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But I'm not quite sure how to calculate the math behind this and how to calculate the probability for winning a single blackjack hand. I figured with 10,000 credits, I can start my bet at 1, then go to 2, then 4, etc (doubling my bet everytime I lose). This allows me to lose up to 12 hands before I am bankrupt. Blackjack Probability I have spent years analyzing roulette statistics and they are very easy to generate (just throw up random numbers from 0-36) but now that I am moving into blackjack, the actual statistics are a mystery to me. Nd the experimental probability of being dealt a blackjack with the rst two cards of a single deck. 2.Now nd the theoretical probability of being dealt a blackjack with the rst two cards. (a)When you are dealt two cards, the order of the cards matters because only one card faces up for example, the hands Q, 8 and 8, Q are di erent. Utah State University DigitalCommons@USU All Graduate Plan B and other Reports Graduate Studies 5-2014 The Expected Value of an Advantage Blackjack player. Blackjack, unlike other gambling games is not considered a game of chance, it is one that you can win if you start applying some knowledge. Unlike many other games where the result depends on player luck only, this game provides probabilities depending on the player decisions.

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Introduction

Let me say loud and clear that card counting is hard and is not as rewarding as television and the movies make it out to be. If it were an easy way to make money, then everyone would be doing it.

If you do not know the basic strategy, trying to count cards is highly ill-advised. Experienced card counters still play by the basic strategy the great majority of the time.There can be no short cut around learning the basic strategy, those who attempt card counting without a firm foundation in the basic strategy are making a big mistake.

To be a successful counter you have to be able to countdown a deck fast and memorize large tables of numbers as well as make it look like you're just a casual player.Furthermore, with today's rules, a realistic advantage the counter will have is only 0.5% to 1.5%. You will not win money slowly and gradually but your bankroll will go up and down like a roller coaster in the short run. Only in the long run, over hundreds of hours of playing, can you count on winning.

The underlying principle behind card counting is that a deck rich in tens and aces is good for the player, a deck rich in small cards is good for the dealer. When the counter knows the odds are in his favor, he will bet more, and adjust his playing strategy to stand, double, and split in some plays where basic strategy says to stand. All the options the player has at his disposal favor the player even more when the deck is ten and ace rich. Here is a list and a brief reason why.

Standing: The player may stand on stiff totals of 12 to 16, and the dealer may not. In ten-rich shoes, hitting stiff hands becomes more dangerous, favoring the more conservative player strategy.

Insurance: On average, when the dealer has an ace up, the remaining cards in blackjack will be 30.87% tens (based on a six-deck game), making insurance a bad bet. However, if the probability gets above 33.33%, it becomes a good bet. Counters know when the remaining cards are ten-rich, and make powerful insurance bets at those times.

Doubling: Usually, when the player doubles he wants a ten. In ten-rich shoes, the player makes better double downs, getting closer to 21.

Blackjack: Both player and dealer will see more blackjacks, but the player gets paid 3 to 2, and the dealer does not.

Surrender: The alternative to surrendering is much worse in ten-rich shoes. If the alternative is hitting, the player is more likely to bust. If the player would otherwise stand, due to the high count, the dealer is still more likely to get a 10. While the counter will surrender more in high counts, the savings will be greater. Poker kombinationen deutsch.

Splits: The player is usually splitting high cards and/or off of a weak dealer card. Either way, a ten-rich shoe helps the player get higher totals, and increases the probability of the dealer busting.

I'm working on an in-depth study of how these effects break down. The contribution to each factor depends on the rules, deck penetration, and bet spread. However, based on average conditions in a six-deck shoe, my initial results break down the benefits of counting as follows.

Why Card Counting Works

Player Option	Portion of Benefit
Stand	40%
Insurance	34%
Double	9%
Blackjack	7%
Surrender	6%
Split	4%

The probability for insurance was taken from Don Schlesinger's 'Illustrious 18' list, as found in Blackjack Attack. The rest of the breakdown is mine.

To gauge the richness of the deck in good cards, the player will keep track of the cards the are already played. Downtown osage casino tulsa oklahoma. Strategies vary, but all assign a point value to each card. For example, the hi-lo count assigns a value of +1 to 2, 3, 4, 5, and 6, and -1 to tens and aces. Everything else is 0, or neutral. At the beginning of a deck or shoe, the count is 0. Then the counter constantly adds and subtracts from the count, according to the cards played. This running total is called the 'running count.' A positive count means that a disproportional number of small cards have already been played, which means that the deck is rich in large cards. To determine the 'true count,' divide the running count by the number of decks left to be played, or in some strategies, the number of half decks. This will tell you the relative richness of the deck in good cards.

The true count is used in two ways, to determine how much to bet and how to play your hand. Unless it is obvious, every situation has a line in which you should play one way if the count is above the line and another if below. For example, a 12 against a 6 may dictate that you stand if the true count is -1 or greater and hit if the true count is less than -1. The counter will also bet more when the true count is high, meaning the deck is rich in good cards.

A problem arises when it comes to treating aces. The player should bet more when the deck is rich in aces since they add to the probability of getting a blackjack. However, when it comes to playing your hand, the number of aces left is not nearly as important as the number of tens, so it is desirable, but not necessary, to distinguish between tens and aces. Some card counting strategies keep a side count of aces. In the Hi-Opt I and Revere Plus/Minus aces are counted separately and only considered when making the wager. This is a more accurate and powerful way to play than assigning a negative value to aces and not keeping a side count, as some strategies do. Yet, many people feel that for the beginner it is too confusing to keep two counts. A player is more likely to make mistakes keeping two counts and that costs money. The efficiency of a strategy that does not keep a side count of aces is only modestly less, but you likely will gain more from fewer mistakes made. Different experts fall in various places in the spectrum in terms of what to recommend for the beginner. The Zen Count takes the middle ground and gives aces a value of -1 and tens -2. Personally, I have tried both and would recommend against a count that requires a side count of aces to a person ready to take up card counting. The Uston Advanced Plus/Minus is a good strategy that does not involve an ace side count and can be found in the book Million Dollar Blackjack. How well you know a counting strategy is much more important than which strategy you know.

Legally speaking, the player may play blackjack any way he wants without cheating or using a computer, and the casinos may do anything from making conditions unfavorable to barring, in an effort to stop anyone who they deem has an advantage over the game. Much of the challenge of card counting is avoiding suspicion that you are anything but a normal non-counting player. The most obvious indica

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