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Probability of getting 17 in blackjack

Blackjack is the name of the game. So what are the odds of getting dealt a blackjack? The probability depends on how many decks are played. Of course the essential ingredients to blackjack are an ace and a ten-value card (10, jack, queen, or king). When the dealer stands on a soft 17, the dealer will bust about % of the time. When the dealer hits on a soft 17, the dealer will bust about % of the time. According to my blackjack appendix 4, the probability of a net win is %. However, if we skip ties, the probability is %. So, the probability of at least one player getting a blackjack is: $$\frac{+,}{1,,}$$ Hence the probability of neither player getting a blackjack is: $$1- \frac{+,}{1,,} \approx \%$$.

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All probabilities are calculated for cases using one or two decks of cards. This happens every time. Let us calculate the probability of achieving 21 points receiving a 4. The probability of both getting blackjack is just the probability of the player getting blackjack and the subsequent probability of the dealer also getting blackjack:. By using our site, you acknowledge that you have read and understand our Cookie Policy , Privacy Policy , and our Terms of Service. The first two columns in this odds chart explain the dealer's chance of busting, depending on the up card that he is showing.

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  •   The casino is the most common place in which suicides are committed
  •  The center of the casino is Las Vegas. Every year 40 million gambling people from all over the world come here.

Blackjack Odds

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Suppose that you are playing blackjack against the dealer. So I deleted the more complicated answer I tried to give earlier. Then for the other player we either give them two aces from the 3 that are left, give them one ace from the 3 that are left and 1 of the 32 cards, or give them two non-aces from the 47 non-aces that are left.

The probability of both getting blackjack is just the probability of the player getting blackjack and the subsequent probability of the dealer also getting blackjack:.

I don't know if this will get you any closer to a closed form solution, but maybe it helps you think about it.

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Details

We first present the probabilities attached to card dealing and initial predictions. In making this calculus, circumstantial information such as fraudulent dealing is not taken into account as in all situations corresponding to card games. All probabilities are calculated for cases using one or two decks of cards. Let us look at the probabilities for a favorable initial hand the first two cards dealt to be achieved. Similarly, we can calculate the following probabilities:.

A good initial hand which you can stay with could be a blackjack or a hand of 20, 19 or 18 points. The probabilities of events predicted during the game are calculated on the basis of the played cards the cards showing from a certain moment. This requires counting certain favorable cards showing for the dealer and for the other players, as well as in your own hand. Any blackjack strategy is based on counting the cards played. Unlike a baccarat game, where a maximum of three cards are played for each player, at blackjack many cards could be played at a certain moment, especially when many players are at the table.

Card counting techniques cannot however be applied in online blackjack. The formula of probability for obtaining a certain favorable value is similar to that for baccarat and depends on the number of decks of cards used. This formula holds for the case of a 1-deck game. In the case of a 2-deck game, the probability is:. Generally speaking, if playing with m decks, the probability of obtaining a card with the value x is:.

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Let us calculate the probability of achieving 21 points receiving a 4. If we want to calculate the probability of achieving 19, 20 or 21 points, all we must do is total the three probabilities just calculated. Unlike in baccarat, where fewer cards are played, the number of players is constant two , and the number of gaming situations is very limited, in blackjack, the number of possible playing configurations is in the thousands and, as a practical matter, cannot be entirely covered by tables of values.

You will also find there other issues of probability-based blackjack strategy. See the Books section for details. Check this. Your ad here See the terms and rates in the advertising page.

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