🎰 Blackjack - Wizard of Odds

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If so, would playing the games using basic table blackjack strategy give the player the best payback percentage? If not, is there a basic strategy for video blackjack.


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Blackjack House Edge - Wizard of Odds
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How to win at blackjack (21) with gambling expert Michael \

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Advanced Blackjack Topics. Analysis and advice for experienced players who have mastered basic strategy, and are looking to add an extra edge to their game​.


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The Wizard of Odds gives the odds, house edge, and proper strategy for the casino coin-op game Derby.


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The Wizard of Odds gives the odds, house edge, and proper strategy for the casino coin-op game Derby.


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Wizard of Odds Interview -- Part 1

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The house edge under proper basic strategy for these rules is indicated in the box below. Number of decks of cards used: 1 2 4 5 6 8. Dealer hits.


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This usually can be explained by the user not using the correct basic strategy for the rules selected. I have also had many comments about the advice on a player​.


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Blackjack by the Wizard of Odds

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a dealer's 10 in a multiple deck (4 or more decks) blackjack game. I checked your web site and I could only find appendixes for multiple card hands in 1 and 2 deck​.


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a dealer's 10 in a multiple deck (4 or more decks) blackjack game. I checked your web site and I could only find appendixes for multiple card hands in 1 and 2 deck​.


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The Wizard of Odds gives the odds, house edge, and proper strategy for the casino coin-op game Derby.


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The Wizard presents the odds, rules and complete strategy charts for casino Blackjack. These are the authoritative charts copied by everyone.


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How to play Blackjack - Learn the Rules and Strategy with our Free Demo Game

It would take about 5 years playing blackjack 40 hours a week before this piece of advice saved the player one unit. For the non-card counter it may be assumed that the odds are the same in each new round. It is more a matter of degree, the more you play the more your results will approach the house edge. The standard deviation of one hand is 1. Take another 8 out of the deck. That column seemed to put the mathematics to that "feeling" a player can get. So the probability of winning six in a row is 0. 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. Repeat step 3 but multiply by 3 instead of 2. Determine the probability that the player will resplit to 4 hands. It may also be the result of progressive betting or mistakes in strategy. There are 24 sevens in the shoe. So standing is the marginally better play. Take the dot product of the probability and expected value over each rank. It depends on the number of decks. 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? Any basic statistics book should have a standard normal table which will give the Z statistic of 0. Unless you are counting cards you have the free will to bet as much as you want. 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. To test the most likely case to favor hitting, 8 decks and only 3 cards, I ran every possible situation through my combinatorial program. 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. However if you were going to cheat it would be much better to remove an ace, which increases the house edge by 0. There are cards remaining in the two decks and 32 are tens. Multiply dot product from step 7 by probability in step 5. Probability of Blackjack Decks Probability 1 4. If there were a shuffle between hands the probability would increase substantially. The fewer the decks and the greater the number of cards the more this is true. 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. Determine the probability that the player will not get a third eight on either hand. I recently replaced my blackjack appendix 4 with some information about the standard deviation which may help. Thanks for your kind words. For each rank determine the probability of that rank, given that the probability of another 8 is zero. There is no sound bite answer to explain why you should hit. 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. Streaks, such as the dealer drawing a 5 to a 16, are inevitable but not predictable. I would have to do a computer simulation to consider all the other combinations. Your question however could be rephrased as, "what is the value of the ace, given that the other card is not a ten. All of this assumes flat betting, otherwise the math really gets messy. 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. Determine the probability that the player will resplit to 3 hands. Here is how I did it. From my blackjack appendix 7 we see that each 9 removed from a single deck game increases the house edge by 0. According to my blackjack appendix 9H the expected return of standing is So my hitting you will save 6. These expected values consider all the numerous ways the hand can play out. 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. Cindy of Gambling Tools was very helpful. You ask a good question for which there is no firm answer. 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. Blackjack is not entirely a game of independent trials like roulette, but the deck is not predisposed to run in streaks. 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. I have no problem with increasing your bet when you get a lucky feeling. So, the best card for the player is the ace and the best for the dealer is the 5. My question though is what does that really mean? Thanks for the kind words.

This is a typical question one might encounter in an introductory statistics class. Following this rule will result in an extra unit once every hands. From my section on the house edge we find the standard deviation in blackjack to be 1.

Blackjack wizard of odds 4 from Phoenix, AZ. You are forgetting that there are two possible orders, either the ace or the ten can be first. 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.

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? Add values from steps 4, 8, and The hardest part of all this is step 3. What you have experienced is likely the result of some very bad losing streaks.

If I'm playing for fun then I leave the table when I'm not having fun any longer. It took me years to get the splitting pairs correct myself. I hope this answers your question. The following table displays the results.

Multiply dot product from step 11 by probability in step 9. Resplitting up to four hands is allowed. 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. This is not even a marginal play. Multiply this dot product by the probability from step 2.

If you were to add a card as the dealer you should add a 5, which increases the house edge by 0. Besides every once in awhile throwing down a bigger bet just adds to the excitement and for some reason it seems logical that if blackjack wizard of odds 4 have lost a string of hands you are "due" for a win.

As I always say all betting systems are equally worthless so flying by the seat of your pants is just as good here flat betting over the long term.

According to my blackjack appendix 4the probability of an overall win in blackjack is I'm going to assume you wish to ignore ties for purposes of the streak.

The best play for a billion hands is the best play for one hand. 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 table cad block 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.

What is important is that you play your cards blackjack wizard of odds 4. In that case, the probability of a win, given a resolved bet, is The probability of winning n hands is a row is 0. For how to solve the problem blackjack wizard of odds 4, see my MathProblems.

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

Expected Values for 3-card 16 Vs. Since this question was submitted, a player held the dice for rolls on May 23, in Atlantic City.