To deal with the Blackjack game effectively, It is necessary to know how to apply the Basic strategy tables. Use the table does not presuppose any mathematical base, as it will be enough to follow the instructions starting from your initial hand and the hand of the dealer.

In this article we try to explain in a simple way how to calculate the Probability of Blackjack Aams/Adm Single deck.

Probability of doing blackjack

the probability of making blackjack served With the initial hand it is not very complex to calculate, First of all, it is necessary to calculate the number of possible initial hands (also applies to Texas Hold'em).

The number of initial hands in Blackjack is given by binomial coefficient C(n, k) Con n= number of cards in the deck (52) e k= number of cards to serve (2).

In the formula the symbol "!" represents the factorial.

C(n,k) = n! / [k! (n-k)!]

C(52,2) = 52! / [2! (52-2)!] = 1326

In total we therefore have 1,326 possible hands, that can be served us. Now we have to calculate with how many initial hands we can do blackjack.

The calculation is very simple: knowing that we have 4 axes and 16 cards of value ten

4x16 = 64 possible combinations of ace and ten.

We just have to calculate the probability of making blackjack served.

64 / 1326 = 0,04826546 = 4,8%

The probability of making blackjack with two cards is therefore 4.8%

Put simply: on a large number of games (of the order at least thousands), We will do blackjack about once every 20 hands.


Probability of having two axes for the split

The calculation is identical, taking into account that there are 4 assi, There are 6 possible combinations of axes. The probability of having two axes served is therefore 6 / 1326 = 0,00452 = 0,45%

On a large number of Blackjack hands, We will have two axes once every 220 hands (also useful for Texas Hold'em)

In a similar way you can calculate a bit all the other probability of the initial hands in the Blackjack that they can come in handy to make your mathematical analyzes.


Useful tables for the chances of Blackjack

Summary table of the player's initial hands

Initial hand Chance
Mano che non sballa (< 12) 26,5%
Hand in which to decide (12-16) 30%
Mano in cui restare (> 16) 38,7%
bblackjack 4,8%

Summary table of the chances of cloving (bust) of the player

Initial hand Probability of bolt
12 31%
13 39%
14 56%
15 58%
16 62%
17 69%
18 77%
19 85%
20 92%

Summary table of the chances of cloving (bust) of the Mazziere

Initial paper Probability of bolt
A 11,7%
10 21,4%
9 23,3%
8 23,6%
7 26%
6 42%
5 42,9%
4 40,3%
3 37,6%
2 35,3%

If any information does not be correct, please leave a comment below or open a post on forum so that the resolution of your doubt can also be read by others.


Know the chances of Blackjack is essential?

What if I wanted to play while not knowing nothing about the chances of doing Blackjack? Well nobody certainly forbids you, only that there are games in the world of azader who lend themselves more to be left to chance as the Slot machine, others where a good one knowledge of appropriate techniques and strategies And the calculation of the probability can make a difference: Blackjack is an excellent example in this sense.

In other words, given that Blackjack is based on mathematical and statistical rules, the knowledge of its functioning and the Calculation of probability in Blackjack can definitely make a difference during the hands by completely changing the fate of the game.

We often notice a rather incorrect behavior from players, in particular beginners, who entrust the fate of their games completely to luck, without worrying about the minimal of adopting a precise strategy and without even taking into consideration the fact of calculating the probability to Blackjack. Certainly Blackjack is a slightly more strategic game than many others and the most impatient players could turn up their noses, but the reality is this: if you want to try to win at Blackjack you must first of all know what not to do and obviously what is right instead do to ensure that the game is in your hands.

In Blackjack, the player's decision to make the difference are in fact, for better or for worse.


Calculation of the probability of Blackjack: Must Know

At this point the less experienced players could start thinking that playing Blackjack is too difficult and that there are too many things to learn especially on the calculation of probability. Instead, what seems complicated at the beginning, after a short practice will prove to be much easier than expected and the results will not be long in coming.

First of all Knowing the number of decks that will be used is essential to calculate the probability in Blackjack, because above we did the example of a single deck, but we must remind us that at Blackjack it is also played with 2, 6, even 8 decks, so knowing the number of decks used in advance will provide us with a precious indication on how to behave later, Especially if you decide to try a count the cards.

Be careful though, what has been said above is valid only for the blackjack live, as online casino tend to mix the cards with each new hand, so the number of decks in these cases completely loses its importance and no longer influences our calculations.

