How can there be more blackjacks in one deck than in two, five or twenty? It comes down to the greater likelihood of pulling a ten on an ace, or an ace on a ten.

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There are subtle differences between a game with a single deck and one online is the huge range of variants with different bets and odds.

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There are subtle differences between a game with a single deck and one online is the huge range of variants with different bets and odds.

Enjoy!

Many casinos have reintroduced the single-deck blackjack game, but don't be fooled into thinking that playing a single-deck game will give you better odds.

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Other basic strategy rules: Never take insurance or "even money." The house edge on insurance is %, based on one deck. If there is no.

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Use this Blackjack chart to get more winning odds when you play online! The use of one deck makes card counting easy, but Casinos caught.

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There are subtle differences between a game with a single deck and one online is the huge range of variants with different bets and odds.

Enjoy!

However, you could have just as easily drawn the ten-value card first then the ace. Therefore, the overall probability of getting a blackjack hand in a single deckβ.

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Many casinos have reintroduced the single-deck blackjack game, but don't be fooled into thinking that playing a single-deck game will give you better odds.

Enjoy!

Other basic strategy rules: Never take insurance or "even money." The house edge on insurance is %, based on one deck. If there is no.

Enjoy!

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. So, the best card for the player is the ace and the best for the dealer is the 5. All of this assumes flat betting, otherwise the math really gets messy. Resplitting up to four hands is allowed. You are forgetting that there are two possible orders, either the ace or the ten can be first. In that case, the probability of a win, given a resolved bet, is The probability of winning n hands is a row is 0. 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. The following table displays the results. 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 depends on the number of decks. 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. Probability of Blackjack Decks Probability 1 4.

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.

I have a very ugly subroutine full of long formulas I determine using probability trees.

You ask a good question for which there is no firm answer. Here is the exact answer for various numbers of decks. My question though is what does that really mean? Following this rule will result in an extra unit once every hands. 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. Any basic statistics book should have a standard normal table which will give the Z statistic of 0. 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. Here is how I did it. There are 24 sevens in the shoe. Add values from steps 4, 8, and The hardest part of all this is step 3. 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? 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. If there were a shuffle between hands the probability would increase substantially. I know, I know, its some sort of divine intervention betting system I am talking about and no betting system affects the house edge. Multiply dot product from step 7 by probability in step 5. For how to solve the problem yourself, see my MathProblems. Multiply this dot product by the probability from step 2. Take the dot product of the probability and expected value over each rank. These expected values consider all the numerous ways the hand can play out. 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. That column seemed to put the mathematics to that "feeling" a player can get. 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. However there are other ways you get four aces in the same hand, for example the last card might be an 8 or 9. 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. Repeat step 3 but multiply by 3 instead of 2. 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. For each rank determine the probability of that rank, given that the probability of another 8 is zero. The fewer the decks and the greater the number of cards the more this is true. This is not even a marginal play. In general the variation in the mean is inversely proportional to the square root of the number of hands you play. Thanks for your kind words. The best play for a billion hands is the best play for one hand. Expected Values for 3-card 16 Vs. 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. Unless you are counting cards you have the free will to bet as much as you want. Streaks, such as the dealer drawing a 5 to a 16, are inevitable but not predictable. Multiply dot product from step 11 by probability in step 9. 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. 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 another 8 out of the deck. Blackjack is not entirely a game of independent trials like roulette, but the deck is not predisposed to run in streaks. If I'm playing for fun then I leave the table when I'm not having fun any longer. There are cards remaining in the two decks and 32 are tens. Determine the probability that the player will resplit to 3 hands. 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. I would have to do a computer simulation to consider all the other combinations. Cindy of Gambling Tools was very helpful. According to my blackjack appendix 9H the expected return of standing is So my hitting you will save 6. Determine the probability that the player will not get a third eight on either hand. 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. What is important is that you play your cards right. 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. The standard deviation of one hand is 1. I have no problem with increasing your bet when you get a lucky feeling. It depends whether there is a shuffle between the blackjacks. Let n be the number of decks. I recently replaced my blackjack appendix 4 with some information about the standard deviation which may help. Steve from Phoenix, AZ. It may also be the result of progressive betting or mistakes in strategy. From my section on the house edge we find the standard deviation in blackjack to be 1. Since this question was submitted, a player held the dice for rolls on May 23, in Atlantic City. If you were to add a card as the dealer you should add a 5, which increases the house edge by 0. It would take about 5 years playing blackjack 40 hours a week before this piece of advice saved the player one unit. It took me years to get the splitting pairs correct myself. I hope this answers your question. So standing is the marginally better play. What you have experienced is likely the result of some very bad losing streaks. Thanks for the kind words.