Blackjack Statistics

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The naive assumption is that the chance of each player getting blackjack is independent of the others. As you say, the chance than one player does not get blackjack is 2524 2652 The chance that none of n players gets blackjack is then (2524 2652) n.


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According to my blackjack appendix 4, the probability of an overall win in blackjack is 42.22%, a tie is 8.48%, and a loss is 49.10%. I'm going to assume you wish to ignore ties for purposes of the streak. In that case, the probability of a win, given a resolved bet, is 46.36%. The probability of winning n. The Statistics of Blackjack electronic book was also re-written and made more user-friendly by Babblefish. The menus and general outlay of SBA was re-designed, and SBA should now be even easier and more natural to use. The major new feature for simulations is the ability to simulate precise wonging-in strategy. The user can use Wong-in. Sometimes you’ll get more blackjacks in two hours of play, sometimes less, but on average you’ll get 10. Each of those blackjack hands cost you $3 on a 6-5 game (the difference between getting paid 3-2 vs. 6-5, or $12 instead of $15, for your $10 wager). Blackjack and Probability Chongwu Ruan Math 190S-Hubert Bray July 24, 2017 1 Introduction Blackjack is an usual game in gambling house and to beat the dealer and make money, people have done lots of research on it. They come up with several basic strategy which is consist.

Blackjack Probability and Blackjack Odds

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.

Blackjack Statistics Simulator

Casino and Dealer Advantage in Blackjack

In most casino games of blackjack, the house advantage (the dealer advantage) is ~ 8%. 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.

By using correct blackjack basic strategy, you can turn the casino edge in blackjack from 7%-8% down to 0.5%. 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.

Probability of Busting on a Hit

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:

Hand Value% Bust If You Hit
21100%
2092%
1985%
1877%
1769%
1662%
1558%
1456%
1339%
1231%
11 or Less0%

Two-Card Count Frequencies

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. The odds of being dealt a natural blackjack are merely 4.8%. Following this chart you will see that the most common two card hand, at 38.7%, is a hand totaling 1-16, which is considered a decision hand.

Blackjack
Two Card Count% Frequency
Natural 214.8%
Hard Standing (17-20)30.0 %
Decision Hands (1-16)38.7%
No Bust26.5%
TOTAL100.0%

Dealer Final Hand Probabilities

This blackjack odds chart shows the dealer final hand probability. These are the percentages that the dealer will end up with a hand totaling each corresponding value (up to 16). Read over this chart to understand the odds that the dealer has to make his final hand.

Dealer Final Hand Value%Cumulative % Total
Natural 214.82%4.83%
21 (3 or More Cards)7.36%12.19%
2017.58%29.77%
1913.48%43.25%
1813.81%57.06%
1714.58%71.64%
1628.36%100.00%

Player Advantage vs. Dealer Up Card

The first two columns in this odds chart explain the dealer's chance of busting, depending on the up card that he is showing. You should note that the dealer has the highest chance of busting when he is showing a 5. The third column in this chart shows the player advantage of using basic strategy, compared to each up card the dealer is showing. You can see that the player has the highest advantage of 23.9%, when the dealer is showing a 5. When the dealer is showing any card that is 9 value or higher, the player is in the negative advantage range.

Dealer Up CardDealer Bust %Player Advantage % with Basic Strategy
235.30%9.8%
337.56%13.4%
440.28%18.0%
542.89%23.2%
642.08%23.9%
725.99%14.3%
823.86%5.4%
923.34%-4.3%
J,Q,K21.43%-16.9%
A11.65%-16.0%

Effects of Removing Cards from a Deck

Blackjack Statistics Card

When looking at the odds of removing certain cards from a 52-card deck, some cards have a much greater effect on blackjack odds. To create the strongest card counting system ever invented, you would have to incorporate all of these slight and subtle differences into the numbers to be a completely accurate system.

Removing every 5 from a deck cards would make the largest impact of improving your blackjack odds, as a player. On the other hand, removing every Ace from a deck of cards would make the largest impact on improving the odds for the casino.

Card% Effect of Removal
20.40%
30.43%
40.52%
50.67%
60.45%
70.30%
80.01%
9-0.15%
10-0.51%
A-0.59%

Statistics Blackjack 21

See also:

Blackjack Statistics Table


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