Blackjack - Probability - Wizard of Odds. How can I determine the odds of flat betting (no counting, no progressions , etc ) of being ahead in a negative game such as blackjack, w/o counting, with a 0. Poker Winning Hand Odds in 5 card Games - There are many poker variants, but unless otherwise specified in the rules of the variant being played, hands are evaluated. POKER PROBABILITIES (FIVE CARD HANDS). Poker Odds - Calculating Hand Odds In Texas Hold'em Poker & Charts. Learning how to properly count your outs and calculate poker odds is a fundamental requirement of. Solution to problem 2.32 in Miller - calculates the probabilities of all possible five card hands in poker. Instant poker calculator tells your immediate odds of winning or losing in every poker scenario - just like poker shows on TV. Is it even possible? Kevin. This is a typical question one might encounter in an introductory statistics class. Probability Of Poker Hands Worksheet![]() 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. From my section on the house edge we find the standard deviation in blackjack to be 1. You won't understand this if you haven't studied statistics, but the probability of being at a loss in your example will be the Z statistic of 4. Any basic statistics book should have a standard normal table which will give the Z statistic of 0. So the probability of being ahead in your example is about 1. I have a few questions regarding blackjack: How often can one expect the dealer to bust and how often can a player expect to win four hands in a row? John from Westminster, USAWhen the dealer stands on a soft 1. ![]() ![]() When the dealer hits on a soft 1. Your information is quite valuable to both the beginning and expert gambler, and you present your findings in a pleasant, understandable, and even humorous manner. I always check out your site before I head to Las Vegas or Lake Tahoe just to remind me how to play smartly. Anyway, on to my question. Well, more of an observation: when the dealer pulls a 5 on a 1. But is there any truth in this? Obviously the dealer is inconsequential to the cards dealt (I like to say the dealer is ? Or is it more like your roulette example, where the odds of each new round are exactly the same? Thanks once again for your web site. Dave K. Streaks, such as the dealer drawing a 5 to a 1. Blackjack is not entirely a game of independent trials like roulette, but the deck is not predisposed to run in streaks. For the non- card counter it may be assumed that the odds are the same in each new round. Putting aside some minor effects of deck composition, the dealer who pulled a 5 to a 1. What are the odds against winning seven hands of blackjack in a row? How about six? James from Palo Alto, California. According to my blackjack appendix 4, the probability of an overall win in blackjack is 4. I'm going to assume you wish to ignore ties for purposes of the streak. So the probability of winning six in a row is 0. Can it actually be true that what I experience has a statistical base? It seems to me that it takes a lot longer to win X number of chips that to lose the same amount (I only play blackjack). For example, if I start with 3. I can lost that number in what seems like almost no time at all. Can this really be true? Also, do you have a rule of thumb about when to leave the table when you are winning? Chris from Gaithersburg, Maryland. What you have experienced is likely the result of some very bad losing streaks. It may also be the result of progressive betting or mistakes in strategy. The basic strategy flat bettor should have a roughly symmetrical expectation in terms of steep ups and downs, slightly favoring steep downs due to the house edge and a 4. The probability of a blackjack is 2*(4/1. If n=6 the probability is 1. Still love your site! I always turn to your site when I'm having questions, most of the time I will find the answer but not always. When playing basic strategy blackjack I understand that I will have ups and downs and over the long run I will roughly break even, my question is what is really ? A month, a year, five years? Any ideas? Kim from Helsinki, Finland. Thanks for the kind words. You ask a good question for which there is no firm answer. It is more a matter of degree, the more you play the more your results will approach the house edge. I recently replaced my blackjack appendix 4 with some information about the standard deviation which may help. For example this table shows that if you play 1. So in 1. 0,0. 00 hands you are likely to win or lose less than 2% of total money bet due to random variation. However if we go up to one million hands the probability is 9. In general the variation in the mean is inversely proportional to the square root of the number of hands you play. All of this assumes flat betting, otherwise the math really gets messy. Please explain how to calculate the probability of a blackjack occurring in a single deck. I can easily work other hands but when a card can be either/or my brain cramps. Mike from Bossier City, USAThe probability that the first card is an ace is 4/5. The probability that the second card is a 1. So the probability of an ace first blackjack is (4/5. Multiply this by 2 because the ten could just as easily be the first card and the answer is 2*(4/5. Do you have any idea what the ? I had someone tell me it was 8. I'm skeptical. It seems it's more possible that 8. I tried to look on the Web but have no idea where I would find something like that. Mike. Since this question was submitted, a player held the dice for 1. May 2. 