those that are still left in the game.

Therefore, in spite of numerous guides that claim to possess the infallible secret, much like fanatical religious/spiritual leaders, you can easily understand why a foolproof methodology has not yet been developed. Joke aside, let’s first clarify the basic concepts of Blackjack.

Quick walkthrough of the rules   

First of all, I have seen numerous guides to the game that suggest the objective of the player consists primarily of accumulating a sum of cards closest to 21, without going over this value. However, the real goal implies accumulating a sum of cards that is higher than the one of the dealer but that does not exceed 21. At first glance, the two statements are largely similar, but in fact there is a world of difference between them.

In the first case, the player should continue hitting (asking for more cards) until he is satisfied with the difference between the sum of his cards and the maximum value of 21, without taking into account the hand of the dealer. This erroneous strategy would substantially increase the house edge. On the other hand, if you remember that you don’t really need to aim for accumulating 21 points, but rather just over the value that the dealer holds, you stand to gain a lot more. The value of the cards in the game of blackjack is as following:

  • 2 to 10 cards have the value imprinted on them
  • The value of all face cards is 10 points
  • The value of the Ace is either 11 (if the sum of the cards does not exceed 21) or 1 (if the sum of the cards exceeds 21)

The bettor will only see one of the cards of the dealer and, after being dealt the first 2 cards he will be able to:

  • Stay, meaning that he will not request any more cards
  • Hit, meaning he will request an additional card
  • Split, meaning the current hand is split into two individual hands when the cards dealt are the same (two Aces, two 8s, two 5s, etc.)
  • Double down, the value of the bet is doubled and the player will only receive one more card

It is necessary to point out that some casinos enable the player to “surrender”, canceling the bet if he does not like the hand that he has been dealt. However, you should inquire on whether or not your current table utilizes this rule.

What is the house edge in Blackjack?

The house edge really depends on the number of decks that are in the game. Assuming that you are only playing with a singular deck, than the house edge is then calculated at 0.17 percent. The house edge increases with each additional deck brought into play, as following:

  • 2 decks, 0.46%
  • 4 decks, 0.60%
  • 6 decks, 0.64%
  • 8 decks, 0.66%

In order to understand why the house gains an edge over the bettor that is directly proportional to the number of decks in play, you need to understand that the game of Blackjack is based on dependant events. To put it simply, it becomes much more difficult to estimate the number of cards that are still in the game and to calculate the odds of the remaining cards accurately, which means that card counting no longer provides you with the same advantage. For example, when you are playing with a single deck, you know that once all the Aces are out, the probability that either you or the deal draws one is 0.

An example of strategy

As mentioned previously, there is no strategy that will function optimally every time, but rather decision making systems that have a mathematically higher chance of winning. For the purpose of understanding that better, we have compiled a list of such decisions in the following table:

Player’s Hard Hands  Dealer’s Hand
2 – 67 – Ace
4 – 8HitHit
9Double DownHit
10 – 11Double DownDouble Down
12 – 16StayHit
17 – 21StayStay
Player’s Soft HandsDealer’s Hand
13 – 15HitHit
16 – 18Double DownHit
19 – 21StayStay
Player’s Split HandDealer’s Hand
2-2, 3-3, 6-6, 7-7, 9-9SplitDon’t split
8-8, Ace-AceSplitSplit
4-4, 5-5, 10-10Don’t SplitDon’t Split


This guest post is written by Andrea, a passionate student of the theory behind casino games and writer at

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