πŸ’ Blackjack - Probability - Wizard of Odds

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Our win rate climbs as session length increases because the more we play the against calculations using a formula in Don Schlesinger's Blackjack Attack.


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

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One of his achievements was to determine the win-rate per hands for six-​deck blackjack, using the Illustrious 18 (see this post), and four.


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Blackjack Expert Explains How Card Counting Works - WIRED

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Use our House Edge Blackjack Calculator to increase your odds over the dealer. Notice how the fewer decks you cut out of play, the greater the win rate and.


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How to Calculate Outs - Poker Tutorials

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Use our House Edge Blackjack Calculator to increase your odds over the dealer. Notice how the fewer decks you cut out of play, the greater the win rate and.


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How to Count Cards (and Bring Down the House)

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How can I determine the odds of flat betting (no counting, no progressions, etc) According to my blackjack appendix 4, the probability of a net win is %. In a six-deck shoe, what is the percentage of times that a blackjack (ace face card​.


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Our win rate climbs as session length increases because the more we play the against calculations using a formula in Don Schlesinger's Blackjack Attack.


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No Bust Blackjack Strategy: Does it Work?

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The Maths Behind Blackjack

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Our win rate climbs as session length increases because the more we play the against calculations using a formula in Don Schlesinger's Blackjack Attack.


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Why You Need a $10,000 Bankroll to Win $10/hour Card Counting Blackjack

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Our win rate climbs as session length increases because the more we play the against calculations using a formula in Don Schlesinger's Blackjack Attack.


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Does blackjack card counting really work? Part 1

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Blackjack House Edge

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