As a starting point, the house has an edge of 8% on us players, but by using the.

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When playing basic strategy blackjack I understand that I will have ups and downs and over the long run I will roughly break even, my question is what is really.

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There are two charts depending on whether the dealer hits or stands on soft Other basic strategy rules. Never take.

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Mathematics, True Odds, Basic Strategy, Card Counting, House.

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Mathematics, True Odds, Basic Strategy, Card Counting, House.

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Actually, C-D basic strategy has been around for a long time, having first been proposed in in the classic book The Theory of Blackjack by the late blackjack.

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As a starting point, the house has an edge of 8% on us players, but by using the.

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As a starting point, the house has an edge of 8% on us players, but by using the.

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A blackjack game has a dealer and one or more players. With soft hands, the basic strategy is to always hit 17 or less and even hit 18 if the dealer's idea of the probability of winning any particular bet when playing some specific strategy.

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When playing basic strategy blackjack I understand that I will have ups and downs and over the long run I will roughly break even, my question is what is really.

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In that case, the probability of a win, given a resolved bet, is The probability of winning n hands is a row is 0. So the probability of winning six in a row is 0. Repeat step 3 but multiply by 3 instead of 2. Determine the probability that the player will not get a third eight on either hand. So, the best card for the player is the ace and the best for the dealer is the 5. The standard deviation of one hand is 1. That column seemed to put the mathematics to that "feeling" a player can get. Determine the probability that the player will resplit to 3 hands. What you have experienced is likely the result of some very bad losing streaks. Thanks for your kind words. Determine the probability that the player will resplit to 4 hands. The fewer the decks and the greater the number of cards the more this is true. If I'm playing for fun then I leave the table when I'm not having fun any longer. If you were to add a card as the dealer you should add a 5, which increases the house edge by 0. To test the most likely case to favor hitting, 8 decks and only 3 cards, I ran every possible situation through my combinatorial program. Take the dot product of the probability and expected value over each rank. Or does it mean that on any given loss it is a 1 in chance that it was the first of 8 losses coming my way? I know, I know, its some sort of divine intervention betting system I am talking about and no betting system affects the house edge. It is more a matter of degree, the more you play the more your results will approach the house edge. There are cards remaining in the two decks and 32 are tens. Add values from steps 4, 8, and The hardest part of all this is step 3. This is not even a marginal play. Here is the exact answer for various numbers of decks. It may also be the result of progressive betting or mistakes in strategy. It depends on the number of decks. I have no problem with increasing your bet when you get a lucky feeling. The best play for a billion hands is the best play for one hand. If there were a shuffle between hands the probability would increase substantially. Any basic statistics book should have a standard normal table which will give the Z statistic of 0. I recently replaced my blackjack appendix 4 with some information about the standard deviation which may help. Is it that when I sit down at the table, 1 out of my next playing sessions I can expect to have an 8 hand losing streak? However there are other ways you get four aces in the same hand, for example the last card might be an 8 or 9. All of this assumes flat betting, otherwise the math really gets messy. You are forgetting that there are two possible orders, either the ace or the ten can be first. Streaks, such as the dealer drawing a 5 to a 16, are inevitable but not predictable. According to my blackjack appendix 9H the expected return of standing is So my hitting you will save 6. When I said the probability of losing 8 hands in a row is 1 in I meant that starting with the next hand the probability of losing 8 in a row is 1 in The chances of 8 losses in a row over a session are greater the longer the session. When the dealer stands on a soft 17, the dealer will bust about When the dealer hits on a soft 17, the dealer will bust about According to my blackjack appendix 4 , the probability of a net win is However, if we skip ties, the probability is So, the probability of a four wins in a row is 0. Steve from Phoenix, AZ. Probability of Blackjack Decks Probability 1 4. From my blackjack appendix 7 we see that each 9 removed from a single deck game increases the house edge by 0. There are 24 sevens in the shoe. In general the variation in the mean is inversely proportional to the square root of the number of hands you play. Multiply this dot product by the probability from step 2. However if you were going to cheat it would be much better to remove an ace, which increases the house edge by 0. Thanks for the kind words. For the non-card counter it may be assumed that the odds are the same in each new round. Take another 8 out of the deck. Because the sum of a large number of random variables always will approach a bell curve we can use the central limit theorem to get at the answer. If you want to deviate from the basic strategy here are some borderline plays: 12 against 3, 12 against 4, 13 against 2, 16 against Deviating on these hands will cost you much less. Repeat step 3 but multiply by 4 instead of 2, and this time consider getting an 8 as a third card, corresponding to the situation where the player is forced to stop resplitting. For each rank determine the probability of that rank, given that the probability of another 8 is zero. It would take about 5 years playing blackjack 40 hours a week before this piece of advice saved the player one unit.

This is a typical question one might encounter in an introductory statistics class. Your question however could be rephrased as, "what is the value of the ace, given that the other card is not a ten. Since this question was submitted, a player blackjack basic strategy probabilities the dice for rolls on May 23, in Atlantic City.

So standing is the marginally better play. According to my blackjack appendix 4the probability of an overall win in blackjack is I'm going to assume you wish to ignore ties for purposes of the streak.

Following this rule will result in an extra unit once every hands. Let n be the number blackjack basic strategy probabilities decks.

From my section on the house edge we find the standard deviation in blackjack to be 1. Multiply dot product from step 7 by probability in step 5. Resplitting up to four hands is allowed. Go through all ranks, except 8, subtract that card from the deck, play out a hand with that card and an 8, determine the expected value, and multiply by 2.

The probability of this is 1 blackjack basic strategy probabilities 5,, For the probability for any number of throws from 1 toplease see my craps survival tables. Here is how I did it. If the probability of a blackjack is p then the probability of not getting any blackjacks in 10 hands is 1- 1-p For example in a six deck game the answer would be 1- 0.

My question though is what does that really mean? It depends whether there is a shuffle between the blackjacks. You ask a good question for which there is big apple roller coaster price firm answer.

For how to solve the problem yourself, see my MathProblems. These expected values consider all the numerous ways the hand can play out.

I have a very ugly subroutine blackjack basic strategy probabilities of long formulas I determine using probability trees.

Besides every once in awhile throwing down a bigger bet just adds to the excitement and for some reason it seems logical that if you have lost a string of hands you are "due" for a win. Blackjack is not entirely a game of independent trials like roulette, but the deck is not predisposed to run in streaks. Expected Values for 3-card 16 Vs. Unless you are counting cards you have the free will to bet as much as you want. The following table displays the results. As I always say all betting systems are equally worthless so flying by the seat of your pants is just as good as flat betting over the long term. It took me years to get the splitting pairs correct myself. Putting aside some minor effects of deck composition, the dealer who pulled a 5 to a 16 the last five times in a row would be just as likely to do it the next time as the dealer who had been busting on 16 for several hours. I would have to do a computer simulation to consider all the other combinations. Multiply dot product from step 11 by probability in step 9. I hope this answers your question. Cindy of Gambling Tools was very helpful. There is no sound bite answer to explain why you should hit. What is important is that you play your cards right.