Probability of dealer and player getting blackjack
The probability of a blackjack in a single deck game is 4*16/combin(52,2) = 64/ So the probability of four in a row is (64/) 4 = / = 1 in However the actual probability is much less, because as the player gets each blackjack the . Then look up the dealer upcard across the top, and read down the column to see the probability of each dealer outcome. The probabilities of each outcome other than Blackjack assume that the dealer has checked the hole card and did not have blackjack. (Therefore, the columns under dealer Ten and dealer Ace add up to more than %. Jan 21, · This page shows the probability that the dealer will draw to any total from 17 to 21 or bust, given the dealer's up card, number of decks, and whether the dealer hits or stands on soft This page assumes the dealer already peeked for blackjack, eliminating that possibility.
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The most important frequencey to note is the chance of being dealt a natural blackjack natural 21 value. Blackjack also known as twenty-one or sometimes pontoon is one of the most popular casino card games in the world. Read over this chart to understand the odds that the dealer has to make his final hand. Related 0. One of those was a to-1 payoff for a hand consisting of the ace of spades and a black jack that is, the jack of spades or the jack of clubs.
To fully understand the game of blackjack, you must understand and master blackjack odds. It's crucial to know how the casino gains its edge and how it helps them win. It's also important to understand blackjack odds such as the odds of hitting a 10 or the odds of being dealt a blackjack. You can read over these blackjack odds charts to help understand the logistics behind blackjack. The house gets this advantage by the dealer being the last player to act.
By acting last, all other players have already made their decisions and could quite possibly bust before the dealer has his turn. If you correctly use advanced card counting techniques, you can often change blackjack odds and give yourself the advantage over the casino. Manipulating the house odds to your favor is the reason most casinos don't allow card counters to play blackjack.
It's very important to know the probability of your hand busting when you are holding any total in the game of blackjack. The following odds chart shows the blackjack odds of busting, depending on your current hand value:. This interesting blackjack odds chart is the two card count frequency chart.
This chart shows the percentage chance that you will be dealt a hand in each given value range. The most important frequencey to note is the chance of being dealt a natural blackjack natural 21 value.
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.
This happens every time. With a branching factor of five I know , we have two aces, once ace, two whatevers, one 10, two 10s. 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. 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.
Because the chance of one player getting blackjack is small, the enrichment is small as well, so this is not far off. Home Questions Tags Users Unanswered. Blackjack Probability Ask Question. Asked 4 years, 11 months ago. Active 1 year, 2 months ago. Viewed 17k times. Nolohice 5 5 silver badges 12 12 bronze badges. The use of neither indicates that. Your calculation for the first player is correct. Michael Cotton Michael Cotton 3 3 silver badges 6 6 bronze badges.
I can't help but wonder if there perhaps is a less hideous way of acquiring the same answer though. MaxWell MaxWell 2 2 bronze badges. Ross Millikan Ross Millikan k 24 24 gold badges silver badges bronze badges. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name.
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