Blackjack is one of the most advantageous casino games as in it, an efficient preparation and strategy can really make the difference between winning and.

Enjoy!

Decision Hands ().

Enjoy!

The most important frequencey to note is the chance of being dealt a natural blackjack (natural 21 value. The odds of being dealt a natural blackjack are merely

Enjoy!

There are cards remaining in the two decks and 32 are tens. So the probability of a blackjack is 32/=%. What percentage of hands are suited.

Enjoy!

Software - MORE

The Probability of Obtaining a Blackjack. Blackjack 21 Naturals are the strongest hands you can obtain in the game of Not only it is impossible to lose with a.

Enjoy!

BLACKJACK ODDS: 16 AGAINST DEALER 10 in your hand when you hold a , you slightly lower your chances of breaking with a hit just enough to tip theβ.

Enjoy!

The odds to get a blackjack (natural) as arrangement: / = β%. % is equivalent to about 1 in 21 blackjack hands. (No wonder the game isβ.

Enjoy!

Decision Hands ().

Enjoy!

Software - MORE

The Probability of Obtaining a Blackjack. Blackjack 21 Naturals are the strongest hands you can obtain in the game of Not only it is impossible to lose with a.

Enjoy!

Software - MORE

The Probability of Obtaining a Blackjack. Blackjack 21 Naturals are the strongest hands you can obtain in the game of Not only it is impossible to lose with a.

Enjoy!

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.

This is a typical question one might encounter in an introductory statistics class. Multiply blackjack probability odds product from step 7 by probability in step 5.

Probability of Blackjack Decks Probability 1 4. From my section on the house edge we find the standard deviation in blackjack to be 1. Because the sum of a large number of random variables always will approach a bell curve we can use the central limit theorem to blackjack probability odds at the answer.

Steve from Phoenix, AZ. So the probability of winning six in a row is 0. Putting aside some minimum bet blackjack online 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 have a very ugly subroutine full of long formulas I determine using probability trees.

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