The dealer will most often bust with 4, 5 or 6, followed by 2 and 3. The odds above are static. However, you can find ways to improve your odds so that you lose fewer hands and less money. And the less money you lose, the more you can keep to play more blackjack.
I wanted to finish up this article with a brief explanation of odds, and how they work over the long run. The thing is, odds and statistics are all about the long run. Long run usually meaning sample size, or the total number of hands or games played.
That column seemed to put the mathematics to that "feeling" a player can get. My question though is what does that really mean? 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?
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? I know, I know, its some sort of divine intervention betting system I am talking about and no betting system affects the house edge. 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.
Steve from Phoenix, AZ. I have no problem with increasing your bet when you get a lucky feeling. What is important is that you play your cards right. Unless you are counting cards you have the free will to bet as much as you want. 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. 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.
I hope this answers your question. 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 would have to do a computer simulation to consider all the other combinations. It took me years to get the splitting pairs correct myself. Cindy of Gambling Tools was very helpful. Resplitting up to four hands is allowed. Here is how I did it.
Determine the probability that the player will not get a third eight on either hand. 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 each rank determine the probability of that rank, given that the probability of another 8 is zero.
Take the dot product of the probability and expected value over each rank. Multiply this dot product by the probability from step 2. Determine the probability that the player will resplit to 3 hands. Take another 8 out of the deck. Repeat step 3 but multiply by 3 instead of 2.
Multiply dot product from step 7 by probability in step 5. Determine the probability that the player will resplit to 4 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.
Multiply dot product from step 11 by probability in step 9. Add values from steps 4, 8, and The hardest part of all this is step 3. I have a very ugly subroutine full of long formulas I determine using probability trees. It gets especially ugly when the dealer has a 10 or ace up. The number of ways to draw 3 suited sevens is the number of suits 4 times the number of ways to choose 3 out of 6 sevens of that suit in the shoe. Yes, I calculate blackjack odds using a combinatorial approach, analyzing every possible ways the player and dealer cards can come out, taking the greatest expected value at every decision point.
This is harder to program than a simulation but I feel is more elegant and a nice challenge in recursive programming. However I still respect my peers to do simulations. Not too many places allow resplitting aces, so be glad you were playing somewhere that did. Your seat position does not matter. I seem to get a variation of this question at least once a month.
If the probability of something happening is p then the probability of it happening n times in a row is p n. However the actual probability is much less, because as the player gets each blackjack the ratio of aces to cards left in the deck decreases. Every legitimate blackjack expert agrees the house edge decreases as the number of decks goes down, all other rules being equal. However it is hard to explain why. First, it is true that you are more likely to get one small card and one big card in single-deck than multiple-deck.
Although stiffs can cut both ways the player has the free will to stand, the dealer must always hit them. Following are the probabilities: Player 1 0. Thanks for the compliment. It took me years to get my blackjack engine to work perfectly splits when the dealer had a 10 or ace showing was very tricky. An easier way to get the house edge for blackjack is to write a random simulation.
Assuming a six-deck game, where the dealer stands on soft 17, and the player plays basic strategy here are the rounded results based on a million hand simulation. So the larger the bankroll the better your chances. The house edge will lower the probability of success by an amount that is hard to quantify. For a low house edge game like blackjack, the reduction in the probability of success will be small. It would take a random simulation to know for sure.
Forgive me if I don't bother with that. VegasClick did a small simulation about the probability of success with the Martingale.
This is not true. The remaining deck needs to be exhibit more than a certain degree of skewness for the odds to swing to the player's favor. Consider a hypothetical side that pays 3 to 1 for any suited pair in a one-deck game. What all this shows is that if cards are removed at a uniform distribution the odds of winning go down, however at a very skewed distribution the odds go up.
As the deck is played down sometimes your odds get better, and sometimes worse, but in the long run they average out and stay at a Under typical Vegas rules 6-deck, dealer hits soft 17 the house edge by always standing is At Cryptologic they use 8 decks and the dealer stands on a soft According to my blackjack appendix 2 , the probability of the dealer busting with a 6 up is 0. So the probability of not busing is 1 - 0. The probability of not busing 7 times out of 7 is 0.
Assuming liberal Vegas Strip rules six decks, dealer stands on soft 17, double after split allowed, late surrender allowed, resplitting aces allowed the following are the probabilities of each possible outcome when doubling on the initial two cards. This does not include doubling after splitting.