3, 2. 00. 9 in Atlantic City. The standard deviation of one hand is 1. So, one standard deviation in your example is $5*1. So, the probability of losing $2. Z statistic for - 3). If the first card dealt is an ace what is the probability the dealer will have a blackjack? Assume two decks. T from Las Vegas, U. S. There are 1. 03 cards remaining in the two decks and 3. So the probability of a blackjack is 3. What percentage of hands are suited blackjacks? Six- deck shoe, any suit. RWR from Tuscon, USAThe probability of a suited blackjack in a six- deck game is 2*(4/1. For blackjack, which is the probability to obtain three suited seven in a 6- deck shoe? Rodrigo from Costa Rica. I attempt to work this out in my blackjack appendix 8 but I’ll work through it more slowly here. We’ll ignore dealer blackjacks to keep things simple and assume the player always hits after two cards. The number of ways to arrange 3 cards in a 6- deck shoe is combin(3. There are 2. 4 sevens in the shoe. The number of ways to arrange 3 sevens out of 2. The probability is the number of winning combinations divided by total combinations, or 2. What piece of information am I missing? If the odds of pulling a ten count card out of a deck is about 3. Why do blackjack simulators and blackjack authors state that the odds for a blackjack are 4. What am I missing? Jeffrey from Loveland. You are forgetting that there are two possible orders, either the ace or the ten can be first. Multiply by 2 and you’ll have your answer. You go, wiz. Our local casino hands out promotional coupons, which act as a first- card ace in blackjack. From your BJ appendix, most hands containing an ace have a positive expectation, without counting the BJs you’ll get four out of every thirteen plays. Do you know the overall expectation of having an ace as your first card? Thanks. Victor from Yakima, Washington. According to Stanford Wong’s ’Basic Blackjack’ he says the player’s edge given the first card is an ace is 5. Your question however could be rephrased as, . Doing some simple algebra we get x=2. I have just read an article that says it’s proper basic strategy to stand on a multiple card 1. Vs. I checked your web site and I could only find appendixes for multiple card hands in 1 and 2 deck games. Is this article correct? Rodney from Clarence, New York. Yes! Good question, even I didn’t know this. The fewer the decks and the greater the number of cards the more this is true. To test the most likely case to favor hitting, 8 decks and only 3 cards, I ran every possible situation through my combinatorial program. The following table displays the results. Expected Values for 3- card 1. Vs. 1. 0 in 8- deck game. Hand. EV Hit. EV Stand. Best. Play. Probability. Return. Hit. Return. Stand. 1/5/1. 0- 0. Stand. 0. 1. 32. 02. Hit. 0. 0. 59. 83. Stand. 0. 0. 59. 83. Hit. 0. 2. 37. 47. Stand. 0. 0. 39. 89. Hit. 0. 0. 59. 83. Stand. 0. 0. 28. 98. Hit. 0. 1. 15. 02. Stand. 0. 0. 59. 83. Stand. 0. 0. 39. 89. Hit. 0. 0. 59. 83. Stand. 0. 0. 28. 98. Stand. 0. 0. 39. 89. Hit. 0. 0. 28. 98. Stand. 0. 0. 09. 66. Total. 1- 0. 5. 40. The two right numbers in the bottom row show that the overall expected value for hitting is - 0. So standing is the marginally better play. Following this rule will result in an extra unit once every 1. It would take about 5 years playing blackjack 4. I play 6 deck blackjack in Tunica, MS. The dealer hits on soft 1. I wonder what the odds are of standing on 1. It seems only a 1. Also, since most strategies are based on millions of calculations done on a computer, I wonder if those of us who will never play a million hands can rely on slight variations like this one. Is this a poor, fair or bad move to make? Richard S. So my hitting you will save 6. This is not even a marginal play. There is no sound bite answer to explain why you should hit. These expected values consider all the numerous ways the hand can play out. The best play for a billion hands is the best play for one hand. If you want to deviate from the basic strategy here are some borderline plays: 1. Deviating on these hands will cost you much less. My friend and I are debating two blackjack issues that arose from his Caribbean Vacation. House favor or player favor? If the player is guaranteed to lose no more than the original wager then it doesn’t matter if the dealer takes a second card or not. If the player stands to lose the total amount bet after doubling or splitting and the dealer gets a blackjack then that works to the dealer’s advantage. If the number of decks is n then the probability is 2*pr(ace)*pr(1. Assume the cards are reshuffled after each play? Matt from Radford, USAIf the probability of a blackjack is p then the probability of not getting any blackjacks in 1. For example in a six deck game the answer would be 1- 0. What are the odds of getting 3 blackjacks in a row with 1 deck 4 players and one dealer. Joe P from Parma Heights, USAI’m going to assume there is never a shuffle between hands. The three other players don’t matter. The answer would be 2.
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