Blackjack expected values

Mar 25,  · Las Vegas discussion forum - Calculation of Expected Values in Blackjack, page 1. You can run the Blackjack software to complete exact expected values, but some of those calculations take a long time. The longest, by far, are the exact results for splitting. The longest, by far, are the exact results for splitting. In this video we learn about games of cards, and how to calculate probabilities. We look at the game of Blackjack and calculate the probability of.

Blackjack: Finding Expected Values of Games of Chance with Cards

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Blackjack Expected Values

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Login or Sign up. Calculating probabilities with games of cards can be quite complicated depending on the game and the amount of players. In this video, we will simplify the games for ease of calculation. Suppose you draw two cards from a standard deck of 52 cards, what is the probability they are both Aces?

Just in case you were not sure, a standard deck of cards has 4 suits called diamonds, hearts, clubs and spades. Thus, there are 13 cards of each suit numbered from 2 to 10 and then the face cards of Jack, Queen and King.

The final card, Ace, is also considered 1. So, we are looking for two aces. Even though two cards are being dealt, to calculate the probability, they must be thought of as two cards being dealt one after the other. Let's call them card 1 and card 2. Since there are 4 aces in the pack and 52 cards, the probability that card 1 is an ace is 4 out of Assuming we do not replace this card, there are now 51 cards left in the pack and only three Aces left.

Slowly, he died, spewing blood and bile out all over the alter. He was an amiable character, and was a popular community figure, always having a smile and a greeting for everyone who passed. Пышногрудая синявка любящая носить чулки может раздеться в абсолютно любой момент, если конечно в это время она находится дома. After fucking Jake like a buggerizing beast, he came. Голая красавица наслаждается природой и позволяет себе делать непристойные вещи без одежды.

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This web site describes a free Blackjack software package that does many exact calculations of blackjack expected values. Its unique feature is that it can even do exact calculations for pair splitting. Until recent algorithm development by the author , these calculations have not been possible.

Although exact splitting calculations are now possible, they are time consuming. This web site, therefore, also has tables of exact expected values output from the software. You can use them without needing to download and run the software. All tables of expected values given below were calculated using the free Blackjack software. You can visit the software web site to download the source code and read instructions on how to compile and run the calculations.

The exact calculation of pair splitting is much more time consuming then all other expected value calculations combined. An estimate predicted that non-optimized or conventional blackjack software methods would take about 11, years of computer time to complete all splitting calculations. Fortunately, it is possible to do better.

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The author of the Blackjack software has written a paper describing the process. The final result was that all splitting calculations were reduces to 45 days of computer time. The paper also describes an new approximate method that do get accurate splitting results in much less time. The Blackjack software can do both the exact and the approximate methods. You can download a draft of the submitted paper here.

Tables of Results You can run the Blackjack software to complete exact expected values, but some of those calculations take a long time. The longest, by far, are the exact results for splitting. Alternatively, you can just look up results in the tables listed below. These tables are direct output from the Blackjack software formatted for nice display for most expected values. Exact results for splitting have only been completed for the single deck game.


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The first one was when online blackjack and online gambling became available. Historically, one had to visit a casino to play blackjack for real money , but now, thanks to the magic of the internet, the casino came to you, right into your home, on your home computer. The next big leap happened when online casinos went mobile. Now, rather than being limited to playing at home on your computer, you can bring all the fun of the game with you wherever you go, and play right on your Android phone or tablet.

The Android platform dominates the mobile device market, and about three quarters of all devices now use the Android operating system, so while the online casino industry may have been a little slow to roll out apps for certain platforms, such as Windows or Blackberry, the Android market is the pound gorilla here. There are some games, online poker for instance, that may involve compromises moving from a large screen home computer monitor to something as small as a phone screen.

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For instance, depending on the size of the screen on your device, you may only be able to play one poker table at a time, instead of the several tables that some players like to play, and even that might involve this table being displayed smaller than you prefer. Smartwatch blackjack which recently became available prove the point.

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A lot of people even choose playing blackjack on their phone at home on Wi-Fi rather than logging into a blackjack site on their computer. You just have to pick up your phone, launch the app and start playing, without being tethered to your desk. This allows you to play from anywhere inside the house or even out on the patio, enjoying both nature and this wonderfully entertaining way to gamble.

Not to mention, that using your phone is always socially acceptable. There are two main ways that Android devices connect to the internet, which are through Wi-Fi and through mobile data transmission. All Android devices can connect to Wi-Fi, you just need a Wi-Fi connection and set them up to log into it. A lot of home internet packages these days come with a Wi-Fi enabled modem, essentially broadcasting the internet throughout your home, which your Android phone or tablet can access.



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