From my blackjack appendix 4 we see the following probabilities for each initial hand. So the probability of going exactly 19 losses in a row is 0. By way of comparison, the probability of being dealt a royal flush in video poker is 1 in ,, or 2. The reason the strategy changes, according to the number of cards in your hand, as shown in appendix 18, is that every card that leaves the deck changes the probabilities of every card left to be played.
A good example is the single-deck basic strategy says to surrender 7,7 against a 10; but for any other 14 you should hit. The reason you should surrender is half the sevens have already been removed from the deck. You need another seven to make 21, the only hand that will beat a dealer So the shortage of sevens lowers the expected value of hitting to under half a bet, making surrender the better play.
In an eight-deck shoe there are cards. That may seem like a lot, but 16 against a 10 is such a borderline hand that removal of just one card can making standing a better play. The rule is that for eight or fewer decks if your 16 is composed of three or more cards, and the dealer has a 10, then you should stand. In a two-card 16 the average points per card is 8, with a 3-card 16 the average is 5. With more small cards out of the deck in the 3-card hand the remaining deck becomes more large card rich, making hitting more dangerous, swaying the odds in favor of standing.
I show that rule is worth 0. Despite the incentive to hit 7,7 against a dealer , the player should still follow basic strategy and split. Maybe you can take advantage of his complaining by offering to buy his hand for less than the fair 79 cents on the dollar. Single deck. Dealer stands on soft Winning blackjack pays even money. Player may double any first two cards. No double after split. Player may resplit to four hands, including aces.
No draw to split aces. No surrender. Six-card Charlie player unbusted six cards automatically wins. Cards shuffled after every hand. If game runs out of cards, all unbusted player hands automatically win. The house edge using total-dependent basic strategy is 2. I ran a 7-player simulation, using total-dependent basic strategy, and the average number of cards used per round was In almost million rounds played, the most cards ever used was 42, which happened 7 times.
It is my educated opinion that even with computer perfect composition-dependent strategy the player would still realistically never see the last card. You could cut down the house edge much more using composition-dependent strategy, according to all the cards seen as you go along.
However bucking 2. I just wanted to express my disappointment in this change, if it is true. I never had a chance to take advantage of the promotion and doubt I will be able to now. Also, you have thirty days in which to complete the card. I hope you understand this is not a task that is unreachable with that much time.
Hope you can give it a try and win some money! What is the probability of getting 30 blackjacks in four hours? According to my game comparison , blackjack players play about 70 hands per hour. I assume a blackjack tie still gets a stamp. The probability of filling the card in 4 hours, assuming hands, is 1 in 30, playing one hand at a time. I suspect any player achieving the goal in four hours was playing at least two hands at a time.
This question was raised and discussed in the forum of my companion site Wizard of Vegas. The probability of the dealer getting exactly a 9-card 21 under those rules is 1 in 32,, Here is the probability for various numbers of decks and whether dealer hits or stands on soft Probability of Dealer 9-Card 21 Decks Stand Soft 17 Hit Soft 17 1 1 in ,, 1 in ,, 2 1 in 67,, 1 in 41,, 4 1 in 38,, 1 in 22,, 6 1 in 32,, 1 in 18,, 8 1 in 29,, 1 in 17,, Assuming six decks and the dealer stands on soft 17, here is the probability of the dealer getting a 21 or a blackjack in the case of two cards , according to the total number of cards.
If you're still looking for something that tells you how good a hand the dealer is likely to make, consult the following chart. It was put together by computing your relative chances to beat her with 17, 18 or Although a direct calculation the dealer's actual "average" final hand is not feasible due to the ambiguous value of her busted totals , this chart does give you an accurate picture of where you stand with any hand you may currently have.
It is also proportionally accurate regarding your margins of advantage and disadvantage. For example, notice that when the dealer has an 8 up, you'd be a small favorite over her if you had But if you had only 17, you'd appear to be the underdog by a four times larger margin than when you were favored with This is in fact true.
Yet, if you had 19, your edge on the hand would in fact be six times as large as with Also notice that for a dealer's 10 and Ace up, there are two sets of numbers. The first set applies before she checks her hole card to see if she has blackjack. The numbers in parentheses tell you where she's at if she doesn't have blackjack.
As you can see, a player's 19 would be the favorite over both a dealer's 10 and Ace if she has to play her hand out against yours. This article is provided by the Frank Scoblete Network. Melissa A.
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