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Sick and tired of losing money on Ban Luck (Blackjack) every Chinese New Yearβ? to at least win some back this year with the help of Mathematics and Statisticsβ. Total value of hand, Probability of exceeding 21 points.

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BJ Stats explains blackjack rules in a few simple steps. Learn about blackjack 21 rules here. How to Play Blackjack. Blackjack Stats will teach you how to.

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I have seen lots of search strings in the statistics of my Web site related to the probability to get a blackjack (natural 21). This time (November 15, ), the.

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Blackjack, formerly also Black Jack and Vingt-Un, is the American member of a global family of Blackjack has inspired other casino games, including Spanish 21 and pontoon. The expected loss rate of players who deviate from basic strategy through poor play will be greater, often much greater. Dealer hits soft

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In a six-deck shoe, what is the percentage of times that a blackjack (ace face What is the probability that you play ten hands and never obtain a (two-card) 21?

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BJ Stats explains blackjack rules in a few simple steps. Learn about blackjack 21 rules here. How to Play Blackjack. Blackjack Stats will teach you how to.

Enjoy!

I have seen lots of search strings in the statistics of my Web site related to the probability to get a blackjack (natural 21). This time (November 15, ), the.

Enjoy!

In a six-deck shoe, what is the percentage of times that a blackjack (ace face What is the probability that you play ten hands and never obtain a (two-card) 21?

Enjoy!

BJ Stats explains blackjack rules in a few simple steps. Learn about blackjack 21 rules here. How to Play Blackjack. Blackjack Stats will teach you how to.

Enjoy!

Blackjack, formerly also Black Jack and Vingt-Un, is the American member of a global family of Blackjack has inspired other casino games, including Spanish 21 and pontoon. The expected loss rate of players who deviate from basic strategy through poor play will be greater, often much greater. Dealer hits soft

Enjoy!

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