Another thing to consider in Calculation of the probability of Blackjack is the advantage of the counter, who, only for the fact of deciding last is placed on a higher step than the player and could win very easily even at the beginning without the slightest effort.

On the other hand, it must be said that the same bench is the subject of particular rules that force him to “stare” o "Ask paper" Depending on the score he has in his hand, while the player is completely free to act as he believes and this brings him back to decreasing the advantage of the Croupier a little. It would be good to always know how to exploit this "detail" in his favor.

Once these initial considerations have been made, you can start by calculating the probability to Blackjack following what reported in the tables illustrated above, which make the job much easier than it might seem like. In most cases you just look to the tables and you are clearly clear the strategy to follow.


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P. Min per blackjack
1.000 $
P. Max per blackjack
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0,10 $
P. Min per blackjack
10.000 $
P. Max per blackjack
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0,10 $
P. Min per blackjack
2.500 $
P. Max per blackjack
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hi massimiliano, thank you so much for the report, there was a mistake in the table, the values were translated up of one. as you rightly point out, it is not possible to get busy starting from 11 with one card, at least i don't even know cards that are worth 12;) and as you rightly note the probability of bouncing starting with the initial hand 20 is not 100% but 92% since there are 4 axes in the deck that allow you to get to 21 and therefore not to be busy.



idon'tunderstandsomethings,howcanyougetbusywithascoreof11ifthemaximumyoucanaddisa10?11+10=21and21isthehighestscoreyoucando,itisnotbusyanyway. inaddition,itisnottruethatwith20itis100%busy(92%isbuzzed),ifyouaskcarta,itcanhappenthattheaceexitsandthereforethetotalscorerisesto21,maximumpermittedscore. canyouexplaintomehowyougotthesedata? thankyou, massimiliano

hi antonello, sicuramente ci sono diverse persone che la pensano come te e che non ritengono il calcolo delle probabilità nel blackjack attendibile, non considerando però che queste non sono teorie campate in aria ma frutto di studi matematici e statistici di chi ne sa un po’ più di noi a riguardo senza ombra di dubbio. le tabelle sono il risultato di tali studi e chi ci ha lavorato sopra ha dovuto impiegare parecchie risorse fisiche e mentali per riuscire a concepirle e renderle fruibili a noi così come lo sono oggi, in confronto a questo lo sforzo che dobbiamo fare noi per consultarle è assolutamente minimo e non paragonabile. chi non ha molta dimestichezza con i numeri, come nel tuo caso a quanto abbiamo capito, ha delle reticenza di base nel cercare di comprendere un certo tipo di concetti che poi però in realtà, una volta che ci addentriamo nel merito sono molto meno ostici di quanto all’inizio il nostro cervello ci vuole far credere, motivo per il quale ci sentiamo di consigliarti di fare un piccolo sforzo in più e provare a mettere in atto un tipo di gioco come questo. ovviamente se tu però non credi alla strategia e vuoi lasciare tutto al caso sei liberissimo di farlo, la fortuna si sa ci deve essere comunque, non siamo certo noi quelli che dicono che non ce ne sia bisogno, diciamo solo che in un gioco di questo genere non è consigliabile affidarsi soltanto alla sorte per riuscire, c’è bisogno di un qualcosa in più e visto che abbiamo questa opportunità perché non sfruttarla? ci piacerebbe sapere se i nostri consigli ti hanno fatto un po’ cambiare idea, Ciao.



i just can't understand how easy to calculate the probability to the blackjack, you make it seem like something so by everyone but then actually it seems to me that it requires a not indifferent commitment with somewhat questionable results. that is, i am certainly not the most suitable person to talk about mathematics because i never understood anything even at school and not even the most patient in this world, maybe blackjack is not my game for this and i prefer to travel a slot roller to have fun an hour without being studying and doing calculations, but as a game i like because it's fast and every now and then some game when i am inside the casino i do it too. however, i must say that even in blackjack i adopted the same strategy that i use with the slots, that is, having no strategy, i play to have fun i don't want to be there to waste time in theories and systems that if you don't turn your luck from yours part are useless, it will be that i am very practical and very realistic but i all need to calculate the probability in blackjack i don't see it, or rather i see it more difficult than then i can't get, a bit like saying that the game is not worth the candle here.