Your probability of getting an ace on your first card is 4/ You have four aces in the deck, and you have 52 total cards. That reduces down to 1/

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Learn to master the simple and popular game of strategy that requires self-control If a player's first two cards are an ace and a "ten-card" (a picture card or 10).

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Blackjack, formerly also Black Jack and Vingt-Un, is the American member of a global family of If the player is dealt an Ace and a ten-value card (called a "â€‹blackjack" or "natural"), and the dealer does since if the players draws a ten on their first card, the subsequent probability of drawing an ace is higher with fewer decks.

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There are 4 Aces and 16 face-cards and 10s. The blackjack (or natural) can occur only in the first 2 cards. We calculate first all combinations of 52 elements taken.

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Learn more about Blackjack Odds & Probability, the House Edge and the look at what the probability is for the dealer to bust depending on the first card shown. (12 without an ace in the hand) when the dealer's showing a six unless you're.

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Blackjack, formerly also Black Jack and Vingt-Un, is the American member of a global family of If the player is dealt an Ace and a ten-value card (called a "â€‹blackjack" or "natural"), and the dealer does since if the players draws a ten on their first card, the subsequent probability of drawing an ace is higher with fewer decks.

Enjoy!

Learn more about Blackjack Odds & Probability, the House Edge and the look at what the probability is for the dealer to bust depending on the first card shown. (12 without an ace in the hand) when the dealer's showing a six unless you're.

Enjoy!

There are 4 Aces and 16 face-cards and 10s. The blackjack (or natural) can occur only in the first 2 cards. We calculate first all combinations of 52 elements taken.

Enjoy!

Your probability of getting an ace on your first card is 4/ You have four aces in the deck, and you have 52 total cards. That reduces down to 1/

Enjoy!

There are 4 Aces and 16 face-cards and 10s. The blackjack (or natural) can occur only in the first 2 cards. We calculate first all combinations of 52 elements taken.

Enjoy!

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