🤑 What is the probability of winning a blackjack hand? - Mathematics Stack Exchange

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Learn more about Blackjack Odds & Probability, the House Edge and the statistics of winning. ✅ Mr Green will help you master your play at Blackjack.


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Blackjack Odds & Probability Explained | Mr Green Casino
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The Maths Behind Blackjack

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Whether the game is in your favor is independent of the betting system. No system of betting can rescue a losing game. You are correct that with Martingale you.


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Winning Blackjack Basic Strategy

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How to win at blackjack (21) with gambling expert Michael \

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When the dealer hits on a soft 17, the dealer will bust about % of the time. According to my blackjack appendix 4, the probability of a net win is %.


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How to Play (and Win) at Blackjack: The Expert's Guide

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This Man Won $15M at Blackjack, How Did He Do It?

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Michael Shackleford, a gambling aficionado and a mathematician, offers five tips to win at the blackjack table. As the owner of the The Wizard of.


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Odds work differently in Blackjack than in other casino games. Along with The house edge is the small percentage of all wagers that the casino expects to win.


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When the dealer hits on a soft 17, the dealer will bust about % of the time. According to my blackjack appendix 4, the probability of a net win is %.


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No Bust Blackjack Strategy: Does it Work?

I would have to do a computer simulation to consider all the other combinations. In general the variation in the mean is inversely proportional to the square root of the number of hands you play. 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. In that case, the probability of a win, given a resolved bet, is The probability of winning n hands is a row is 0. Thanks for the kind words. Following this rule will result in an extra unit once every hands. It depends on the number of decks. There are 24 sevens in the shoe. Resplitting up to four hands is allowed. Any basic statistics book should have a standard normal table which will give the Z statistic of 0. Take the dot product of the probability and expected value over each rank. If there were a shuffle between hands the probability would increase substantially. Blackjack is not entirely a game of independent trials like roulette, but the deck is not predisposed to run in streaks. According to my blackjack appendix 9H the expected return of standing is So my hitting you will save 6. 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. Here is the exact answer for various numbers of decks. These expected values consider all the numerous ways the hand can play out. You are forgetting that there are two possible orders, either the ace or the ten can be first. 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 have no problem with increasing your bet when you get a lucky feeling. Streaks, such as the dealer drawing a 5 to a 16, are inevitable but not predictable. Here is how I did it. Probability of Blackjack Decks Probability 1 4. Multiply this dot product by the probability from step 2. From my section on the house edge we find the standard deviation in blackjack to be 1. Determine the probability that the player will resplit to 4 hands. The probability of this is 1 in 5,,, For the probability for any number of throws from 1 to , please see my craps survival tables. Take another 8 out of the deck. Cindy of Gambling Tools was very helpful. So the probability of winning six in a row is 0. 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 depends whether there is a shuffle between the blackjacks. 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? It is more a matter of degree, the more you play the more your results will approach the house edge. Determine the probability that the player will not get a third eight on either hand. What you have experienced is likely the result of some very bad losing streaks. Multiply dot product from step 11 by probability in step 9. I recently replaced my blackjack appendix 4 with some information about the standard deviation which may help. Expected Values for 3-card 16 Vs. Add values from steps 4, 8, and The hardest part of all this is step 3. Determine the probability that the player will resplit to 3 hands. However if you were going to cheat it would be much better to remove an ace, 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. The best play for a billion hands is the best play for one hand. That column seemed to put the mathematics to that "feeling" a player can get. You ask a good question for which there is no firm answer. I have a very ugly subroutine full of long formulas I determine using probability trees.{/INSERTKEYS}{/PARAGRAPH} 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. 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. The following table displays the results. There is no sound bite answer to explain why you should hit. The fewer the decks and the greater the number of cards the more this is true. 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. It took me years to get the splitting pairs correct myself. If you were to add a card as the dealer you should add a 5, which increases the house edge by 0. 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. Since this question was submitted, a player held the dice for rolls on May 23, in Atlantic City. So, the best card for the player is the ace and the best for the dealer is the 5. 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. For the non-card counter it may be assumed that the odds are the same in each new round. From my blackjack appendix 7 we see that each 9 removed from a single deck game increases the house edge by 0. Steve from Phoenix, AZ. My question though is what does that really mean? 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. There are cards remaining in the two decks and 32 are tens. So standing is the marginally better play. According to my blackjack appendix 4 , the probability of an overall win in blackjack is I'm going to assume you wish to ignore ties for purposes of the streak. Unless you are counting cards you have the free will to bet as much as you want. Repeat step 3 but multiply by 3 instead of 2. Multiply dot product from step 7 by probability in step 5. {PARAGRAPH}{INSERTKEYS}This is a typical question one might encounter in an introductory statistics class. However there are other ways you get four aces in the same hand, for example the last card might be an 8 or 9. For how to solve the problem yourself, see my MathProblems. It would take about 5 years playing blackjack 40 hours a week before this piece of advice saved the player one unit. It may also be the result of progressive betting or mistakes in strategy. All of this assumes flat betting, otherwise the math really gets messy. This is not even a marginal play. 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. The standard deviation of one hand is 1. I hope this answers your question. Thanks for your kind words. What is important is that you play your cards right. Your question however could be rephrased as, "what is the value of the ace, given that the other card is not a ten. For each rank determine the probability of that rank, given that the probability of another 8 is zero. 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. Let n be the number of decks. If I'm playing for fun then I leave the table when I'm not having fun any longer.