- conditions offered in each specific gambling establishment;
- hands (your own and the dealer’s);
- previously released cards.
Let us dwell in more detail on the quantitative indicators of each parameter. By analyzing and using this information in your game against the casino, you will increase the chances of winning, you will understand the mechanics and statistics of the game, make sure that Blackjack is one of the most profitable games for the player with the right play and the right choice of casino with the necessary game variations.
- 1 Player odds depending on casino conditions
- 2 Probability of hitting the dealer and player’s chances
- 3 Dependence of the player’s chances on the previously issued cards
- 4 Conclusions
Player odds depending on casino conditions
Odds with a standard set of rules
Here is some standard (most popular) set of rules:
- 3 respites are allowed on each box on any cards of the same value;
- “surrender” is allowed if the dealer has a dozen (if there is A, it is prohibited);
- the dealer stops at soft 17;
- there are no restrictions on the “double” on the starting hand;
- it is possible to double after the split, with the exception of the split on aces;
- Blackjack is paid out at the rate of 3 to 2;
- 6 decks in a shoe.
If you strictly follow the basic strategy, the house edge in such conditions will be 0.18%. It can be compensated by applying card counting. How to do it is described here (link). With the correct use of the method, a final superiority of about 1% can be achieved.
What factors can change this indicator?
Deteriorating odds from rule changes. Quantitative analysis
The blackjack payout reduced to 6: 5 reduces the probability of a positive outcome the most – by 1.35%.
Even competent card counting will not allow you to consistently make a profit under such circumstances. Don’t sponsor the casino – give up the game.
The rest of the negatively influencing factors will act to a lesser extent:
- the limit on doubling by 9-11 points will reduce the chances by 0.09%, and only by eleven – by 0.64;
- impossibility of “surrender” when the dealer has ten – 0.27%;
- continuation of the dealer’s recruitment on soft 17 – 0.22%;
- the prohibition to play double after the split – 0.14%;
- exclusion of resplites in general – 0.13%, and only resplites on aces – 0.07%;
- an increase in the number of decks to 8 – 0.1%.
Improving the odds of changing the rules
- The payout is 2 to 1 for a suited Blackjack – 0.56%.
- “Surrender” versus the dealer’s ace – 0.38%.
- Bonuses for various combinations (“6-7-8”, “7-7-7” or any others agreed in advance) – 0.15-0.35%.
- Reducing decks in shoe to:
two – 0.2%;
one – 0.5%.
By comparing all the “cons” and “pros”, one can imagine the true perspectives. However, one must be aware that all of the above is true only with a large number of trials, and the chances of winning in each individual case depend mainly on the initial hands of the opposing sides.
Dealer’s chance of hitting and player’s chances
Table 1 shows the probabilities that the dealer will score a certain number of points for different starting cards. The results were obtained by the method of mathematical modeling.
|Dealer’s starting card||Recruitment probability,%|
Based on Table 1, calculate the player’s odds based on the final score and the dealer’s starting hand.
|Start. dealer’s card||Player set|
|Sub 1||Por 2||Pre||Por||Pre||Por||Pre||Por||Pre||Por||Pre||Por||Pre||Por|
1 – the probability of winning in%
2 – probability of defeat in%
Dependence of the player’s chances on the previously issued cards
By counting the cards coming out of the “out”, it is possible to estimate the decrease or increase in the probability of winning.
Depending on the values of the coefficient K1 (the so-called “true score”) with a standard set of rules, the player’s chances will change as follows:
All results are obtained by mathematical modeling.
The data given in section 1 will be useful when choosing a casino.
The second is for informational purposes only and is not intended to be memorized. But it is the tables displayed in it that are the basis for developing a basic strategy, which must be strictly adhered to in order to obtain stable profits.
With the help of section 3, “counters” can numerically determine the ratio of odds, make accurate decisions about changing the size of bets and adjust the game.