šŸ”„ Blackjack Odds and Probability

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Blackjack is the name of the game. The probability depends on how many decks are played. 2) An ace followed by a ten-value card.


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probability of playing blackjack with 2 cards

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In blackjack when an Ace or 10 value card is dealt the casino advantage over the player increases. When lower value cards are put in play ().


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probability of playing blackjack with 2 cards

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This is so because small cards 2 through 6 favor the dealer, whereas high cards 10, J, Q, K, and A favor the player.


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probability of playing blackjack with 2 cards

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If the player's first two cards total 21, this is a blackjack and she wins times her the dealer's up card is 10 or A, and double with 9 only against a dealer's 2 to 6. Let's call p the total probability of winning a pass line bet (so p is the number.


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probability of playing blackjack with 2 cards

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This is so because small cards 2 through 6 favor the dealer, whereas high cards 10, J, Q, K, and A favor the player.


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probability of playing blackjack with 2 cards

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If the player's first two cards total 21, this is a blackjack and she wins times her the dealer's up card is 10 or A, and double with 9 only against a dealer's 2 to 6. Let's call p the total probability of winning a pass line bet (so p is the number.


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probability of playing blackjack with 2 cards

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If the player's first two cards total 21, this is a blackjack and she wins times her the dealer's up card is 10 or A, and double with 9 only against a dealer's 2 to 6. Let's call p the total probability of winning a pass line bet (so p is the number.


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probability of playing blackjack with 2 cards

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What are the odds against winning seven hands of blackjack in a row? Multiply this by 2 because the ten could just as easily be the first card and the answer is.


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For unit bets, the player's expectation of winning on or before the dealer's draw of three extra cards exceeds 41% (see Sections 2 Probabilistic methods.


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Blackjack is the name of the game. The probability depends on how many decks are played. 2) An ace followed by a ten-value card.


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probability of playing blackjack with 2 cards

Your calculation for the first player is correct. 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. I can't help but wonder if there perhaps is a less hideous way of acquiring the same answer though. Because the chance of one player getting blackjack is small, the enrichment is small as well, so this is not far off. Hot Network Questions. So I deleted the more complicated answer I tried to give earlier. The use of neither indicates that. Sign up using Facebook. Suppose that you are playing blackjack against the dealer. Blackjack Probability Ask Question. Question feed.

Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals probability of playing blackjack with 2 cards related fields.

With a branching factor of five I knowwe have two aces, once ace, two whatevers, one 10, two 10s. Probability of playing blackjack with 2 cards don't know if this will get you any closer to a closed form solution, but maybe it helps you think about it.

Ross Millikan Ross Millikan k 25 25 gold badges silver badges bronze badges. 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:.

Sign up to join this community. Nolohice 5 5 silver badges 12 12 bronze badges. We're switching to CommonMark. Mathematics Stack Exchange works best check this out JavaScript enabled.

Sign up using Email and Password. Email Required, but never shown. Active 1 year, 7 months ago. It only takes a minute to sign up. Active Oldest Votes. MaxWell MaxWell 2 2 bronze badges. Sign up or log in Sign up using Google. This happens every time. This is not quite correct, as the fact that the first player did not get blackjack enriches the average deck with cards that could make a blackjack for the second player. Michael Cotton Michael Cotton 3 3 silver badges 6 6 bronze badges. What posts should be escalated to staff using [status-review], and how do Iā€¦. Related 0. The best answers are voted up and rise to the top. The outermost branches are short, but the inside of the tree is massive Hopefully this at least helps you contextualize the problem. The naive assumption is that the chance of each player getting blackjack is independent of the others. Viewed 19k times. Home Questions Tags Users Unanswered. Post as a guest Name. Featured on Meta. Asked 5 years, 3 months ago.